High-fidelity single-frame computational super-resolution using signal-preserving denoising-enabled deconvolution

Domain: chemistry
Published: 2026-03-17
Editorial outcome: major_revision

Abstract
Computational super-resolution (SR) methods enable nanoscale imaging from single-frame wide-field or
spinning-disk confocal images without hardware modifications, yet face limitations: statistical restoration suffers
from noise and artifacts, while deep learning methods typically lack generalizability. We introduce 3Snet-CLID,
a computational SR method which integrates a hybrid supervised/self-supervised deep learning network for
signal-preserving denoising with direct Richardson–Lucy deconvolution. 3Snet-CLID’s per-pixel denoising
strategy suppresses noise while maintaining signal distribution, mitigating artifacts and enhancing robustness.
The method achieves more than 5-fold resolution improvement on conventional microscopes, revealing diverse
structures such as the mitochondrial outer membrane, endoplasmic reticulum, and nuclear pores in live and fixed
cells under standard labeling. By overcoming key computational SR bottlenecks, 3Snet-CLID offers denoising
capability and an accessible platform for high-fidelity nanoscale live-cell imaging.

Introduction
Live-cell fluorescence imaging is crucial for resolving how nanoscale assemblies such as cytoskeletal filaments,
membrane nanodomains and multi-protein complexes organize and remodel in real time inside intact cells, which
underlies many key physiological and pathological processes. However, in conventional far-field microscope,
Abbe’s diffraction limit1 constrains lateral resolution to roughly λ/(2NA) and axial resolution to several hundred
nanometers, so many subcellular features on the 10–100 nm scale—including protein clusters, transport vesicles
and cytoskeletal cross-links—cannot be resolved as distinct objects2.

The emergence of super-resolution (SR) imaging has overcome this barrier, achieving resolutions at the tens-of-
nanometer or even single-molecule level while preserving molecular specificity2, 3. SR methods fall into two
broad categories: optical SR4-8, which uses engineered excitation or emission light patterns, and computational
SR9-11, which leverages algorithms to reconstruct high-resolution estimates from diffraction-limited images.
Classical Richardson–Lucy (RL) deconvolution is one such computational approach2, 12.

Optical SR techniques can routinely reach 20–100 nm resolution but require dedicated and often complex
instrumentation, high illumination doses (risking phototoxicity), and specific fluorophores. They also typically
trade off field of view and temporal resolution for spatial detail, limiting their practicality for long-term, high-
throughput live-cell imaging2, 12. In contrast, computational SR can be implemented on standard widefield (WF)
or confocal microscopes, reduces demands on illumination intensity and labeling specificity, and is therefore
well-suited for live-cell and large-scale studies2, 13-15. Both deep learning (DL)–based SR (DLSR) and RL-based
deconvolution SR can operate on single diffraction-limited frames, meaning their temporal resolution is
effectively limited only by camera acquisition rates. This single-frame capability simplifies integration into
existing workflows, is particularly advantageous for capturing rapid cellular dynamics, and—unlike multi-frame
SR methods—avoids the phototoxicity, storage overhead, and temporal constraints associated with acquiring
long, high-frame-count time series15, 16.

DLSR methods13, 14, 17-20, which learns an image-to-image mapping from low- to high-resolution examples, have
demonstrated impressive resolution gains and denoising capabilities in fluorescence microscopy, often
surpassing classical deconvolution while enabling rapid 2D/3D reconstruction. However, DLSR models require
large amounts of high-quality SR data as ground truth (GT), making training labor-intensive and often
impractical due to the rapid dynamics in biological specimens20-22, and the low-to-SR mapping remains
inherently ill-posed14, leading to strong dependence on the specific structures represented in the training set and
potential artifacts when generalizing to unseen organelles or sample types. To mitigate these issues, strategies
such as more generalizable architectures, larger and more diverse datasets, and multimodal imaging have been
proposed17, 23, 24, but these solutions themselves increase system and pipeline complexity, and further raise
demands on data volume and computational resources.

RL deconvolution–based SR occupies a special position as a model-based, interpretable computational SR
technique that directly incorporates the image-formation physics: the algorithm iteratively maximizes the
Poisson likelihood of a latent object given a measured image and a point-spread function (PSF), as first
formulated by Richardson and Lucy25, 26. RL deconvolution has been demonstrated to improve resolution in
synthetic, noise-free fluorescence images27,28. However, classical RL SR with real microscopic images faces
several critical challenges: it is highly sensitive to noise and PSF mismatch, so iterative updates tend to amplify
high-frequency noise and produce artifacts unless carefully regularized and appropriately stopped10, 29-31; its
convergence is often ill-conditioned near the diffraction cutoff25, 26, 31-33. A notable recent development is sparse
deconvolution SR technology, which aims to reduce noise influence by incorporating sparsity and continuity as
priori knowledges into the algorithm27. This approach has successfully enhanced the resolution of single-frame
WF microscopy to 120-150 nm27. However, both sparse deconvolution and other RL-based analytical models
rely on assumptions about specimen and image properties to enhance resolution10, 27, 34-36, with multiple
parameters that require manual tuning, making the process time-consuming and heavily reliant on the selected
parameter sets25-27, 34.

Altogether, the constraints of current single-frame computational SR approaches—including training-data
dependence and generalization issues for DL, and noise-sensitivity and convergence bottlenecks in RL-based
SR—still hinder their widespread, quantitative application to live-cell imaging. To address these challenges, we
developed a new RL-based computational SR method that transforms conventional live-cell imaging into a
routine SR tool for cell biology, without requiring prior knowledge. Our approach introduces a two-step (DL
denoising then deconvolution) technique termed clear image deconvolution (CLID) to enhance resolution. First,
we developed a per-pixel denoising strategy called the single-pixel-synchronized switching (3S) method, which
enhances the image signal-to-noise ratio by a factor of 5.8 while preserving the original pixel-wise intensity
distribution. The noise-free images generated by 3S denoising from fixed reversibly switchable fluorescent
proteins (RSFP)-labeled cells serve as GT for training a hybrid supervised/self-supervised denoising network
(3Snet). The trained 3Snet is then applied to perform joint denoising and deconvolution of single-frame images
(3Snet-CLID) from various cellular structures labeled with conventional fluorescent proteins (FPs) or dyes,
thereby improving spatial resolution. 3Snet-CLID is a 2D, single-frame SR technique that achieves
approximately 60 nm resolution on conventional WF and spinning-disk (SD) confocal microscopes,
substantiallyly enhancing image contrast. It is suitable for imaging samples under 10 μm in depth and works best
with confocal spinning-disk and TIRF microscopy modes.

Results
Conception of the single-frame computational SR method 3Snet-CLID
This study mainly focusses on addressing key challenges described above in computational SRs, and enabling
SR imaging of single-frame images from WF or SD confocal microscopy across diverse subcellular structures.
We propose a two-step strategy, 3Snet-CLID, that combines DL denoising with RL deconvolution to achieve
single-frame SR: 1) A DL denoising network is applied to a single noisy input image to obtain a clear image; 2)
Standard RL deconvolution is then directly performed on this clear image to generate the SR output. An ideal
3Snet-CLID framework must meet three criteria: 1) The denoising network must be highly effective so that noise
is not amplified during subsequent RL deconvolution; 2) The denoised image must preserve the original pixel-
wise signal distribution to prevent artifacts during RL deconvolution; 3) The network must generalize well to
denoise single-frame images of various subcellular structures.

While self-supervised DL denoising methods are commonly used for single frame denoising, we found that
existing approaches often introduce artifacts when their outputs are directly fed into RL deconvolution
(Supplementary Fig. 1). We hypothesize that although these methods reduce noise effectively, their denoising
process alters the pixel-wise signal distribution, leading to a mismatch with the PSF during RL deconvolution
and resulting in artifacts. Therefore, we consider effective denoising coupled with signal distribution
preservation as two essential conditions for enhancing spatial resolution in SRL-based SR.

To address this, we propose first generating high-quality GT denoised images from multi-frame acquisitions in
fixed cells, and then using this GT to train a DL denoising network for single-frame image denoising. For the
denoised images to be suitable for CLID, both the GT and the trained network must satisfy specific requirements:
1) The GT must be virtually noise-free while preserving the pixel-wise signal distribution, enabling artifact-free
resolution enhancement via RL deconvolution; 2) The network trained on this GT must retain strong denoising
performance, preserve the signal distribution similarly to the GT, and exhibit high robustness for denoising
single-frame images of different subcellular structures. However, obtaining a suitable GT—a clear image with
low noise and preserved signal distribution remains difficult because conventional denoising methods typically
rely on explicit noise models tailored to specific noise sources (e.g., dark current, readout noise), which are
ineffective against the complex, concurrent noise types encountered in real-world imaging (e.g., shot noise).
Moreover, many methods utilize information from neighboring pixels (e.g., Hessian or sparse methods27, 37,
Gaussian filter38, Wiener filter39) or frequency-domain operations (e.g., Wavelet transforms40, Low-pass filter41),
which inevitably alter the original pixel-wise signal distribution and thus hinder subsequent RL deconvolution.
We therefore introduce a per-pixel denoising strategy that operates on individual pixels independently, rather
than using information from surrounding pixels. This approach aims to achieve effective noise suppression while
strictly maintaining the original pixel-wise intensity distribution, thereby mitigating noise amplification and
reconstruction artifacts during iterative RL deconvolution. Leveraging the property that RSFPs respond to
illumination modulation while noise does not, we perform single-pixel-level computations on image series
corresponding to the "ON" and "OFF" states of the FP. This enables the effective removal of multiple noise types
while preserving the original pixel-wise intensity distribution. The resulting denoised images are used to train a
hybrid supervised/self-supervised denoising network, which is designed to retain the characteristics of the per-
pixel denoising strategy and be applicable to CLID SR imaging. We name the denoising method single-pixel-
synchronized switching (3S) denoising, the corresponding DL network 3Snet, and the overall SR imaging
framework combining 3Snet with RL deconvolution 3Snet CLID.

Per-pixel 3S denoising strategy
The 3S per-pixel denoising strategy is designed to differentiate signal from noise at the level of individual pixels.
This method operates without explicit models of noise or background sources. Instead, we classify noise for each
pixel based on its temporal characteristics into two distinct modes: a random component that fluctuates from
frame to frame, and a fixed-pattern component that remains constant across frames. The denoising process is
achieved by treating each pixel individually and applying two specific operations: multi-frame averaging to
suppress the random noise component, and a subtraction operation between carefully defined image sets to
eliminate the fixed-pattern noise.

We implement this denoising theory by leveraging RSFPs. The controlled on/off switching of RSFPs, triggered
by specific light wavelengths, provides a precise pixel-level correspondence between fluorescent (signal-present)
and non-fluorescent (signal-absent) states. Both the acquired 'ON' and 'OFF' image sets contain the mixed noise
(random and fixed). Our 3S-denoising technique, proceeds in two steps: first, multi-frame averaging of the 'ON'
and 'OFF' images independently suppresses the random noise in each state; second, the averaged OFF image
(AVG(OFF)) is subtracted from the averaged-ON image (AVG(ON)) to suppress the averaged fixed background,
thereby simultaneously isolating the true signal and removing both noise components. This approach preserves
the original pixel-wise signal distribution essential for optimal deconvolution.

We developed a denoising strategy depicted in Fig. 1a, involving two steps: signal acquisition and noise removal.
Initially, Skylan-S (a green RSFP) underwent repeated switching cycles using 405 nm and 488 nm illumination
for ON and OFF states, respectively. Multiple frames of ON and OFF images were captured under the same 488
nm illumination. We then conducted noise reduction by averaging multiple frames for both ON and OFF images
to eliminate/suppress random noise (Gaussian and signal-related Poisson noises, et al.). Subsequently, we
performed AVG(ON) - AVG(OFF) to eliminate/suppress fixed-pattern systematic noise, resulting in the final
denoised image, referred to the clear image.

Evaluation of 3S-denoising and 3S-CLID on synthetic microtubule and cellular structure
We first assessed the performance of 3S denoising using synthetic microtubules. To mimic real imaging
conditions, background images from a blank region under WF illumination were acquired, and both Gaussian
and Poisson noise were added to the synthetic microtubule image. The pixel size was set to 65 nm to match that
of the Flash 4.0 camera coupled with a 100× objective. The 3S-denoised clear image substantially outperformed
images reconstructed through frame averaging (AVG(ON)), pixel-wise median of image sequences (MED(ON)),
and median-based difference images (MED(ON–OFF)), exhibiting substantially higher peak signal to noise ratio
(pSNR) and structural similarity index (SSIM) (Fig. 1b). These results indicate that 3S denoising generates
higher-quality images with reduced noise and improved signal integrity and distribution compared to
conventional averaging.

Both optical and software-based upsampling are critical to RL deconvolution. Optical oversampling provides
genuine signal information but reduces the SNR per pixel, whereas software upsampling provides a finer
computational grid without adding new signal content. This grid refinement enhances the numerical stability of
RL deconvolution and reduces artifacts without degrading SNR. Specifically, RL deconvolution produces
substantial gain at high frequencies near the optical cutoff, which is inherently unstable and noise-sensitive.
According to Cramér–Rao Lower Bound (CRLB) analysis, the CRLB diverges as spatial frequencies approach
the diffraction limit, resulting in severe noise amplification and poor convergence in high-frequency regions31.
A finer sampling grid helps numerically manage the algorithm’s pronounced gain near the cutoff, underscoring
the utility of software upsampling for stabilization.

In the current study, we combined modest optical oversampling (65 nm pixel size) and software upsampling
prior to RL deconvolution. Synthetic structures denoised with the 3S method were upscaled by a factor of 2, and
several upsampling methods were evaluated. Lanczos interpolation42 produced higher pSNR and SSIM in the
resulting 3S-CLID images compared to Linear, Fourier, or Bicubic interpolation (Supplementary Fig. 2). Further
testing with Lanczos interpolation at 3× and 4× scaling showed that 3× upsampling achieved the highest pSNR
and SSIM, outperforming both 2× and 4× factors (Supplementary Fig. 2). Thus, we use 3× Lanczos upsampling
for following study.

We then assessed the performance of 3S-CLID on the denoised images. While RL deconvolution of raw,
AVG(ON) or MED(ON) images failed to separate 65 nm lines and introduced artifacts, 3S denoising followed
by CLID processing achieved 65 nm resolution with improved contrast (Fig. 1b and Fig.1c). Although MED(ON-
OFF) outperformed AVG(ON), it remained inferior to the 3S denoising approach (Fig. 1b and Fig. 1c). Notably,
Fig. 1b highlights excellent performance of 3S-CLID: the reconstruction obtained from a strongly noisy
measurement is nearly identical to the reconstruction obtained by deconvolving a blurry but noise-free image.
Starting from the raw noisy input (pSNR/SSIM = 8.2/0.15), 3S denoising step substantially suppresses noise
while preserving the per-pixel signal distribution, resulting in a denoised estimate with pSNR/SSIM = 47.5/0.98.
Applying RL deconvolution to this denoised image (i.e., 3S-CLID) yields a super-resolved reconstruction with
pSNR/SSIM = 24.5/0.93, which closely matches the result of deconvolution applied to a blurry, noise-free image
(pSNR/SSIM = 23.9/0.94). This near-equivalence indicates that 3S effectively recovers an accurate blurred
signal estimate under severe noise, enabling the downstream deconvolution to operate in a regime comparable
to the ideal noise-free case. Overall, 3S-CLID combines (i) efficient single-pixel-based denoising, (ii) faithful
preservation of the signal distribution, and (iii) high-fidelity SR reconstruction.

We then proceeded by labeling actin with RSFP and imaging fixed cells using WF and SD microscopy. The
fluorescence signal acquisition was conducted following the procedure outlined in Fig. 1a. In both instances (Fig.
1d, e, WF and Fig. 1f, g, SD), 3S denoising substantially enhanced the SNR and structural continuity.
Furthermore, 3S-CLID improved resolution by factors of 3.7 (WF) and 4.9 (SD), respectively, resolving finer
structural details of actin bundles and microfilaments (Fig. 1e and Fig. 1g).

Design of hybrid supervised/self-supervised DL denoising network 3Snet
DLSR suffers from limited robustness and poor generalization across organelles, as it learns an ill-posed, end-
to-end mapping where a single low-resolution pixel can correspond to many high-resolution outputs, causing
overspecialization. In contrast, DL-based denoising offers greater robustness43 by enforcing a strict pixel-by-
pixel mapping that preserves the original signal distribution. Inspired by 3S-CLID, we propose to leverage the
inherent robustness of denoising networks to overcome the generalization limitations of DLSR.

A major obstacle in supervised denoising is obtaining reliable GT data for training. We postulate that per-pixel
3S denoising method, which effectively removes noise while preserving signal fidelity and spatial distribution,
is well-suited to produce accurate and reliable GT images. We hypothesize that a denoising network trained on
such data will retain these pixel-level preservation properties. The network’s output would maintain the original
signal distribution, yielding denoised images that are directly applicable to RL deconvolution for enhanced
spatial resolution.

Inspired by evidence that incorporating GT improves self-supervised denoising performance44, we developed
3Snet, a hybrid U-net-based network that integrates supervised and self-supervised learning (Fig. 2a). By
averaging ON images with varying frames, we generated noisy images with different noise levels, and randomly
selected two noisy images at each noise level to train the self-supervised network for every training iteration.
Concurrently, 3S-denoised images were utilized as GT for training supervision (Supplementary Fig. 3). The
3Snet network was employed to denoise single-frame images via WF or SD, subsequently upsampling and
applying CLID to accomplish single-frame SR imaging (Fig. 2b). This methodology was termed 3Snet-CLID
SR technology.

Validation of 3Snet-CLID by standard known structures and cross-validation
We evaluated the performance of 3Snet-CLID in imaging standard structures obtained through WF microscopy.
To do this, we conducted a comparison of the outcomes of 3Snet-CLID and direct deconvolution with other
denoising methods on an identical image. Initially, we examined fluorescent beads in ball shape of different sizes.
Both 3Snet-CLID and sparse deconvolution successfully distinguished the close proximity of 100-nm beads
spaced 126-nm apart, whereas Poisson unbiased risk estimate (PURE)45 and denoising convolutional neural
networks (DnCNN)46 did not achieve the same level of resolution (Fig. 2c). With smaller beads (20 and 40 nm),
3Snet-CLID was able to separate beads spaced 65/66 nm apart—a capability that was not possible with WF
microscopy, sparse, PURE and DnCNN deconvolution approaches (Fig. 2c). Following this, we utilized the
linear structure of the commercial Argo-SIM as previously reported27. Line spacings from 60 nm to 150 nm were
indistinguishable under WF microscopy with DnCNN, and Noise2Self47, but were clearly resolved using 3Snet-
CLID (Fig. 2d). Sparse deconvolution can resolve two lines separated by 150 nanometers (Fig. 2d), in agreement
with previous reports27. PURE and N2V48 deconvolution introduce significant artifacts into the resulting images
(Fig. 2d). For cell samples, 3Snet-CLID more accurately reconstructs endoplasmic reticulum (ER) structures,
yielding more continuous, complete morphologies with a higher SNR and less artifacts than other denoising
methods (Supplementary Fig. 1). Subsequently, we conducted a cross-validation between 3Snet-CLID and
STORM using DNA origami samples labeled with paired fluorophores. The origami structure incorporated two
fluorescent sites labeled with FITC-488 molecules, positioned 60 nm apart for STORM microscopy. Although
the paired molecules were barely distinguishable under WF microscopy, they were clearly resolved by either
3Snet-CLID or STORM (Fig. 2e). These results emphasize the effectiveness of 3Snet-CLID in processing
structures of diverse shapes, leading to a nearly 5-fold enhancement in spatial resolution compared to WF
microscopy and almost a twofold improvement compared to sparse deconvolution.

3Snet-CLID enable fixed and live-cell single-frame SR imaging
We first assessed the imaging capabilities of 3Snet-CLID on single-frame biological samples from WF and SD
imaging. 3Snet-CLID substantially enhanced spatial resolution and contrast in WF imaging, allowing for clear
visualization of actin meshes and filaments within a dense actin network in fixed HeLa cells. Additionally, it
provided more detailed insight into the actin structures compared to sparse deconvolution (Fig. 3a and 3b). Using
a parameter-free decorrelation analysis method49, the spatial resolution was improved from 216 nm with WF to
82 nm with 3Snet-CLID reconstruction (Fig. 3c).

Notably, once trained for a specific imaging system, 3Snet-CLID generalizes across different fluorophores
without requiring retraining or fine-tuning (Supplementary Fig. 4). Thus, 3Snet-CLID can be effectively utilized
in dual-color imaging, improving resolution across different wavelengths to enhance visualization of fixed
cellular structures (Fig. 3d). The dual-color imaging of F-actin (blue) and PMP (peroxisomal membrane protein,
magenta) in fixed HeLa cells demonstrated that 3Snet-CLID produced sharper actin filaments with higher
contrast compared to WF imaging (Fig. 3d). Additionally, it allowed the previously blurred fluorescent punctum
of peroxisomes to be resolved as a ring-shaped structure located within the actin network. In comparison with
sparse deconvolution, 3Snet-CLID has an advantage in resolving small ring structures. (Fig. 3d).

In live Jurkat T cells, 3Snet-CLID enabled the analysis of dynamic actin changes during immune synapse
formation with single-frame temporal resolution (Fig. 4, Supplementary Movie 1). The enhanced spatial
resolution facilitated detailed observation of the dynamic retrograde flow of lamellipodial actin networks and
the centripetal movement of lamellar actin networks corresponding to the distal supramolecular activation cluster
(dSMAC) and peripheral supramolecular activation cluster (pSMAC), respectively (Fig. 4a). In line with
previous findings50, the rate of actin retrograde flow across the dSMACS appeared constant, as indicated by the
consistent slopes in the kymographs for this region using both 3Snet-CLID and sparse deconvolution techniques
(Fig. 4a, dSMAC, red dash lines). However, the centripetal flow rates across the pSMAC were found to be
variable, indicated by differing linearities in the kymograph slopes for this area (Fig. 4a, pSMAC, red dash lines),
contrary to previous report50. Furthermore, both the 3Snet-CLID and sparse deconvolution techniques clearly
confirmed that certain actin arcs at the pSMAC converge along the same trajectory over time (Fig. 4a, white
arrow heads), highlighting the variability in the velocity of these arcs. Unlike the uniform distribution observed
with WF imaging, the enhanced spatial resolution of 3Snet-CLID and sparse deconvolution revealed non-
uniform intensity distributions along the trajectories within both dSMAC and pSMAC regions (Fig. 4a).
Additionally, variations in the size of actin clusters at the outer edge of the pSMAC were observed at different
time points (Fig. 4a), suggesting potential dynamic assembly or disassembly of actin during movement.
Moreover, the formation of concentric actin arcs at the boundary between the dSMAC and pSMAC remains
ambiguous due to the resolution limitations of WF imaging. In comparison to sparse deconvolution, 3Snet-CLID
provides a clearer and more straightforward observation of individual actin bundles or multiple bundles
coalescing into an actin arc at the boundary and progressing inward across the pSMAC (Fig. 4a, yellow arrows).
Studies have indicated that actin structures in different regions of the pSMAC layer exhibit diverse orientations
and polarities, underscoring the importance of quantifying the anisotropy of these structures to understand their
influence on pSMAC actin arc organization51. Through the analysis of angles and anisotropy radius using
FibrilTool52, the examination of actin arc anisotropy within the pSMAC region (Fig. 4a, highlighted in yellow
and Fig. 4b) demonstrated that, due to enhanced resolution, 3Snet-CLID and sparse deconvolution were more
proficient in quantitatively assessing the orientation and polarity of actin arcs compared to WF microscopy.
Notably, 3Snet-CLID exhibited the greatest actin arc anisotropy within the pSMAC region in various directions
(Fig. 4b). The decorrelation analysis showed the resolution was improved 4.3-fold following 3Snet-CLID
processing (Fig. 4c, d).

In a dual-color imaging mode, 3Snet-CLID enabled the visualization of dynamic movement of F-actin, labeled
with F-tractin-StayGold (green) and microtubule plus-ends, labeled by EB1-mScarlet-I (magenta)
(Supplementary Fig. 5a, Supplementary Movie 2). Employing a StarDist model provided in TrackMate53,
microtubule plus-ends were automatically tracked over time (Supplementary Fig. 5b). These tracking results
demonstrated the ability of 3Snet-CLID to resolve the two poles of the microtubule-organizing center (MTOC)
within the cell. Observations revealed the dynamic movement of EB1 proteins radially from the poles along the
microtubule length towards the periphery, with varying densities of growing microtubules in different radial
directions, indicating a polar generation and distribution of microtubules. Using single-molecule tracking
technology, it was observed that the movement trajectories of EB1 molecules mostly did not overlap, with EB1
showing up at different growing microtubule plus ends at distinct time intervals. Interestingly, some EB1
molecules did not stem from the MTOC. As time passed, certain EB1 molecules disappeared earlier within the
cell, while others vanished in the distant dSMAC layer of the immune synapse. These results suggest that during
the immune synapse formation, EB1 molecules can detach and reattach from specific growing microtubules
dynamically, indicating intermittent microtubule growth and dynamic circulation of EB1 proteins along the
growing microtubules.

We further demonstrated the SR capability of 3Snet-CLID by applying it to visualize the ring-shaped nuclear
pore complex (NPC) labeled with Nup96, a resolution standard for SR microscopy54. While conventional SD
microscopy depicted Nup96 as diffuse puncta (Fig. 5a), 3Snet-CLID clearly resolved the distinct annular
morphology of the NPC (Fig. 5b). The dimensions of the resolved structures (Fig. 5c, d) closely matched those
established by electron microscopy54. In a final evaluation, we examined the efficacy of dual-color 3Snet-CLID
for live cellular structures using SD microscopy. At single-frame temporal resolution, 3Snet-CLID enabled
visualization of the dynamic interactions between the ER and mitochondria (Supplementary Movie 3). In the
green channel, 3Snet-CLID clearly resolved the outer membranes of closely positioned mitochondria, along with
the potentially stretched thin mitochondrial outer membrane (Fig. 5e, Supplementary Fig. 6). In the red channel,
3Snet-CLID also demonstrated diffraction-unlimited spatial resolution, allowing for the precise resolution of
finer and sharper tubular ER structures, as well as grid-like tubular ER sheet structures (Fig. 5e, Supplementary
Fig. 6). Quantitative assessment showed that the averaged resolution was improved from 363 nm (mitochondria),
346 nm (ER) to 68 nm and 64 nm, respectively, following 3Snet-CLID processing (Fig. 5f). Notably, 3Snet-
CLID effectively captured the dynamic changes in the outer membrane structure of mitochondria, a feature that
SD cannot analyze, and accurately tracked the dynamic alterations in the tubular and sheet structures of the ER.
Using 3Snet-CLID, numerous dynamic events were observed, such as the dynamic generation and disappearance
of ER leading to mitochondrial morphology changes, as well as the stretching, recycling and fusion (Fig. 5g, h).
Interesting, we found previously unreported the lateral fusion event of mitochondrial outer membranes (Fig. 5g,
h region 3 and Supplementary Movie 3).

Methods
3S-CLID frameworks
We imaged Lifeact-Skylan-S labeled F-actin in fixed U-2 OS cells. The acquisition protocol generated 20
training datasets in under 30 minutes. Each dataset comprised 50 ON/OFF cycles with a 50-ms exposure per
frame. Specifically, Skylan-S was activated with 405 nm illumination (50 ms, 1.29 W/cm²), and multiple ON-
state frames were captured under 488 nm illumination (50 ms, 5.39 W/cm²). The same 488 nm illumination was
then used to switch the molecules off, followed by an equal number of OFF-state frames captured using identical
settings. To obtain a clear image, we averaged the images captured in the ON state and subtracted the average
from those taken in the OFF state. The denoised clear image were then upsampled by factor 3 using Lanczos.
RL deconvolution was performed on the clear image to enhance its resolution, using Bessel function as the PSF
following
𝐻 =𝐼 [\frac{2∗𝐵𝑒𝑠𝑠𝑒𝑙1(𝑘∙NA∙𝑟)}{𝑘∙NA∙𝑟}]^2 (1)
Where 𝐵𝑒𝑠𝑠𝑒𝑙 is the Bessel function of the first kind of order zero, 𝐼 is the intensity of the incident radiation,
1 0
𝑘 =2π⁄𝜆, λ is the wavelength, NA is numerical aperture, r is the circular radius of the polar coordinate. The
theoretical 2D PSF used for deconvolution was parameterized based on empirical measurements from
fluorescent beads57.

Workflow of 3Snet-CLID
The 3Snet-CLID method integrates a three-stage computational imaging pipeline to achieve high-resolution,
noise-suppressed images. The process begins with the acquisition of noise-free GT data, uses this data to train a
denoising network, and finally applies the network for superior image restoration.

1) Data acquisition and GT generation (3S Denoising)
The sample, expressing a RSFP, is imaged under modulated illumination to capture multiple frames in both ON
and OFF states. These frames are averaged to produce a mean ON image AVG(ON) and a mean OFF image
AVG(OFF). A high-fidelity, noise-free GT image is then generated by subtracting AVG(OFF) from AVG(ON).

2) Neural network training
This phase involves training a U-net architecture through two complementary strategies:

i) Self-supervised training:
Images with varying SNRs are synthesized from the acquired data. As shown in Supplementary Fig. 3, to
generate training sets with diverse noise levels, we started by gathering 50 frames of images from the ON state
and organizing them into five datasets using the combination formula 𝐶𝑘, where n equals 50 and k is 1, 2, 4, 8
n
or 16. Next, we randomly selected 50 elements from each dataset and calculated the average of the k images in
each chosen element. Thereafter we randomly selected two images in each dataset as the input (x) and target (y)
images for the U-net model.

ii) Supervised training:
The network is further refined using the high-quality GT image from Stage 1) as a definitive target, enhancing
its denoising accuracy.

The resulting predictions were calculated by the following loss function to execute the training stage.
loss=[‖𝑥̃−𝑦‖2+𝜆‖𝑥̃−GT‖2]/(1+𝜆) (2)
where 𝑥̃ represents the network outcome of the input x, and ‖ ‖2 refers to the l norm, GT is GT. λ>0 denotes
the weighting factor between the self-supervised term and the supervised term in the loss function. A larger λ
indicates a higher weight assigned to the supervised term. When λ=0, the supervised term becomes zero and the
DL model reduces to a self-supervised model; when λ=∞, the self-supervised term becomes zero and the DL
model reduces to a fully supervised model. To determine the optimal λ, we set λ to 0/1/2/4/8/16/∞ and trained
the model on the same dataset for each setting. The dataset consists of two parts: an image set for training the
denoising network (train) and an image set for evaluating the denoising performance (test). The λ used in the
loss function is chosen as the value that yields the highest average pSNR on the denoised images in the test set.

3) Application: joint denoising and deconvolution
The trained network is deployed to process single-frame images from diverse samples, including those labeled
with conventional, photoactivatable, or photoconvertible FPs. A single frame—from either fixed cells or a live-
cell time-lapse sequence—is first denoised by the network. The output is then further enhanced by RL
deconvolution, resulting in a final SR image.

Simulations of synthetic microtubule structures
To conduct benchmarks with simulated GT, microtubule-like structures were created using the ‘Random Walk’
process, and the maximal curvatures in the program were utilized27. The GT objects were then convolved with a
microscope PSF (1.49 NA, 488 nm excitation, 65 nm pixel) to generate simulated blurred ground-truth images
(GT_blur). Subsequently, the images were normalized to a 0-255 range and contaminated with Poisson noise
(setting lam, the expected number of events occurring, to 5) and Gaussian noise (setting STD, the standard
deviation of the distribution, to 5). The raw images were captured by a camera with a pixel size of 65 nm and
pixel amplitudes of 16 bits.

Optical setups
The WF system
The WF system was based on a commercial inverted fluorescence microscope (IX83, Olympus) equipped with
an objective (100×/NA 1.49 oil, UAPON, Olympus) and laser light with wavelengths of 405 nm (LBX-405-300-
CIR-PP, Oxxius), 488 nm (Genesis MX488-500 STM, Coherent) and 561 nm (Jive 500-561 nm, Cobolt).
Acoustic optical tunable filters (AOTFnC-400.650-TN, AA Opto-Electronic) were used to combine, switch, and
adjust the illumination power of the lasers. A collimating lens (20×/NA 0.40, Plan N, Olympus) was used to
couple the lasers to a polarization-maintaining single-mode fiber (QPMJ-3AF3S, Oz Optics).

The output lasers were collimated and then expanded by a beam expander (GCO-2503, Daheng Optics). The
light passed through several mirrors (PF10-03-P01, Thorlabs) and a tube lens (ITL200, Thorlabs) was used to
focus on the back focal plane of the objective. A multiband filter cube was used and emitted fluorescence
collected by the same objective passed through a dichroic mirror (ZT405/488/561/640-phase R, Chroma) and an
emission filter (FF01-446/523/600/647-25, Semrock). For dual-color imaging, an image splitter (Optosplit II,
Cairn) was used before the sCMOS camera (Flash 4.0V2 C11440-22CU, Hamamatsu) to split the emitted
fluorescence into two channels.

The SD confocal microscopy
The Olympus SpinSR10 system utilized an inverted fluorescence microscope (IX83, Olympus) with four lasers
(405 nm, 488 nm, 561 nm and 647 nm) and an objective (100×/NA 1.50 oil, Olympus). The setup included a
scanning system (CSU-W1, Yokogawa) and a microscope incubator (Okolab) specifically designed for live cell
imaging. The system is operated using CellSens Dimension software and the image capture is performed using
an sCMOS camera (ORCA-Fusion BT, C15440-20UP, Hamamatsu).

The Nikon SoRa system utilized an inverted fluorescence microscope (Ti2-E, Nikon) equipped with four lasers
(405 nm, 488 nm, 561 nm, and 647 nm) and a 100×/NA 1.45 oil objective (Nikon). The setup included a scanning
system (CSU-W1, Yokogawa) and a microscope incubator (TokaiHit STXG-SP400NX) specifically designed
for live-cell imaging. The system was operated using NIS-Elements software, and images were captured with an
sCMOS camera (Prime BSI, Photometrics).

The DeltaVision™ OMX microscope
The DeltaVision OMX system, developed by GE Healthcare, was equipped with an objective (60× PLAPON
/1.42 NA), four lasers (405 nm, 488 nm, 561 nm, and 640 nm), four filter sets, and four sCMOS cameras,
enabling high-speed imaging in 4-channel modes.

Standard and cell samples for 3Snet-CLID imaging
DNA origami materials
The M13mp18 phage DNA sourced from New England BioLabs was used directly without additional
purification. All staple strands, including Alexa Fluor 488-labeled and biotin-modified staple strands, were
obtained from Tsingke Biotech (Beijing). The DNA origami staple strands were pre-mixed and stored at -20℃.
The DNA origami nanostructure and synthesis were performed as previously described with slight
modifications58, 59. Briefly, the DNA origami structures were assembled in a single reaction, including 10 nM
M13mp18, 100 nM unmodified staple strands, 100 nM biotin-modified strands, and 400 nM Alexa Fluor 488-
labeled strands with DNA-PAINT extensions in DNA origami folding buffer. The annealing process, carried out
by a PCR device, entails initially holding the temperature at 25℃ for 20 seconds, then gradually increasing it to
90℃ over 15 minutes at a rate of 0.5℃ per second. Subsequently, maintaining the temperature at 90℃ for 1
minute, and then decreasing it by 1℃ per cycle at a rate of 0.1℃ per second until reaching 70℃. At 70℃,
maintaining this temperature for 3 minutes, while decreasing the temperature to 30℃ by 1℃ per cycle at the
same rate. After holding it for 30 seconds, the temperature is finally lowered to 4℃ at a rate of 0.5℃ per second.
For the purification process, a 100 kDa ultrafiltration concentrator was utilized. Initially, 500 μL of DNA origami
purification buffer (15 mM MgCl in TAE buffer) was added and centrifuged at 5,000 g at 4°C for 7 min. Then,
2
50 μL of annealed solution was mixed with 450 μL of DNA purification buffer and centrifuged at 2,000 g at 4°C
for 20 min. Subsequently, 450 μL of DNA purification buffer was added, and centrifugation at 2,000 g at 4°C
for 20 min was repeated twice. The filter was then inverted into a fresh tube and centrifuged at 2,000 g at 4°C
for 3 min, and the collected solution was stored at -20°C.

STORM imaging
Confocal imaging dishes (Cellvis) were coated with 1 mg/mL biotin-labeled BSA (Solarbio) for 5 min at room
temperature. After three washes with PBS, NeutrAvidin (1 mg/mL in PBS) was added to the microwell, incubated
for 5 min, and washed three times with PBS. Subsequently, the 60 nm DNA origami structure was diluted in
DNA origami imaging buffer (10 mM MgCl in PBS) and incubated for 5 min at room temperature, followed by
2
three washes with the same buffer. Once the imager strands were added, the sample was ready for imaging. For
the 60 nm structure, an exposure of 200 ms and an illumination power intensity of approximately 4-8 mW/cm2
were applied, with 100 frames acquired for the reconstruction. The acquired images were reconstructed with
thunderSTORM the Fiji plugin60.

Argo-SIM slide
We also utilized a commercial fluorescent sample (the Argo-SIM slide, Argolight) with GT patterns consisting
of fluorescing double line pairs (with spacing ranging from 0 nm to 210 nm; λ = 300-550 nm) to validate the
ex
resolution (http://argolight.com/products/argo-sim).

FluoSpheres imaging
To further validate the resolution, FluoSpheres of different sizes (20 nm-, 40 nm- and 60 nm-diameter, Thermo
Fisher Scientific) were diluted with PBS and loaded onto glass coverslips. After allowing the fluorescent beads
to settle for 30 min, a single-frame image was taken for analysis.

Live cell samples
For live 3Snet-CLID experiments, U-2 OS cells or COS-7 cells were labeled with Lifeact-StayGold (Lifeact-
SG)/Tom20-SG/Sec61-mScarlet-I using Lipofectamine™ 3000 transfection reagent (Thermo Fisher Scientific)
according to the manufacturer's instructions. Jurkat T cells, on the other hand, were transfected with F-tractin-
SG/EB1-mScarlet-I via electroporation.

Fixed cell samples
Cells transfected with genetic indicators were fixed using 4% paraformaldehyde in PBS for 15 min at 37℃,
followed by thorough washing with PBS.

Cell culture and preparation
The U-2 OS and COS-7 cell lines were purchased from ATCC, while the Jurkat T cell line was acquired from
the National Infrastructure of Cell Line Resources. U-2 OS and COS-7 cells were grown in McCoy's 5A medium
(Gibco(Gibco) or DMEM (Gibco), respectively, both supplemented with 10% FBS (Gibco) and 0.1% Mycoplasma
prevention reagent (Transgen). Jurkat T cells were cultured in RPMI 1640 medium (Gibco) supplemented with
10% FBS, 1 mM sodium pyruvate solution, 50 μM β-mercaptoethanol (Gibco), and 0.1% Mycoplasma
prevention reagent at 37℃ and 5% CO . For imaging experiments, cells were seeded onto glass coverslips,
2
which were precoated with 10 μg/mL fibronectin for 30 min at 37℃. For imaging Jurkat T cells, coverslips were
coated overnight at 4°C with 2.5 μg/mL monoclonal anti-CD3 (eBiosciences) and washed with PBS three times.
Cell imaging commenced within 10 min after loading cells onto coverslips. To generate homozygous Nup96-
sfGFP knock-in U-2 OS cell lines, we employed CRISPR–Cas9-mediated homology-directed repair (HDR).
sgRNA sequences61 were synthesized, annealed, and cloned into the BbsI site of a GFP-deleted pSpCas9(BB)-
2A-GFP (PX458) vector (Addgene #48138). Homology arms flanking the gRNA and PAM cleavage sites were
amplified and seamlessly inserted into a pUC19 backbone to generate pUC19-Donor plasmids.

Electroporation conditions
Cells were seeded at a density between 5105 and 1106 cells/mL to ensure that cells were in the exponential
growth phase with high viability. Prior to electroporation, the cells were washed with PBS, counted, and
resuspended in Opti-MEM™ medium (Gibco) to a cell density of 5 × 106 cells/mL, and mixed with DNA
plasmids (10 μg).
Following gentle mixing of the cells and plasmids in Opti-MEM™ medium (Gibco), the mixture was transferred
into electroporation plates with a 0.2 cm gap (Bio-Rad). The electroporation process involved applying a voltage
of 120 V, pulse interval of 0.1 s, 2 pulse cycles, and pulse lengths of 50 ms using square waveform pulses (Bio-
Rad). Subsequently, 100 μL of the electroporated cells were transferred to 12-well plates containing 1 mL of
culture media for Jurkat T cells and were then incubated at 37℃ for 24 hours.

C. elegans strains and 3D reconstruction using SD microscopy
The C. elegans strain yqIs198 (P :TOMM-20::GFP) was cultured and maintained under standard conditions62.
hyp-7
For SD confocal imaging, adult worms were mounted on 2% agarose pads in M9 buffer containing 5 mM
levamisole to induce paralysis. For 3D reconstruction, z-series of 100 optical sections were acquired at a step
size of 100 nm. Image stacks were processed and analyzed using Fiji (ImageJ).

Date analysis
We calculated pSNR values between reconstructed images (I) and GT images by:
pSNR=10log( (𝑝𝑒𝑎𝑘𝑣𝑎𝑙𝑢𝑒)2 ) (3)
𝑀𝑆𝐸
MSE= 1 ∑𝑋 ∑𝑌 [𝐺𝑇(𝑥,𝑦),𝐼(𝑥,𝑦)]2 (4)
𝑋𝑌 𝑥=1 𝑦=1
Structural similarity (SSIM) values between reconstructed images (I) and GT images by:
SSIM=
(2𝜇𝐴𝜇𝐵+𝐶1)(2𝜎𝐴𝜎𝐵+𝐶2)
(5)
(𝜇
𝐴
2+𝜇
𝐵
2+𝐶1)(𝜎
𝐴
2+𝜎
𝐵
2+𝐶2)
where  and  are the local means,  and  are the standard deviations for reconstructed images (A) and GT
A B A B
(B) images sequentially.
Standard deviation (STD) is obtained by:
STD= ∑ √(𝐷(𝑥,𝑦)−〈𝐷(𝑥,𝑦)〉)2 (6)
𝑥𝑦
𝑛−1
where n is the number of pixels; D(x, y) represents the difference between noisy images and GT images, and
〈𝐷(𝑥,𝑦)〉 is the averaged intensity of the difference images.
To measure full width at half maximum (FWHM), the intensity profile is fitted by the normal distribution
function as following:
𝑓(x)=
1
exp⁡[−
(𝑥−𝑥0)2
] (7)
𝜎√2𝜋 2𝜎2
where σ is the standard deviation and x is the expected value, then FWHM is calculated by:
FWHM=2√2ln⁡(2)𝜎 (8)
The anisotropy of actin arcs was examined using the Fiji plug-in FibrilTool52. FibrilTool was integrated into a
macro that conducted orientation and polarity analysis within specified regions of interest nested within a grid-
like layout that encompassed the overall image. The main fiber orientation was represented as a cyan line in each
subregion of interest.
Object tracking was conducted utilizing the TrackMate53 plug-in for Fiji, and the maximum distance covered by
EB1 tracks in each instance in Jurkat T cell was calculated using TrackMate as previously mentioned.

FRC and the decorrelation analysis
FRC resolution63 is calculated from two independently recorded images of the same field under identical
conditions. For WF, SD confocal, and CLID data we therefore acquired the sample twice in succession; the
resolution is taken as the inverse of the spatial frequency at which the FRC curve falls below the 1/7 threshold.
We used the plugin ‘ImageDecorrelationAnalysis_plugin.jar’ to perform the decorrelation analysis49. All SR
images subjected to decorrelation analysis were first inspected visually at an appropriate iteration number to
ensure no obvious texture artifacts were present before the analysis was performed.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review of \"Single-frame wide-field and spinning-disk confocal microscopy with 65 nm resolution\"\nSummary and Assessment\nThe authors present CLID (Clear Image Deconvolution) microscopy, an innovative super-resolution imaging approach that\ncombines noise removal with deconvolution. This paper introduces two complementary implementations: 3S-CLID, which\nleverages the optical switching properties of reversibly switchable fluorescent proteins (RSFPs) to separate signal from\nnoise, and 3Snet-CLID, a deep learning-based method that enables single-frame super-resolution imaging.\nThe authors' approach is highly innovative and commendable. Their method of utilizing ON/OFF states of RSFPs to\neffectively separate signal and noise components, producing high-quality \"clear images,\" demonstrates excellent\nunderstanding of a key challenge in microscopic image processing. Noise reduction prior to deconvolution is crucial for\nrecovering high-resolution components, and this approach significantly enhances the performance of traditional Richardson-\nLucy deconvolution. The development of 3Snet-CLID, which uses high-quality images obtained through 3S-CLID as training\ndata for deep learning, further extends the applicability of this technique to single-frame super-resolution imaging. The\nauthors have conducted comprehensive validation using various standard samples, including fluorescent beads, DNA\norigami, and commercial resolution targets, while also demonstrating excellent performance in live-cell imaging. The\ncomputational efficiency, reported to be 50-240 times faster than sparse deconvolution methods, presents a significant\nadvantage for practical applications. This technique is particularly valuable because it can be applied to existing wide-field\nand spinning-disk confocal microscopes without additional specialized hardware, making it an accessible contribution to the\nbroader research community.\nMajor Issues\n1. Resolution claims could benefit from further contextualization:\nReference (L21-23): \"We present CLID (Clear Image Deconvolution) microscopy, powered by deep learning-based\ndenoising, which achieves an unprecedented 65 nm spatial resolution (sixfold improvement) in single-frame images\"\nThe manuscript would benefit from a more detailed explanation of how the 65 nm resolution is achieved in relation to the\ntheoretical limitations of Richardson-Lucy deconvolution when dealing with spatial frequencies near and beyond the\ndiffraction limit. While the authors mention super-resolution techniques in L30-37, providing a clearer definition of \"super-\nresolution\" early in the introduction and discussing the theoretical context of the claimed resolution would strengthen the\nmanuscript.\n2. The theoretical context could be expanded:\nReference (L59-72): \"Deconvolution algorithms and other analytical model-based methods show promise in achieving\nsingle-frame SR imaging...\"\nThis section would be enhanced by a more comprehensive discussion of the theoretical considerations in image restoration\ntechniques. Including insights on the challenges faced by statistical image restoration methods when attempting to resolve\nfeatures beyond twice the diffraction limit (such as those discussed in Liu Y+, Nat Commun 2025) would provide readers\nwith a more complete understanding of the field.\n3. Additional perspectives on image upsampling would be valuable:\nReference (L115-117): \"To further overcome the Nyquist sampling limit, we upscaled the denoised clear image by a factor of\n2 using Lanczos and applied deconvolution (3S-CLID) to enhance the resolution.\"\nThe manuscript would be strengthened by discussing the relative merits of software-based upsampling versus optical\noversampling during image acquisition. Given that RL deconvolution typically benefits from several-fold oversampling\nrelative to the Nyquist frequency, explaining the rationale behind choosing Lanczos interpolation and addressing how this\nchoice compares to optical oversampling would provide valuable context for readers.\n4. The comparative analysis could be more comprehensive:\nReference (L125-129): \"The results demonstrated that the clear image produced by the 3S denoising method significantly\noutperformed the images generated by image averaging (AVG(ON)) and pixel-wise median of image sequences\n(MED(ON)), with notably higher peak signal-to-noise ratio (pSNR) and structural similarity index (SSIM)\"\nIncluding a comparison with MED(ON)-MED(OFF) would provide a more complete evaluation, particularly given that median\nfiltering can be especially effective for Poisson noise reduction. Additionally, providing more detailed information about the\nRL deconvolution parameters (L344-347) and clarifying whether AVG and MED methods underwent the same 2×\nupsampling would help readers better understand the experimental conditions.\n5. Further validation of generalizability would strengthen the claims:\nReference (L319-324): \"Secondly, the denoising network of 3Snet-CLID features a simpler relationship between input and\noutput data, with subsequent deconvolution handled as a separate process. This results in a more robust SR imaging effect\nthat can be applied to a wide array of cellular structures, including lines, puncta, rings, tubules, and filaments, captured by\nWF and/or SD microscopes\"\nThe manuscript presents promising results for the 3Snet-CLID approach across various cellular structures. This claim would\nbe further strengthened by including additional validation across different cell types, fluorophores, and microscope systems\nbeyond those used for training data acquisition. Such cross-validation would address potential concerns about domain-\nspecific performance that are common in machine learning applications, as noted in L142-148.\nMinor Issues\nQuantitative characterization of SNR improvement would be beneficial:\nReference (L79-81): \"...which leverages reversibly switchable fluorescent proteins (RSFPs) to drastically improve the signal-\nto-noise ratio (SNR) of the image\"\nThe manuscript would be enhanced by including specific numerical values to quantify the improvement in SNR, rather than\nusing qualitative expressions like \"drastically improve.\"\nFigure clarity could be enhanced:\nReference (Fig. 1b): Additional labeling to clearly indicate which methods underwent upsampling prior to deconvolution\nwould improve the interpretability of the figure.\nQuantitative assessment of live-cell imaging would add value:\nReference (Fig. 4): Supplementing the impressive visual comparisons in live-cell imaging demonstrations with quantitative\nmetrics of resolution improvement would provide readers with a more objective basis for evaluation.\nThe connection between learning strategy and Extended Data could be clarified:\nReference (L152-161): \"Inspired by the efficacy of supervised-to-self-supervised transfer learning...\"\nWhile Extended Data Fig. 2 provides information about dataset generation with varying noise levels for training, the\nconnection between this figure and the self-supervised learning strategy described in the main text could be more explicitly\nlinked. Clarifying how the approach shown in Extended Data Fig. 2 relates to the \"supervised-to-self-supervised transfer\nlearning\" concept mentioned in L152-161 would help readers better understand this innovative methodology aspect.\n(Remarks on code availability)\nThe necessary information, including the Readme file and installation instructions, is well organized.\nHowever, only the 100 nm bead images are attached, and the folder does not include any other images.\nIt would be advisable to upload all images reported in the paper for reproducibility and to enable comparison with other\nmethods.", "reviewer_2": "In this work by Xue et al., the authors present a new framework, called CLID (Clear Image Deconvolution), for enhancing the\nresolution of widefield and spinning-disk microscopy images, through a combination of denoising via photoactivation\nsequences (3S), background removal using activation/deactivation image series, and deconvolution. They further introduce\na self-supervised deep learning component, 3Snet, to predict denoised images from single sequences, claiming that this\napproach achieves 65nm resolution using standard fluorophores and conventional setups.\nWhile the proposed workflow is appealing in its conceptual simplicity and implementation potential, I have significant\nconcerns regarding several of the assumptions, methodological choices, and evaluation strategies used in this study.\nA core assumption of the method is that averaging a sequence of photoactivated images yields a noise-free ground truth,\nsuitable for training and deconvolution. However, for dynamic or live samples, such an approach is vulnerable to motion\nartifacts, particularly motion blur, which could undermine the validity of the averaged image as a clean reference, and pose\nproblem in the deconvolution process. The authors should clarify how they mitigate or compensate for such motion during\nacquisition, or whether their framework is restricted to fixed or minimally dynamic samples.\nIn contrast to prior studies, such as Wang et al. 2021, which employ transfer learning to address temporal variability in image\nsequences, the authors here suggest that a single snapshot suffices to train their denoising model. This assumption should\nbe closely evaluated, especially when considering biological variability across time and space. It remains unclear how a\nmodel trained on a single sequence can generalize robustly without overfitting or misrepresenting dynamic features.\nThe choice of fluorophores also raises practical concerns. The method appears to rely on reversible photoswitchable labels,\nsuch as Skylan-S, to distinguish signal from background through the 3S strategy. However, the manuscript does not clarify\nwhether this is a strict requirement. It remains unclear whether the method can operate effectively with conventional\nfluorophores like GFP, or whether dedicated photoswitchable probes are indispensable. If a photoswitchable fluorophore is\nindeed required during a preliminary labeling step, the authors should clarify what assumptions are made about their spatial\ncorrespondence and background characteristics. Without such clarification, it is difficult to assess the general applicability of\nthe method. These constraints should be explicitly addressed, illustrated with examples if possible, and discussed in terms\nof feasibility for broad adoption by the biological imaging community.\nSimilarly, the source and treatment of background signals are not sufficiently explained. The background images acquired\nduring the deactivation phase could include various contributions, such as dark current, autofluorescence, or incomplete\nphotoswitching. A clear explanation of these components is necessary to understand the benefit of this approach over\nstandard background subtraction, particularly under sparse labeling conditions where simple methods often perform well.\nIt is also unclear why the 3S background removal method would outperform conventional strategies unless these sources of\nsignal are well characterized.\nThe manuscript evaluates its denoising approach mainly in comparison to basic strategies like median or mean filtering.\nHowever, recent developments in self-supervised denoising, such as Noise2Void and Noise2Self, have demonstrated\nstrong performance across a range of microscopy contexts. These approaches should be included in the evaluation to\ncontextualize the contribution of 3Snet more rigorously. The authors are encouraged to apply these established methods\nwhile keeping the rest of their pipeline consistent, to isolate the impact of the denoising component.\nAnother important concern relates to the use of 3Snet for denoising images acquired with conventional fluorophores, when\nthe network has been trained on data obtained using reversible photoswitchable fluorophores. This raises questions about\nthe generalization capacity of the model: to what extent can a network trained under specific photophysical conditions\nreliably predict denoised outputs for fluorophores with different emission characteristics, background profiles, and labeling\ndistributions? The manuscript should explicitly address this important point, and whether retraining or fine-tuning of the\nnetwork is required for each new fluorophore.\nFurthermore, the distinction between averaging images and subtracting dark current images remains ambiguous. The\nmanuscript should explain why 3S denoising outperforms a combination of simple averaging and dark frame subtraction. If\nthe contribution of dark current is dominant in the background signal, then the added value of 3S denoising must be explicitly\nquantified and justified beyond conventional background approaches much straight forward to implement. For instance, in\nthe simulations presented in Figure 1, a substantial portion of the background could likely be removed through standard dark\ncurrent correction alone or background subtraction functions. If other sources of background, such as\nautofluorescence, incomplete fluorophore switching, or camera readout noise, are present, these should be clearly identified,\nquantified, and their impact on performance thoroughly discussed.\nThe manuscript lacks details on the acquisition process itself. The authors should report how many images are acquired per\nON/OFF cycle, the acquisition time, and the temporal cost associated with the approach. These factors are particularly\nimportant for live-cell imaging, where exposure time, motion, and phototoxicity are limiting factors. Without this information,\nit is difficult to assess whether the method is broadly applicable in biological settings.\nA major technical concern is the use of a theoretical 2D Airy PSF for deconvolution, without any experimental validation and\ninclusion of 3D blur. Given that spinning-disk and wide-field deconvolution microscopy are often employed for optical\nsectioning and 3D imaging, the exclusive use of a 2D PSF model appears limiting. Deconvolution in microscopy typically\nrequires a 3D PSF model to handle out-of-focus contributions, especially for thicker specimens, more especially because\nthe main contribution of blur comes from the axial direction. If the method is only valid for flat or 2D structures, this should be\nexplicitly stated. Otherwise, the authors should validate their technique using 3D experimental and simulated datasets to\ndemonstrate broader applicability.\nThe simulations and reconstructions shown in the manuscript lack essential parameter information. The nature of the PSF,\nnoise levels, and deconvolution settings such as iteration number and regularization terms are not disclosed. This omission\nhinders reproducibility and makes it difficult to assess whether the results are generalizable or finely tuned to specific\nconditions.\nThere are also noticeable artifacts in the deconvolved images, which resemble mismatches between the PSF model and the\nexperimental imaging conditions. These textures are typical when the PSF does not match the sample or when sampling is\nsuboptimal. The authors should explore whether PSF model, oversampling parameters or improved background subtraction\nprior to deconvolution could mitigate these effects.\nFinally, the resolution claims of 65 nm are based from simulations involving idealized flat 1D filament structures or\nexperimental isolated beads, with no tridimensional structure, which are inherently favorable to single frame deconvolution\nalgorithms and are less prone to artifacts. While such examples can serve as useful proof-of-concept demonstrations, they\ndo not provide sufficient evidence to support claims of generalizable high-resolution performance on 3D objects. More\ncomplex and heterogeneous structures should be employed. Synthetic test objects that span a wide range of spatial\nfrequencies, such as the sector test pattern (DOI:10.1364/OE.543403), would be particularly informative, as they allow for the\nsimultaneous assessment of resolution recovery in fine-detail regions and artifact generation in coarser areas.\n3D blur contributions arising from extended objects imaged with widefield or spinning-disk microscopy should be\nincorporated into the simulations to more accurately reflect typical imaging conditions. This would help reveal both the\nstrengths and the limitations of the CLID approach when dealing with volumetric samples, where out-of-focus light can\nsignificantly degrade image quality and challenge the effectiveness of single frame image deconvolution.\nNotably, the reported resolution of 65 nm corresponds approximately to twice the pixel size after 2× oversampling, raising\nthe possibility that this value may reflect sampling limits or the convergence of deconvolution-induced texture rather than\neffective resolution gain. The authors should investigate whether the resolution estimate stems from true resolution\nimprovement or is merely a byproduct of digital resampling. Varying the degree of upsampling and analyzing its effect on the\nrecovered resolution would help distinguish between these possibilities.\n(Remarks on code availability)", "reviewer_3": "This manuscript describes a method to improve resolution in microscopy images by using a custom, deep-learning based\ndenoising method before a Richardson-Lucy deconvolution. The denoising method uses reversible switchable fluorescent\nprobes to quickly take ‘on’ and ‘off’ images where the ‘off’ images are intended to model background and noise. A UNet is\ntrained to produce denoised images with the target being a ‘denoised’ image generated from the ‘off’ images subtracted from\nthe ‘on’ images.\nDenoising before a RL deconvolution would indeed improve the results. There is a long history of the general concept and\nthe manuscript would benefit from doing a better job of explicitly handling this in the introduction.\nMy main issue with the paper is the theoretical underpinning of the treatment of the noise, which calls into question the\nability of the method to be generalized. It also not compared well to other denoising approaches. The biggest contributions to\nthe noise and background are typically the sample itself through Poisson noise, and out of focus sample (even in optically\nsectioning methods to some degree). Therefore using the ‘off’ images to remove that doesn’t seem to make sense. Also, you\ncan’t subtract noise – subtracting two noisy images makes them more noisy. Averaging multiple images is the same as\ntaking a longer exposure. It seems like what is fundamentally happening is the DL network is learning to produce an image\nthat resembles a longer exposure image (with better SNR) that a noisy image. This isn’t necessarily a bad thing, but how this\nprocess is presented doesn’t make sense.\nComparing to a noise-free RL would be nice in the simulated images section.\nThe math in the Abstract is confusing because the numbers seem to suggest a factor of 4 improvement compared what is\nstated as 6.\nThere are very minor grammatical issues.\n(Remarks on code availability)"}, "author_response": "POINT-BY-POINT RESPONSE TO EDITOR AND REVIEWER’S COMMENTS\nResponse to editor:\nWe sincerely appreciate the opportunity to revise our manuscript and thank all three reviewers for\ntheir valuable comments and suggestions, which have helped improve our work. We have carefully\nrevised the manuscript in response to all comments from the reviewers. Below, we address each\ncomment point by point, and all changes in the main manuscript are highlighted in yellow.\nReviewer #1 (Remarks to the Author):\nReview of \"Single-frame wide-field and spinning-disk confocal microscopy with 65 nm\nresolution\"\nSummary and Assessment\nThe authors present CLID (Clear Image Deconvolution) microscopy, an innovative\nsuper-resolution imaging approach that combines noise removal with deconvolution. This paper\nintroduces two complementary implementations: 3S-CLID, which leverages the optical switching\nproperties of reversibly switchable fluorescent proteins (RSFPs) to separate signal from noise, and\n3Snet-CLID, a deep learning-based method that enables single-frame super-resolution imaging.\nThe authors' approach is highly innovative and commendable. Their method of utilizing ON/OFF\nstates of RSFPs to effectively separate signal and noise components, producing high-quality \"clear\nimages,\" demonstrates excellent understanding of a key challenge in microscopic image\nprocessing. Noise reduction prior to deconvolution is crucial for recovering high-resolution\ncomponents, and this approach significantly enhances the performance of traditional\nRichardson-Lucy deconvolution. The development of 3Snet-CLID, which uses high-quality\nimages obtained through 3S-CLID as training data for deep learning, further extends the\napplicability of this technique to single-frame super-resolution imaging. The authors have\nconducted comprehensive validation using various standard samples, including fluorescent beads,\nDNA origami, and commercial resolution targets, while also demonstrating excellent performance\nin live-cell imaging. The computational efficiency, reported to be 50-240 times faster than sparse\ndeconvolution methods, presents a significant advantage for practical applications. This technique\nis particularly valuable because it can be applied to existing wide-field and spinning-disk confocal\nmicroscopes without additional specialized hardware, making it an accessible contribution to the\nbroader research community.\nResponse:\nWe sincerely appreciate your positive feedback and the valuable time. Your insightful suggestions\nhave significantly strengthened our manuscript, enhancing its accuracy, clarity, and\ncomprehensiveness. Moreover, they have improved the feasibility of our methods for broad\nadoption within the biological imaging community.\nMajor Issues\n1. Resolution claims could benefit from further contextualization:\nReference (L21-23): \"We present CLID (Clear Image Deconvolution) microscopy, powered\nby deep learning-based denoising, which achieves an unprecedented 65 nm spatial resolution\n(sixfold improvement) in single-frame images\"\nThe manuscript would benefit from a more detailed explanation of how the 65 nm resolution\nis achieved in relation to the theoretical limitations of Richardson-Lucy (RL) deconvolution when\ndealing with spatial frequencies near and beyond the diffraction limit. While the authors\nmention super-resolution techniques in L30-37, providing a clearer definition of\n\"super-resolution\" early in the introduction and discussing the theoretical context of the\nclaimed resolution would strengthen the manuscript.\nResponse:\nWe greatly appreciate your valuable suggestions. As recommended, we have provided a\nclearer definition of \"super-resolution\" early in the introduction (Line 31-37 in the revised\nmanuscript，highlighted): “However, inherent limitations arise because the imaging system\nacts as a low-pass filter: the optical transfer function (OTF) restricts the transmission of\nspatial frequencies. Consequently, high-spatial-frequency components beyond the classical\ndiffraction limit are suppressed or lost, defining the system's diffraction-limited resolution.\nSuper-resolution (SR) imaging aims to recover these lost fine-scale details—representing the\nhigh-frequency end of an object's spectrum—from low-resolution measurements.”\nWe have provided a detailed explanation of how the 65 nm resolution was achieved,\ncontextualizing it within the theoretical limitations of Richardson-Lucy (RL) deconvolution. To\nfurther clarify our methodology, we have underscored the fundamental distinctions between\nour denoising approach and existing methods. Specifically, we emphasize that the single-pixel\ndenoising capability of 3Snet enhances network robustness and preserves pixel-wise signal\ndistribution. These properties are pivotal, as they directly contribute to improved spatial\nresolution and signal fidelity in the subsequent deconvolution process.\nThese modifications and clarifications have been primarily incorporated into the Results and\nDiscussion sections. The Conception of 3S-CLID (Line 109-145, highlighted) and Conception\nof 3Snet-CLID (Line 199-224, highlighted) now offer a more detailed account of the core\nprinciples underlying our denoising method, its unique advantages over traditional\napproaches, and its subsequent impact on signal distribution, high-frequency signal\nrestoration via deconvolution, and spatial resolution enhancement. The Discussion section\nhas been revised to include a comprehensive summary and analysis of these points (Line\n369-419).\n2. The theoretical context could be expanded:\nReference (L59-72): \"Deconvolution algorithms and other analytical model-based methods\nshow promise in achieving single-frame SR imaging...\"\nThis section would be enhanced by a more comprehensive discussion of the theoretical\nconsiderations in image restoration techniques. Including insights on the challenges faced by\nstatistical image restoration methods when attempting to resolve features beyond twice the\ndiffraction limit (such as those discussed in Liu Y+, Nat Commun 2025) would provide\nreaders with a more complete understanding of the field.\nResponse:\nWe sincerely thank you for your insightful comments and valuable suggestions. As\nrecommended, we have incorporated a discussion regarding the challenges confronting\ncurrent image restoration techniques in this section (Lines 63-76):\n“Statistical or frequency-extrapolation-based image restoration methods hold potential for\nachieving SR imaging from single frames13, 19-25. These approaches rely on mathematical\nmodeling of the image degradation process—commonly comprising blur (modeled via a point\nspread function, PSF), noise (typically assumed to be Gaussian or Poisson), and sampling\nartifacts—along with suitable priors to infer high-frequency information beyond the\ndiffraction limit. While such methods can approach the diffraction limit under high\nsignal-to-noise ratio (SNR) and well-characterized degradation models, reliably resolving\nfeatures beyond twice the diffraction limit remains a fundamentally ill-posed problem. This is\ndue to the acute sensitivity of high-frequency reconstruction to minute noise or errors26, 27,\nwhich often leads to significant artifacts and renders the restoration process unstable and\ncritically dependent on strong—and often unverifiable—prior assumptions19, 21, 28. For\ninstance, the iterative Richardson-Lucy (RL) deconvolution23, 29, though effective in enhancing\ncontrast and recovering certain high-frequency components, encounters inherent limitations\nnear and beyond the diffraction limit, primarily stemming from noise amplification and the\nseverely ill-posed nature of the inverse problem at these spatial frequencies30.”\n3. Additional perspectives on image upsampling would be valuable:\nReference (L115-117): \"To further overcome the Nyquist sampling limit, we upscaled the\ndenoised clear image by a factor of 2 using Lanczos and applied deconvolution (3S-CLID) to\nenhance the resolution.\"\nThe manuscript would be strengthened by discussing the relative merits of software-based\nupsampling versus optical oversampling during image acquisition. Given that RL\ndeconvolution typically benefits from several-fold oversampling relative to the Nyquist\nfrequency, explaining the rationale behind choosing Lanczos interpolation and addressing\nhow this choice compares to optical oversampling would provide valuable context for readers.\nResponse:\nWe sincerely appreciate the insightful comment. We apologize for the omission in the previous\nversion of the manuscript, where we compared various upsampling methods in Extended Data\nFig. 1 but did not elaborate on the comparative results or justify our selection of Lanczos\ninterpolation in the main text. As suggested, we have now included a discussion in the revised\nmanuscript (Lines 156–174) addressing the relative advantages of software-based upsampling\nversus optical oversampling during image acquisition, their respective implications for RL\ndeconvolution-based SR, the rationale behind our choice of Lanczos interpolation, and all\nCLID-related results presented in the revised article have been regenerated using 3×\nupsampling, as detailed below:\n“Both optical and software-based upsampling play essential roles in RL deconvolution.\nOptical oversampling provides genuine signal information at the expense of reduced SNR per\npixel, whereas software upsampling does not introduce new signal content but supplies a finer\ncomputational grid. This grid refinement enhances the numerical stability of RL\ndeconvolution and suppresses artifacts without incurring an SNR penalty. Specifically, RL\ndeconvolution produces substantial gain at high frequencies near the optical cutoff, which is\ninherently unstable and highly sensitive to noise. The Cramér–Rao Lower Bound (CRLB)\nanalysis of RL deconvolution indicates that the CRLB diverges as spatial frequencies\napproach the diffraction limit, resulting in severe noise amplification and poor convergence in\nhigh-frequency regions30. This underscores the importance of a finer sampling grid to\nnumerically accommodate the algorithm’s pronounced gain near the cutoff—supporting the\nutility of software upsampling for stabilization.\nIn the current study, we employed a combination of modest optical oversampling (65 nm pixel\nsize) and software-based upsampling prior to RL deconvolution. We upscaled 3S-denoised\nsynthetic structures by a factor of 2 and evaluated several upsampling methods. The results\ndemonstrated that the Lanczos interpolation41 approach yielded higher peak SNR (pSNR) and\nstructural similarity index (SSIM) in the resulting 3S-CLID images compared to linear,\nFourier, or bicubic interpolation following RL deconvolution (Extended Data Fig. 1). Further\nupsampling with Lanczos interpolation at factors of 3 and 4 revealed that 3× upsampling\nachieved superior pSNR and SSIM relative to both 2× and 4× upsampling (Extended Data\nFig. 1). Consequently, all CLID-related results presented in this article have been generated\nusing 3× upsampling. Since the underlying structures remain consistent across different\nupsampling factors, the resolution enhancement observed in 3S-CLID images reflects a\ngenuine improvement in resolution rather than a mere consequence of digital resampling.”\nExtended Data Fig. 1 | Assessment of upsampling approaches for 3S-CLID. a, 3S-denoised synthetic structures were\nupsampled by linear, Fourier, Bicubic or Lanczos interporation approache for RL deconvolution. 5% Poisson noise and 5%\nGaussian noise were added to the acquired a blank region of a fixed cell under WF illumination, and 3S-denoised images\nwere processed using different upsampling approaches by a factor of 2, followed by RL deconvolution with a theoretically\nderived Bessel PSF, using 1000 iterations. The pSNR and SSIM of 3S-CLID images were measured to compare the\nperformance of the four upsampling approaches. Scale bar: 1 μm. b, 3S-denoised images were processed using Lanczos\nupsampling approach by different factors, followed by RL deconvolution with a theoretically derived Bessel PSF, using 1000\niterations.\n4. The comparative analysis could be more comprehensive:\nReference (L125-129): \"The results demonstrated that the clear image produced by the 3S\ndenoising method significantly outperformed the images generated by image averaging\n(AVG(ON)) and pixel-wise median of image sequences (MED(ON)), with notably higher\npeak signal-to-noise ratio (pSNR) and structural similarity index (SSIM)\"\nIncluding a comparison with MED(ON)-MED(OFF) would provide a more complete\nevaluation, particularly given that median filtering can be especially effective for Poisson\nnoise reduction. Additionally, providing more detailed information about the RL\ndeconvolution parameters (L344-347) and clarifying whether AVG and MED methods\nunderwent the same 2× upsampling would help readers better understand the experimental\nconditions.\nResponse:\nWe sincerely appreciate your valuable suggestion. In response, we have incorporated a\ncomparison with the MED(ON)-MED(OFF) method in the revised manuscript. Additionally,\nwe have provided more comprehensive details regarding the RL deconvolution parameters\nand clarified that both the AVG and MED methods were evaluated under the same 3×\nupsampling conditions (Line 801-803, Fig. 1 Legend).\nThe MED(ON)-MED(OFF) results, now included in Fig. 1b, 1c, demonstrate that while\nMED(ON)-MED(OFF) yields better performance than AVG(ON), it does not achieve the same\nlevel of improvement as the 3S denoising approach. (Line 188-189)\nFig. 1 | Workflow and validation of 3S-CLID on synthetic microtubule and cellular structure. b, Validation of 3S-CLID using\nsynthetic microtubule. Top row: peak signal-to-noise ratio (pSNR) and structural similarity (SSIM), from left to right: noisy image,\nimage averaging of ON image sequences, median of ON image sequences, median of the ON minus OFF image sequence,\n3S-denoising result (Clear) and blured ground truth. The color bar black to cyan means the relative intensity of images. Middle\nrow: Data uncertainty results of top row indicated by the averaged standard deviation (STD). The color bar blue to red represents the STD\nvalue. Bottom row: deconvolution of noisy image, deconvolution of averaged ON image, deconvolution of median\naveraged ON image, deconvolution of median ON minus OFF image, 3S-CLID result and ground truth. The noisy images were created by\nacquiring a blank region of a fixed cell under WF illumination, and further injection of 5% Poisson noise and 5% Gaussian noise.\nThe resulting images from various approaches were processed using Lanczos upsampling by a factor of 3, followed by RL\ndeconvolution with a theoretically derived Bessel PSF, using 1000 iterations. c, Normilized intensity profiles along the red arrow heads in the left\nground truth (GT) and deconvoled images.\n5. Further validation of generalizability would strengthen the claims:\nReference (L319-324): \"Secondly, the denoising network of 3Snet-CLID features a simpler\nrelationship between input and output data, with subsequent deconvolution handled as a\nseparate process. This results in a more robust SR imaging effect that can be applied to a wide\narray of cellular structures, including lines, puncta, rings, tubules, and filaments, captured by\nWF and/or SD microscopes\"\nThe manuscript presents promising results for the 3Snet-CLID approach across various\ncellular structures. This claim would be further strengthened by including additional\nvalidation across different cell types, fluorophores, and microscope systems beyond those\nused for training data acquisition. Such cross-validation would address potential concerns\nabout domain-specific performance that are common in machine learning applications, as\nnoted in L142-148.\nResponse:\nThank you for your comments and suggestions. In response, to better demonstrate the general\napplicability of the 3Snet-CLID method, we have applied it to image intracellular structures\nacross various imaging systems. We have also replaced some of the original images with\nhigher-quality examples for clearer demonstration. In the revised manuscript, we have\nincluded a Supplementary Table 2 listing the diverse cell types, fluorophores, and microscope\nsystems used — extending beyond those in the training dataset — and have further discussed\nthe robustness of 3Snet-CLID in the Discussion section (Line 391-404).\nMinor Issues\n1. Quantitative characterization of SNR improvement would be beneficial:\nReference (L79-81): \"...which leverages reversibly switchable fluorescent proteins (RSFPs) to\ndrastically improve the signal-to-noise ratio (SNR) of the image\"\nThe manuscript would be enhanced by including specific numerical values to quantify the\nimprovement in SNR, rather than using qualitative expressions like \"drastically improve.\"\nResponse:\nThank you for your suggestion. We have quantified the improvement in SNR with specific\nnumerical values. The SNR was increased from 8.2 to 47.5, representing a 5.8-fold\nimprovement. (Line 97-98)\n2. Figure clarity could be enhanced:\nReference (Fig. 1b): Additional labeling to clearly indicate which methods underwent\nupsampling prior to deconvolution would improve the interpretability of the figure.\nResponse:\nWe apologize for the lack of clarity in the figure legend. As requested, we have updated the\nlegend to explicitly state that, the resulting images from various approaches were processed\nusing Lanczos upsampling by a factor of 3, followed by RL deconvolution with a theoretically\nderived Bessel PSF, using 1000 iterations. (Line 801-802).\n3. Quantitative assessment of live-cell imaging would add value:\nReference (Fig. 4): Supplementing the impressive visual comparisons in live-cell imaging\ndemonstrations with quantitative metrics of resolution improvement would provide readers\nwith a more objective basis for evaluation.\nResponse:\nThank you for this valuable suggestion. In response, we have incorporated a quantitative\nmetric to complement the visual comparisons in our live-cell imaging demonstrations.\nSpecifically, we implemented an image resolution estimation method based on decorrelation\nanalysis (A. Descloux，et al., Nature Methods, 2019) to provide an objective assessment of\nresolution improvement. This addition offers readers a more rigorous and quantitative basis\nfor evaluating the performance of our method.\nThe updated results, now included in Fig. 4c, d and Fig. 5h, demonstrate not only a noticeable\nvisual enhancement but also a measurable improvement in resolution, as quantified by this\napproach. (Line 316-317, 348-350)\nFig. 4 | Single-frame live-cell SR imaging with 3Snet-CLID acquired on a WF microscope. a, Utilizing 3Snet-CLID to analyze the\nintricate actin structures within the immune synapse of Jurkat T cells. Top: WF microscopy, sparse-deconvolution and 3Snet-CLID\nimaging of F-actin labeled with F-tractin-StayGold in live Jurkat T cells. Bottom: Kymographs of F-tractin-StayGold in the region\ncorresponding to the red line. b, The actin arcs anisotropy of the peripheral supramolecular activation cluster (pSMAC) in (a)\nmeasured by FibrilTool. Compared to WF microscopy and sparse-deconvolution, 3Snet-CLID resolves more clear actin arc structure\nof the pSMAC, and provides more accurate quantified anisotropy data reflecting the effects of actin arc in the pSMAC organization.\nc. Decorrelation analysis applied to the WF image for resolution estimation. d. Decorrelation analysis applied to the 3Snet-CLID\nimage for resolution estimation.\nFig. 5 | Single-frame SR imaging with 3Snet-CLID acquired on a SD microscope. e, Dual color imaging of\nTOM20-StayGold-labeled mitochrondria (green) and mScarlet3-S2-labeled ER (magenta) in live U-2 OS cells. Scale bars\n= 5 μm. f and g, Time-lapse of zoomed-in regions 1–4 from (e), showing the corresponding SD (f) and 3Snet-CLID\nreconstruction (g) images. Scale bars = 500 nm. h, Decorrelation analysis applied to the SD and 3Snet-CLID images for\nresolution estimation. Data are presented as mean ± S.E.M. For the box-and-whisker plots, the center line represents the\nmedian, the box spans the interquartile range (IQR; 25th to 75th percentiles), and whiskers extend to 1.5× IQR. Outliers\nare plotted as individual points. n = 9 from three biological replicates.\n4. The connection between learning strategy and Extended Data could be clarified:\nReference (L152-161): \"Inspired by the efficacy of supervised-to-self-supervised transfer\nlearning...\"\nWhile Extended Data Fig. 2 provides information about dataset generation with varying noise\nlevels for training, the connection between this figure and the self-supervised learning strategy\ndescribed in the main text could be more explicitly linked. Clarifying how the approach\nshown in Extended Data Fig. 2 relates to the \"supervised-to-self-supervised transfer learning\"\nconcept mentioned in L152-161 would help readers better understand this innovative\nmethodology aspect.\nResponse:\nThank you for this insightful suggestion. We apologize for the lack of clarity in our original\ndescription. To clarify, our approach was inspired by the cited article’s key finding — that\nincorporating ground truth into a self-supervised framework enhances denoising performance,\nrather than the use of transfer learning per se.\nWhile the cited method employs two separate networks, our model, 3Snet, uses only a single\nnetwork and does not involve any form of transfer learning. Specifically, 3Snet integrates\nsupervised and self-supervised learning within one architecture: the supervised component\nuses ground truth images (3S-denoised clear images) as targets, while the self-supervised\ncounterpart is trained on the same set of raw images degraded with varying signal-to-noise\nratios.\nIn response to your comment, we have revised Extended Data Fig. 2 to more clearly illustrate\nthe integrated supervised and self-supervised learning pathways of 3Snet.\nExtended Data Fig. 2 | Dataset generation for 3Snet-CLID. To generate dataset for self-supervision, we first extract ON state\nimages from the raw ON/OFF image sequences captured using SkylanS photoswitching. To generate training sets with diverse\nnoise levels, 50 frames of images from the ON state are organized into five datasets using the combination formula C_n^k, where n\nequals 50 and k is 1, 2, 4, 8 or 16. Next, 50 elements are randomly selected from each dataset and the average of the k images in\neach chosen element is calculated. Finally, two images in each batch are randomly selected as the input and target data to the U-net\nmodel. For supervision, the clear image obtained by 3S-denoising was used as the ground truth.\n5. Remarks on code availability:\nThe necessary information, including the Readme file and installation instructions, is well\norganized.\nHowever, only the 100 nm bead images are attached, and the folder does not include any other\nimages.\nIt would be advisable to upload all images reported in the paper for reproducibility and to\nenable comparison with other methods.\nResponse:\nThank you for your valuable suggestions. As recommended, we have now uploaded all images\nreferenced in the manuscript: “All essential raw datasets, including files for supplementary\nfigures and raw unprocessed images, are available at figshare via\nhttps://doi.org/10.1038/s41592-024-02294-7. Source data are provided with this paper.”\nReviewer #2 (Remarks to the Author):\nIn this work by Xue et al., the authors present a new framework, called CLID (Clear Image\nDeconvolution), for enhancing the resolution of widefield and spinning-disk microscopy images,\nthrough a combination of denoising via photoactivation sequences (3S), background removal\nusing activation/deactivation image series, and deconvolution. They further introduce a\nself-supervised deep learning component, 3Snet, to predict denoised images from single sequences,\nclaiming that this approach achieves 65nm resolution using standard fluorophores and\nconventional setups.\nResponse：\nThank you for your summary of our manuscript. We would like to clarify that 3Snet integrates\nsupervised and self-supervised learning within a U-net architecture.\n1. While the proposed workflow is appealing in its conceptual simplicity and implementation\npotential, I have significant concerns regarding several of the assumptions, methodological\nchoices, and evaluation strategies used in this study. A core assumption of the method is that\naveraging a sequence of photoactivated images yields a noise-free ground truth, suitable for\ntraining and deconvolution. However, for dynamic or live samples, such an approach is\nvulnerable to motion artifacts, particularly motion blur, which could undermine the validity of\nthe averaged image as a clean reference, and pose problem in the deconvolution process. The\nauthors should clarify how they mitigate or compensate for such motion during acquisition, or\nwhether their framework is restricted to fixed or minimally dynamic samples.\nResponse:\nWe apologize for the insufficient clarity regarding the application scenarios of 3S-CLID and\n3Snet-CLID in our original manuscript. 3S-CLID is a multi-frame imaging technique\ndesigned exclusively for fixed cells labeled with reversibly switchable fluorescent proteins\n(RSFPs). In contrast, 3Snet-CLID is a deep learning-based, single-frame method applicable\nto both fixed and living cells labeled with any FP.\nThe noise-free ground truth images are generated using 3S denoising on fixed RSFP-labeled\nsamples. These images are then used either for direct deconvolution with 3S-CLID or for\ntraining the denoising neural network underlying 3Snet-CLID. For dynamic or live-cell\nimaging, it is not necessary to produce new ground truth data using 3S denoising. Instead, the\npre-trained 3Snet network — established on fixed cells — is applied to denoise single-frame\nimages, which are subsequently enhanced through deconvolution to improve resolution. Since\nthis approach does not require multi-frame acquisition or processing of live samples, it\neffectively avoids motion artifacts and motion blur, making it particularly suitable for live-cell\napplications.\nWe clearly described the application scenarios of 3S-CLID and 3Snet-CLID in the revised\nmanuscript: “Here, we present two novel SR techniques based on RL deconvolution. The first,\n3S-CLID, is a multi-frame method designed for fixed cells labeled with RSFPs. The second,\n3Snet-CLID, is a cutting-edge, deep learning-based, single-frame technique that achieves\nrobust, high-fidelity DLSR imaging in both WF and SD systems. It is compatible with both\nfixed and living cells labeled with any FP or dye. Both methods achieve a spatial resolution of\n65 nm, more than doubling the performance of conventional restoration techniques and\nrepresenting a 5.4 folds improvement over the diffraction limit. This marks the highest\nreported resolution for a method not requiring a dedicated SR module. 3Snet-CLID, in\nparticular, demonstrates exceptional spatiotemporal resolution and robustness across diverse\ncellular structures.” (Line 365-373)\n2. In contrast to prior studies, such as Wang et al. 2021, which employ transfer learning to\naddress temporal variability in image sequences, the authors here suggest that a single\nsnapshot suffices to train their denoising model. This assumption should be closely evaluated,\nespecially when considering biological variability across time and space. It remains unclear\nhow a model trained on a single sequence can generalize robustly without overfitting or\nmisrepresenting dynamic features.\nResponse:\nSimilar to the approach described by Wang et al. (2021), our denoising model was trained\nusing multiple image frames rather than individual snapshots. Specifically, we acquired 20\nsets of fixed-cell samples, with each sample imaged across 50 “ON” and 50 “OFF” frames.\nFor each sample, the following procedure was applied:\n1) The ground truth image was computed as AVG(ON) – AVG(OFF);\n2) From the 50 “ON” frames, five distinct image groups with varying signal-to-noise ratios\n(SNRs) were generated by averaging different number of raw frames, and each group contains\n50 images);\n3) For each SNR group, two frames were randomly selected to form input-target pairs for\nself-supervised U-net denoising training;\n4) The ground truth image served as the target for supervised network training.\nThe description has been included in Methods (Line 450-465). Please see also the Workflow\nof 3Snet-CLID (Line 440-470) and Extend Data Fig. 2 for detailed information:\nExtended Data Fig. 2 | Dataset generation for 3Snet-CLID. To generate dataset for self-supervision, we first extract ON state\nimages from the raw ON/OFF image sequences captured using SkylanS photoswitching. To generate training sets with diverse\nnoise levels, 50 frames of images from the ON state are organized into five datasets using the combination formula 𝐶𝑘, where n\n𝑛\nequals 50 and k is 1, 2, 4, 8 or 16. Next, 50 elements are randomly selected from each dataset and the average of the k images in\neach chosen element is calculated. Finally, two images in each batch are randomly selected as the input and target data to the U-net\nmodel. For supervision, the clear image obtained by 3S-denoising was used as the ground truth.\n3. The choice of fluorophores also raises practical concerns. The method appears to rely on\nreversible photoswitchable labels, such as Skylan-S, to distinguish signal from background\nthrough the 3S strategy. However, the manuscript does not clarify whether this is a strict\nrequirement. It remains unclear whether the method can operate effectively with conventional\nfluorophores like GFP, or whether dedicated photoswitchable probes are indispensable. If a\nphotoswitchable fluorophore is indeed required during a preliminary labeling step, the authors\nshould clarify what assumptions are made about their spatial correspondence and background\ncharacteristics. Without such clarification, it is difficult to assess the general applicability of\nthe method. These constraints should be explicitly addressed, illustrated with examples if\npossible, and discussed in terms of feasibility for broad adoption by the biological imaging\ncommunity.\nResponse:\nThank you for your comments. RSFP is needed for both 3S-CLID and 3Snet-CLID. For\n3S-CLID, the noise-free image produced by 3S denoising is acquired on fixed cells labeled\nwith reversibly switchable fluorescent proteins (RSFPs), and is used for direct deconvolution\n(3S-CLID) to improve resolution.\nFor 3Snet-CLID, noise-free ground truth is produced with RSFP-labeled fixed sample for\ntraining 3Snet denoising neural network underlying 3Snet-CLID. Then, the pre-trained 3Snet\nnetwork is applied to denoise single-frame images of samples labeled with conventional\nFP/dyes. Specifically, 3Snet-CLID method operates through a sequence of three principal\nsteps: (1) 3S denoising for ground truth generation: we use RSFP under modulated\nillumination to acquire noise-free ground truth images. (2) neural network training: these\ndenoised images serve as the ground truth for training a u-net-based denoising network. (3)\njoint denoising and deconvolution: the trained network is applied to denoise single-frame\nimages from samples labeled with a wide range of fluorescent proteins (conventional,\nphotoactivatable, or photoconvertible), which are then further enhanced by RL deconvolution\nto improve resolution.\nUsing RSFPs in CLID is straightforward. They share key advantages with conventional FPs:\neasy fusion to proteins of interest and proven compatibility with SR techniques like\nPALM/STORM, SOFI, SRRF, NL-SIM, and RESOLFT. Their switching is also easily\ncontrolled on standard microscopes by altering excitation wavelengths, similar to\nconventional multicolor imaging protocols.\nAcquiring the training dataset is efficient, requiring the imaging of only 20 fixed samples (we\nused actin) labeled with RSFPs on a widefield or spinning-disk confocal microscope, with a\ntotal acquisition time typically under 30 minutes. Notably, each imaging system requires only\na single training session. Once complete, the network can be widely applied to denoise\nimages of samples labeled with conventional FPs under standard operating conditions. The\n3SnetCLID framework enables rapid processing, typically taking about 2 seconds to denoise a\n512 × 512 field of view. Thus, our approach is not only straightforward and time-efficient but\nalso offers broad applicability across diverse biological imaging contexts.\nFor clarity, we have included the processing steps for 3Snet-CLID in the revised manuscript.\n(Line 440-470)\n4. Similarly, the source and treatment of background signals are not sufficiently explained. The\nbackground images acquired during the deactivation phase could include various\ncontributions, such as dark current, autofluorescence, or incomplete photoswitching. A clear\nexplanation of these components is necessary to understand the benefit of this approach over\nstandard background subtraction, particularly under sparse labeling conditions where simple\nmethods often perform well. It is also unclear why the 3S background removal method would\noutperform conventional strategies unless these sources of signal are well characterized.\nResponse:\nWe thank you for this insightful comment. In the revised manuscript, we have now detailed the\ntheoretical foundation of the 3S denoising and its specific advantages over conventional\nstrategies. While we acknowledge the excellent denoising results achieved by existing methods,\nour primary goal is resolution enhancement through deconvolution after denoising. We\ndeveloped the 3S method precisely because we found that images denoised with conventional\ntechniques were often not optimal for direct deconvolution, a crucial distinction we have now\nemphasized in the revised manuscript as following (Line 119-145):\n“We posit that CLID's effectiveness requires both effective denoising and the precise\npreservation of the original pixel-wise signal distribution. However, conventional denoising\nmethods often fail to achieve this simultaneously because they typically rely on explicit noise\nmodels for specific sources (e.g., dark current, readout noise), which are ineffective against\nthe complex, concurrent noise types found in real-world imaging (e.g., shot noise, out-of-focus\nfluorescence). Furthermore, these methods use information from surrounding pixels (e.g.,\nHessian or sparse methods22, 36, Gaussian filter37, Wiener filter38) or frequency-domain\noperations (e.g., Wavelet transforms39, Low-pass filter40), which alters the original signal\ndistribution and hinders subsequent deconvolution.\nTo overcome these limitations, we propose a per-pixel denoising strategy designed to\ndifferentiate signal from noise at the level of individual pixels. This method operates without\nexplicit models of noise or background sources. Instead, we classify noise for each pixel based\non its temporal characteristics into two distinct modes: a random component that fluctuates\nfrom frame to frame, and a fixed-pattern component that remains constant across frames. The\ndenoising process is achieved by treating each pixel individually and applying two specific\noperations: multi-frame averaging to suppress the random noise component, and a\nsubtraction operation between carefully defined image sets to eliminate the fixed-pattern\nnoise.\nWe implement this theory by leveraging RSFPs. The controlled on/off switching of RSFPs,\ntriggered by specific light wavelengths, provides a precise pixel-level correspondence between\nfluorescent (signal-present) and non-fluorescent (signal-absent) states. Both the acquired 'ON'\nand 'OFF' image sets contain the mixed noise (random and fixed). Our technique, termed\nsingle-pixel-synchronized switching (3S) denoising, proceeds in two steps: first, multi-frame\naveraging of the 'ON' and 'OFF' images independently suppresses the random noise in each\nstate; second, the operation AVG(ON)-AVG(OFF) is performed to subtract the averaged fixed\nbackground, thereby simultaneously isolating the true signal and removing both noise\ncomponents. This approach preserves the original pixel-wise signal distribution essential for\noptimal deconvolution.”\n5. The manuscript evaluates its denoising approach mainly in comparison to basic strategies like\nmedian or mean filtering. However, recent developments in self-supervised denoising, such as\nNoise2Void and Noise2Self, have demonstrated strong performance across a range of\nmicroscopy contexts. These approaches should be included in the evaluation to contextualize\nthe contribution of 3Snet more rigorously. The authors are encouraged to apply these\nestablished methods while keeping the rest of their pipeline consistent, to isolate the impact of\nthe denoising component.\nResponse:\nThank you for your suggestion. In the revised manuscript, in addition to comparisons with\nconventional filtering methods (e.g., median and mean filtering) and supervised deep learning\napproaches (previously shown using ArgoSIM data in Fig. 2), we included new quantitative\nand qualitative comparisons against self-supervised methods — such as Noise2Void and\nNoise2Self — applied to our live-cell imaging data (Fig. 2d，Extended Data Fig. 3). To ensure\na fair comparison, all methods were evaluated using identical datasets and consistent\npost-processing pipelines, thereby isolating the performance contribution of the denoising\ncomponent itself. The results show that 3S method achieves a more effective denoising effect\nthan self-supervised deep learning networks, yielding the highest spatial resolution and the\nfewest artifacts when used for RL deconvolution.\nWe believe these additions will provide a more comprehensive and contextualized assessment\nof 3SNet’s capabilities relative to contemporary denoising strategies.\nFig. 2 | Workflow and validation of 3Snet-CLID using standard structures. d, 3Snet-CLID\nhas achieved a spatial resolution of 60 nm on the commercial Argo-SIM under WF\nmicroscopy. The intensity profiles of the corresponding double-line pairs (30 nm, 60 nm,\n90 nm, 120 nm, 150 nm, 180 nm and 210 nm distances) are displayed.\nExtended Data Fig. 3 Comparison of 3Snet-CLID with other deep learning denoising methods. The ER structure of U-2 OS cells\nwas labeled with mScarlet3-S2. Single-frame images were denoised using various approaches were processed using Lanczos\nupsampling by a factor of 3, followed by RL deconvolution with a theoretically derived Bessel PSF, using 500 iterations. Scale bar:\n5 μm.\n6. Another important concern relates to the use of 3Snet for denoising images acquired with\nconventional fluorophores, when the network has been trained on data obtained using\nreversible photoswitchable fluorophores. This raises questions about the generalization\ncapacity of the model: to what extent can a network trained under specific photophysical\nconditions reliably predict denoised outputs for fluorophores with different emission\ncharacteristics, background profiles, and labeling distributions? The manuscript should\nexplicitly address this important point, and whether retraining or fine-tuning of the\nnetwork is required for each new fluorophore.\nResponse:\nThank you for your thoughtful comments. We would like to kindly clarify that, once trained for\na specific imaging system, our network generalizes across different fluorophores without\nrequiring retraining or fine-tuning. While the initial training is system-specific — necessary to\ncalibrate the network to the particular optical setup — the resulting model achieves robust\nsuper-resolution imaging that is agnostic to the fluorescent protein employed.\nThis generalization is possible because 3Snet learns a denoising process that is independent\nof fluorophore type. During training, the RSFP is used solely to generate noise-free ground\ntruth images. The network is trained using fluorescent images — specifically, low\nsignal-to-noise ratio inputs and their corresponding ground truths — enabling it to learn a\npixel-level correspondence that is not specific to any particular chromophore.\nIn this regard, 3Snet behaves similarly to established methods such as DnCNN and\nNoise2Void, generalizing effectively from one fluorescent protein to others unseen during\ntraining. A distinct advantage of our approach, however, is that the denoised images produced\nby 3Snet are particularly well-suited for subsequent deconvolution to enhance spatial\nresolution. This is because the training process preserves pixel-level signal distribution, a\ncrucial requirement for high-quality deconvolution. Further details can be found in the\nConcept of 3Snet-CLID section (Line 198-224).\nOur experimental results demonstrate that the denoising performance of our RSFP-trained\nnetwork generalizes effectively across fluorescent probes with vastly different emission\nspectra, background profiles, and subcellular labeling distributions. This is evidenced in Fig.\n3d, which presents a super-resolution image of a sample labeled with a 647 nm dye, denoised\nusing a model trained exclusively on Skylan-S. Moreover, we demonstrated that 3Snet-CLID\ntrained on Slylan S can also resolve structures labeled with conventional red FPs (Extended\nData Fig. 4). Critically, despite significant variations in the background fluorescence (Fig. 5e,\nThe background fluorescence levels of the ER are different in regions close to the nucleus\ncompared to regions far from the nucleus) and the distinct morphological distributions of the\nendoplasmic reticulum and mitochondria (labeled in different colors) within the field of view,\napplication of our singular trained network yields high-quality super-resolution images\nacross all structures.\nExtended Data Fig. 4 3Snet-CLID trained on Slylan S can resolve structures labeled with conventional red FPs. a, Representative\nsingle frame image showing the ER in a live U-2 OS cell, labeled with the red fluorescent protein mScarlet3-S2. b, SR image of\nmScarlet3-S2 labeled ER obtained using Skylan S-trained 3Snet model. c, SR image of mScarlet3-S2 labeled ER obtained using\nrsRFP-trained 3S model. d, Merge image of b and c to indicate that the network trained on green RSFP successfully reconstructed\nstructures labeled with traditional red FP, which is consistent with the results from the network trained on red RSFP. Scale bar:\n2 μm.\nFig. 5 | Single-frame SR imaging with 3Snet-CLID acquired on a SD microscope. e, Dual color imaging of\nTOM20-StayGold-labeled mitochrondria (green) and mScarlet3-S2-labeled ER (magenta) in live U-2 OS cells. Scale bars = 5 μm.\nf and g, Time-lapse of zoomed-in regions 1–4 from (e), showing the corresponding SD (f) and 3Snet-CLID reconstruction (g)\nimages. Scale bars = 500 nm. h, Decorrelation analysis applied to the SD and 3Snet-CLID images for resolution estimation. Data\nare presented as mean ± S.E.M. For the box-and-whisker plots, the center line represents the median, the box spans the interquartile\nrange (IQR; 25th to 75th percentiles), and whiskers extend to 1.5× IQR. Outliers are plotted as individual points. n = 9 from three\nbiological replicates.\n7. Furthermore, the distinction between averaging images and subtracting dark current images\nremains ambiguous. The manuscript should explain why 3S denoising outperforms a\ncombination of simple averaging and dark frame subtraction. If the contribution of dark\ncurrent is dominant in the background signal, then the added value of 3S denoising must be\nexplicitly quantified and justified beyond conventional background approaches much straight\nforward to implement. For instance, in the simulations presented in Figure 1, a substantial\nportion of the background could likely be removed through standard dark current correction\nalone or background subtraction functions. If other sources of background, such as\nautofluorescence, incomplete fluorophore switching, or camera readout noise, are present,\nthese should be clearly identified, quantified, and their impact on performance thoroughly\ndiscussed.\nResponse:\nThank you for your comments. The real-world images contain a complex mixture of noise\nsources. A strategy that requires explicit identification and sequential removal of each noise\ntype is inherently inefficient and fails to address unknown or uncharacterized noise\ncomponents. As stated in Response 4, the core innovation of our denoising method is its\nability to extract and preserve the true signal distribution across pixels for robust\ndeconvolution, without requiring a priori knowledge of specific noise types. Instead, we\nleverage the photophysical properties of RSFPs and the 3S acquisition protocol to remove\nnoise based on its spatiotemporal characteristics (both fixed-pattern and random) at the\nsingle-pixel level. Crucially, RSFP optical modulation ensures that illumination conditions\nare identical for the ON and OFF states at each pixel. The AVG(ON) - AVG(OFF) operation\nis therefore a single-pixel-dependent, in-cell subtraction that effectively removes the actual\nnoise present during imaging. Since dark current noise exhibits both fixed and random\npatterns, our pixel-specific denoising framework simultaneously mitigates it alongside other\nnoise sources.\nWhile dark current correction can improve image quality, its effectiveness is limited. The\nacquisition conditions for dark frames differ from those of light frames, meaning a standard\ndark frame does not fully represent the camera's noise profile under illumination.\nConsequently, the operation AVG(ON) - offset is suboptimal. As the results showed below, this\napproach yields a lower signal-to-noise ratio compared to the ground truth (GT) acquired\nwith our 3S method and is prone to introducing artifacts during deconvolution.\nA more fundamental issue with traditional background subtraction is its assumption of\nuniform noise. In reality, noise levels are pixel-dependent. Subtracting a global background\nvalue from signal-free pixels alters the intrinsic statistical distribution of the signal across the\nsensor, which adversely affects subsequent RL deconvolution (see the results showed below,\nAVG(ON)-AVG(bg)).\nComparison of the 3S denoising effect with dark current reduction or background reduction methods. a, Representative images\nprocessed with different denoising methods, showing the results before and after RL deconvolution. b, Normalized intensity\nprofiles for the different denoising methods. c, Normalized intensity profiles for the different denoising methods after RL\ndeconvolution. d-f, Decorrelation analysis used for resolution estimation.\n8. The manuscript lacks details on the acquisition process itself. The authors should report how\nmany images are acquired per ON/OFF cycle, the acquisition time, and the temporal cost\nassociated with the approach. These factors are particularly important for live-cell imaging,\nwhere exposure time, motion, and phototoxicity are limiting factors. Without this information,\nit is difficult to assess whether the method is broadly applicable in biological settings.\nResponse:\nWe appreciate your suggestion. Regarding the acquisition of training data, our protocol\nacquired 20 full training datasets in under 30 minutes. Each dataset consisted of 50 ON/OFF\ncycles with a 50 ms exposure per frame. It is important to note that during actual sample\nimaging, the duration is determined entirely by experimental requirements.\nA comprehensive description of the 3Snet workflow, along with detailed imaging experimental\nparameters — such as the number of images per ON-OFF cycle, acquisition times, and the\noverall temporal cost of the approach — has been provided in the Methods section (Line\n424-426, 440-470).\n9. A major technical concern is the use of a theoretical 2D Airy PSF for deconvolution, without\nany experimental validation and inclusion of 3D blur. Given that spinning-disk and wide-field\ndeconvolution microscopy are often employed for optical sectioning and 3D imaging, the\nexclusive use of a 2D PSF model appears limiting. Deconvolution in microscopy typically\nrequires a 3D PSF model to handle out-of-focus contributions, especially for thicker\nspecimens, more especially because the main contribution of blur comes from the axial\ndirection. If the method is only valid for flat or 2D structures, this should be explicitly stated.\nOtherwise, the authors should validate their technique using 3D experimental and simulated\ndatasets to demonstrate broader applicability.\n3D blur contributions arising from extended objects imaged with widefield or spinning-disk\nmicroscopy should be incorporated into the simulations to more accurately reflect typical\nimaging conditions. This would help reveal both the strengths and the limitations of the CLID\napproach when dealing with volumetric samples, where out-of-focus light can significantly\ndegrade image quality and challenge the effectiveness of single frame image deconvolution.\nResponse:\nThank you for your comment. We have revised the manuscript to clarify that the theoretical\n2D point-spread function (PSF) used for deconvolution was parameterized based on\nempirical measurements from fluorescent beads (Line 437-438).\nWe agree entirely that background noise and out-of-focus light are central challenges in\ndeconvolution microscopy that significantly impact performance. As the primary focus of our\nwork is to mitigate noise in RL deconvolution, we introduced a practical denoising step to\nenhance its resolution and reliability. We recognize that in the field of deconvolution\nmicroscopy, out-of-focus blur presents a distinct challenge, which we plan to address in a\ndedicated future study. Nevertheless, we have now included a new analysis using 3D\nexperimental and simulated data to assess how out-of-focus signals affect 3Snet-CLID and to\nquantify its practical imaging depth.\nOur findings, which are now presented in the Discussion section (Line 410-414), confirm that\n3Snet-CLID demonstrates robust performance in practical single-cell imaging. Specifically,\nsimulations show that 3Snet-CLID produces reliable super-resolution images without\nnoticeable artifacts in samples up to 10 microns thick. Experimentally, 3Snet-CLID is\nparticularly well-suited for TIRFM and can also excel when paired with optical sectioning\ntechniques such as spinning-disk (SD) confocal microscopy. This is evidenced by imaging in C.\nelegans, where CLID achieves excellent performance at depths of up to 10 µm\n(Supplementary Fig. 1).\nSupplementary Figure 1: Impact of out-of-focus blur on 3Snet-CLID performance. a, Simulation data analysis. b,\nPerformance of 3Snet-CLID at different imaging depths in SD microscopy of C. elegans (Phyp-7::TOMM-20::GFP). Scale\nbar: 10 μm (left), and Scale bar: 2 μm (middle and right).\nIn the Discussion section, we stated: “Although CLID is a 2D SR technique and, like other\nmethods using 2D PSFs, affected by out-of-focus blur, it reliably retains SR resolving\ncapability in samples about 10 μm thick for both WF and SD microscopies (Supplementary\nFig. 1, Supplementary Video 4). It is particularly suited for TIRFM and SD confocal\nmicroscopy for imaging subcellular structures in adherent cells. While this study focuses on\n2D SR, the underlying approach holds significant potential for 3D imaging via axial scanning.\nBy extending the denoising and deconvolution framework of 3Snet-CLID into three\ndimensions, it could be integrated into 3D deconvolution pipelines to improve resolution and\nsuppress out-of-focus blur. Developing such 3D modules—incorporating volumetric denoising\nand deconvolution—to enhance axial resolution and enable robust volumetric imaging will be\na primary objective of our future work.”\n10. The simulations and reconstructions shown in the manuscript lack essential parameter\ninformation. The nature of the PSF, noise levels, and deconvolution settings such as iteration\nnumber and regularization terms are not disclosed. This omission hinders reproducibility and\nmakes it difficult to assess whether the results are generalizable or finely tuned to specific\nconditions.\nResponse:\nWe sincerely apologize for the oversight in not providing the essential parameter details in\nour original manuscript. In response to this comment, we have now included comprehensive\ninformation regarding the PSF model, noise levels, and all relevant deconvolution parameters\n— such as iteration numbers — in Figure 1 legends. We do not need regularization terms for\nRL deconvolution when using CLID. This addition will ensure full reproducibility of our\nsimulations and reconstructions and allow readers to better evaluate the robustness and\ngeneralizability of our results.\n11. There are also noticeable artifacts in the deconvolved images, which resemble mismatches\nbetween the PSF model and the experimental imaging conditions. These textures are typical\nwhen the PSF does not match the sample or when sampling is suboptimal. The authors should\nexplore whether PSF model, oversampling parameters or improved background subtraction\nprior to deconvolution could mitigate these effects.\nResponse:\nThank you for your comments. We fully agree that the choice of PSF model, oversampling\nstrategy, and background handling significantly influence the quality of deconvolved images.\nTo address these factors systematically, we conducted a series of comparative analyses. First,\nwe evaluated the performance of Gaussian versus Bessel PSF models within the RL\ndeconvolution framework and observed superior reconstruction quality using the Bessel PSF\n(shown as below).\nComparation of Gauss PSF with Bessel PSF for CLID processing\nWe also examined multiple upsampling techniques and determined that the Lanczos method\nprovided the optimal balance between resolution enhancement and artifact suppression\n(Extended Data Fig. 1). Regarding background subtraction, we optimized several acquisition\nparameters—including exposure time and the number of ON/OFF image frames used for\naveraging—to minimize noise. A comparative assessment revealed that the AVG(ON) –\nAVG(OFF) method outperformed simple dark current subtraction or surrounding background\nsubstruction for RL deconvolution in preserving signal integrity (shown as below). Finally, we\ncarefully optimized the number of RL deconvolution iterations to maximize resolution while\nminimizing the introduction of artifacts. These comprehensive optimizations collectively\nenhance the robustness and reproducibility of our image processing pipeline.\nAlthough parameter optimization reduces artifacts, residual imperfections persist—a\ncharacteristic shared with other RL-based deconvolution techniques. These artifacts likely\noriginate from slight inaccuracies in the PSF model or oversampling parameters, incomplete\nnoise suppression, and interference from defocus signals. To ensure an equitable comparison\nwith state-of-the-art methods (PURE, DnCNN, and Sparse), all approaches were evaluated on\nthe same sample under identical imaging conditions. Our 3Snet method exhibits superior\nresolution and fewer artifacts compared to these alternatives (Fig. 2d，Extended Data Fig. 3),\nwith comprehensive comparisons detailed in the supplementary material.\nExtended Data Fig. 1 | Assessment of upsampling approaches for 3S-CLID. a, 3S-denoised synthetic structures were upsampled\nby linear, Fourier, Bicubic or Lanczos interporation approache for RL deconvolution. 5% Poisson noise and 5% Gaussian noise\nwere added to the acquired a blank region of a fixed cell under WF illumination, and 3S-denoised images were processed using\ndifferent upsampling approaches by a factor of 2, followed by RL deconvolution with a theoretically derived Bessel PSF, using\n100 0 iterations. The pSNR and SSIM of 3S-CLID images were measured to compare the performance of the four upsampling\napp roaches. Scale bar: 1 μm. b, 3S-denoised images were processed using Lanczos upsampling approach by different factors,\nfollowed by RL deconvolution with a theoretically derived Bessel PSF, using 1000 iterations.\nFig. 2 | Workflow and validation of 3Snet-CLID using standard structures. d, 3Snet-CLID has achieved a spatial resolution of 60\nnm on the commercial Argo-SIM under WF microscopy. The intensity profiles of the corresponding double-line pairs (30 nm, 60\nnm, 90 nm, 120 nm, 150 nm, 180 nm and 210 nm distances) are displayed.\nExtended Data Fig. 3 Comparison of 3Snet-CLID with other deep learning denoising methods. The ER structure of U-2 OS cells\nwas labeled with mScarlet3-S2. Single-frame images were denoised using various approaches were processed using Lanczos\nupsampling by a factor of 3, followed by RL deconvolution with a theoretically derived Bessel PSF, using 500 iterations. Scale bar:\n5 μm.\n12. Finally, the resolution claims of 65 nm are based from simulations involving idealized flat 1D\nfilament structures or experimental isolated beads, with no tridimensional structure, which are\ninherently favorable to single frame deconvolution algorithms and are less prone to artifacts.\nWhile such examples can serve as useful proof-of-concept demonstrations, they do not\nprovide sufficient evidence to support claims of generalizable high-resolution performance on\n3D objects. More complex and heterogeneous structures should be employed. Synthetic test\nobjects that span a wide range of spatial frequencies, such as the sector test pattern\n(DOI:10.1364/OE.543403), would be particularly informative, as they allow for the\nsimultaneous assessment of resolution recovery in fine-detail regions and artifact generation\nin coarser areas.\nResponse:\nWe appreciate your comment. We would like to clarify that ArgoSIM structure is\nthree-dimensional, with dimensions of φ0.52 × 36 μm, featuring nanometer-scale line spacing\nthat enables nanoscale resolution characterization. In contrast, the referenced “sector test\npattern” consists of micrometer-scale features, making it unsuitable for nanometer-resolution\nassessment.\nIn line with established practices, as exemplified in a recent Nature Methods publication\n(2025), we further validated our resolution using biological structures—specifically, nuclear\npore complex and actin filaments—together with the ArgoSIM standard. We generated\nhomozygous Nup96-sfGFP knock-in U-2 OS cell line and evaluated 3Snet-CLID’s\nperformance. Results demonstrated that 3Snet-CLID clearly resolved the distinct annular\nmorphology of the NPC (Fig. 5a, 5b). The dimensions of the resolved structures (Fig. 5c, d)\nclosely matched those established by EM (PMID: 31562488).\nSingle-frame SR imaging with 3Snet-CLID acquired on a SD microscope. a, Representative confocal image of the\ngenome-edited fixed U-2 OS cell line with endogenously labeled Nup96-sfGFP. Green, Nup96-sfGFP. Scale bars = 2 μm.\nb, Zoom in regions (1-4) from (a) with 3Snet-CLID reconstruction. Scale bars = 1 μm. c, Intensity profiles of the nuclear pore\nindicated by the arrow heads in region 1 of (b). d, Averaged diameters of rings formed by Nup96 (103 ± 14 nm; n = 64 from\nseven cells).\nBy applying the full width at half maximum (FWHM) criterion, a widely accepted metric in\nthe field (as supported by PMID: 18796604, PMID: 31501551, PMID: 34782739), we\nresolved individual actin filaments measuring ~ 60 nm in width at representative locations\n(shown as below). Moreover, using a parameter-free decorrelation analysis method (PMID:\n31451766), the spatial resolution was improved from 285 nm with SD to 58 nm with\n3Snet-CLID reconstruction (Fig. 1f, g).\nSpatial resolution quantified by FWHM\nFig. 1 | Workflow and validation of 3S-CLID on synthetic microtubule and cellular structure. f, 3S-denoised clear and 3S-CLID\nimages of Lifeact-SkylanS-labeled F-actin in fixed U-2 OS cells imaged by Spining-disk (SD) confocal. g. Decorrelation analysis\napplied to the SD image for resolution estimation. Scale bars: 5 μm.\n13. Notably, the reported resolution of 65 nm corresponds approximately to twice the pixel size\nafter 2× oversampling, raising the possibility that this value may reflect sampling limits or the\nconvergence of deconvolution-induced texture rather than effective resolution gain. The\nauthors should investigate whether the resolution estimate stems from true resolution\nimprovement or is merely a byproduct of digital resampling. Varying the degree of\nupsampling and analyzing its effect on the recovered resolution would help distinguish\nbetween these possibilities.\nResponse:\nThank you for your comments. As shown in Fig. 2 of the original manuscript, all methods\ncompared with 3S denoising—including PURE, DnCNN, DnCNN, and Sparse—utilized 2× upsampling,\nyet only 3S achieved a resolution of 65 nm. As you suggested, we performed additional\nexperiments using 3× and 4× upsampling; however, no further improvement in resolution was\nobserved (Extended Data Fig. 1). These results confirm that the enhanced resolution arises\nfrom genuine physical or algorithmic improvements in the imaging capability, rather than\nfrom digital resampling artifacts.\nAlthough the resolution was not further improved, upsampling with Lanczos interpolation\nrevealed that 3× upsampling achieved superior pSNR and SSIM relative to both 2× and 4×\nupsampling (Extended Data Fig. 1). Consequently, all CLID-related results presented in the\nrevised manuscript have been generated using 3× upsampling. This result has been\nincorporated into the revised manuscript (Line 167-174).\nExtended Data Fig. 1 | Assessment of upsampling approaches for 3S-CLID. a, 3S-denoised synthetic structures were upsampled\nby linear, Fourier, Bicubic or Lanczos interporation approache for RL deconvolution. 5% Poisson noise and 5% Gaussian noise\nwere added to the acquired a blank region of a fixed cell under WF illumination, and 3S-denoised images were processed using\ndifferent upsampling approaches by a factor of 2, followed by RL deconvolution with a theoretically derived Bessel PSF, using\n100 0 iterations. The pSNR and SSIM of 3S-CLID images were measured to compare the performance of the four upsampling\napp roaches. Scale bar: 1 μm. b, 3S-denoised images were processed using Lanczos upsampling approach by different factors,\nfollowed by RL deconvolution with a theoretically derived Bessel PSF, using 1000 iterations.\nReviewer #3 (Remarks to the Author):\nThis manuscript describes a method to improve resolution in microscopy images by using a\ncustom, deep-learning based denoising method before a Richardson-Lucy deconvolution. The\ndenoising method uses reversible switchable fluorescent probes to quickly take ‘on’ and ‘off’\nimages where the ‘off’ images are intended to model background and noise. A UNet is trained to\nproduce denoised images with the target being a ‘denoised’ image generated from the ‘off’ images\nsubtracted from the ‘on’ images.\nResponse:\nThank you for your thoughtful summary of our manuscript. While we generally agree with your\noverview, we would like to clarify that the \"OFF\" image serves not only to model background and\nnoise but also to establish a pixel-wise correspondence with the \"ON\" image. This pairing\npreserves the spatial distribution of the signal when the \"OFF\" image is subtracted from the \"ON\"\nimage—unlike conventional denoising methods (e.g., low-pass/Gaussian filtering, OLID, or\neccentricity-based approaches), which redistribute or alter the signal’s spatial distribution.\nPreserving this distribution is critical for subsequent deconvolution.\nConceptually, our method is single-pixel-dependent and differs from traditional denoising\ntechniques. By leveraging light modulation, we distinguish signal from noise and extract the\nsignal while maintaining its spatial integrity. Furthermore, our denoising process combines two\nkey operations: subtraction and multi-frame averaging. Specifically, we train a UNet to generate\ndenoised images, where the target output is derived by subtracting the averaged \"OFF\" image\nfrom the averaged \"ON\" image.\n1. Denoising before a RL deconvolution would indeed improve the results. There is a long\nhistory of the general concept and the manuscript would benefit from doing a better job of\nexplicitly handling this in the introduction.\nResponse:\nWe sincerely appreciate your valuable suggestions. In the Introduction section of the revised\nmanuscript, we have now included an introduction to denoising's role in improving image\nresolution and quality before RL deconvolution. (Line 63-76)\n2. My main issue with the paper is the theoretical underpinning of the treatment of the noise,\nwhich calls into question the ability of the method to be generalized. It also not compared well\nto other denoising approaches. The biggest contributions to the noise and background are\ntypically the sample itself through Poisson noise, and out of focus sample (even in optically\nsectioning methods to some degree). Therefore using the ‘off’ images to remove that doesn’t\nseem to make sense. Also, you can’t subtract noise – subtracting two noisy images makes\nthem more noisy. Averaging multiple images is the same as taking a longer exposure. It seems\nlike what is fundamentally happening is the DL network is learning to produce an image that\nresembles a longer exposure image (with better SNR) that a noisy image. This isn’t\nnecessarily a bad thing, but how this process is presented doesn’t make sense.\nResponse:\nNoise in imaging systems can arise from various sources, such as shot noise, out-of-focus\nsignals, autofluorescence, camera readout noise, and dark current noise. Traditional\ndenoising methods face two key limitations. First, they typically target a single noise type or\ncombine approaches based on individual noise characteristics. However, distinguishing\nspecific noise types during actual imaging is challenging, and some noises remain\nuncharacterized, making it difficult to suppress all noise components simultaneously. Second,\nthese methods primarily use information from surrounding pixels to perform mathematical\noperations on a target pixel. Because the signal and noise vary across different pixel locations,\nthis computation alters how the signal intensity is distributed, which can interfere with\nsubsequent resolution enhancement via RL deconvolution.\nEssentially, 3S-denoising is a per-pixel denoising method that, unlike traditional approaches,\nremoves most noise while preserving the spatial distribution of the original signal. A key\nadvantage is that it requires no prior knowledge of the noise or background. Instead, for each\npixel we classify noise into two modes based on temporal behavior: a random component that\nvaries from frame to frame, and a fixed-pattern component that is stable across frames for\nthat pixel. For instance, the dark-current noise has two parts: dark-current shot noise\n(random) and dark-current non-uniformity (a fixed spatial component). We reduce both\nrandom and fixed background/noise through optical modulation of photo-switchable\nfluorescent proteins. These proteins transition between ON/OFF states in response to specific\nwavelength modulation. Crucially, background/noise components remain unresponsive to this\nmodulation. Both \"ON\" and \"OFF\" images contain background/noise with fixed and random\npatterns. We simultaneously extract signal and suppress background/noise through a\ncomputational process combining subtraction and averaging operations. The signal is\nextracted by subtracting the “OFF” state image from the “ON” state image, effectively\nremoving or reducing both background and fixed-pattern noise. To further suppress random\nnoise including Poisson noise, we perform temporal averaging across multiple frames of these\non-minus-off difference images. The key advantage of this method lies in preserving the\noriginal signal distribution across pixels, enabling direct application in subsequent\ndeconvolution processing.\nWe fully agree that subtracting two noisy images increases the overall noise level. However,\nthis effect is effectively mitigated by frame averaging, as demonstrated in Fig. 1: averaging 50\nON-minus-OFF difference images yields a nearly 6× signal-to-noise ratio improvement,\noutperforming results obtained by averaging ON images alone (Fig. 1b, second vs. fifth\ncolumn). While simple image averaging ON images or OFF images reduces random noise, it\ncannot remove fixed-pattern noise and background signals originating from the sample and\nimaging system (camera and optical path). To demonstrate this, we included images of\nnon-fluorescent samples captured by the camera in simulation, which primarily contain these\nbackground and fixed-pattern noise contributions. Our simulations reveal that these noise\nsources significantly degrade RL deconvolution performance, introducing artifacts and\ncompromising resolution (Fig. 1b, second column). In contrast, 3Snet effectively suppresses\nfixed-pattern noise while minimizing RL-induced artifacts, as shown in Fig. 1b, fifth column.\nWe believe the subtraction process in 3SNet plays a critical role in eliminating background\nand fixed-pattern noise. This effectiveness stems from the identical imaging conditions (e.g.,\nexcitation intensity, exposure time) used when capturing the \"ON\" and \"OFF\" images,\nensuring consistent background and fixed-pattern contributions between the two frames. By\nsubtracting the averaged \"OFF\" image from the averaged \"ON\" image, we effectively remove\nnon-modulated background and noise components.\nFig. 1 | Workflow and validation of 3S-CLID on synthetic microtubule and cellular structure. b, Validation of 3S-CLID using\nsynthetic microtubule. Top row: peak signal-to-noise ratio (pSNR) and structural similarity (SSIM), from left to right: noisy image,\nimage averaging of ON image sequences, median of ON image sequences, median of the ON minus OFF image sequence,\n3S-denoising result (Clear) and blured ground truth. The color bar black to cyan means the relative intensity of images. Middle\nrow: Data uncertainty results of top row indicated by the averaged standard deviation (STD). The color bar blue to red represents\nthe STD value. Bottom row: deconvolution of noisy image, deconvolution of averaged ON image, deconvolution of median\naveraged ON image, deconvolution of median ON minus OFF image, 3S-CLID result and ground truth. The noisy images were\ncreated by acquiring a blank region of a fixed cell under WF illumination, and further injection of 5% Poisson noise and 5%\nGaussian noise. The resulting images from various approaches were processed using Lanczos upsampling by a factor of 3,\nfollowed by RL deconvolution with a theoretically derived Bessel PSF, using 1000 iterations. c, Normilized intensity profiles along\nthe red arrow heads in the left ground truth (GT) and deconvoled images.\nWe respectfully disagree with the position that averaging multiple images is equivalent to\nusing a longer exposure. The critical distinction may lie in readout noise reduction: while\nboth methods increase signal integration time, only frame averaging can reduce readout noise\nthrough temporal sampling (PMID: 31901080). This noise reduction is particularly important\nfor RL deconvolution, as readout noise directly contributes to reconstruction artifacts. By\nemploying frame averaging prior to deconvolution, we effectively minimize these\nnoise-induced artifacts, yielding superior results compared to single long exposures.\nWe compared deconvolution results for a 3S-denoised image with those for a longer-exposure\nimage of the same fixed-cell intracellular structure. Results showed that, compared to images\nacquired with longer exposure times, stacking multiple short-exposure images yields stronger\nsignal in high-frequency regions (indicated by arrows in panels a and c) and exhibits lower\nnoise levels, as shown to the right of the dashed line in panels b and d.\nComparation of images with long exposure or with stacked short exposure for CLID processing\nWe have added a description to the paper outlining the theoretical underpinnings of our noise\ntreatment approach. (Line 119-145)\n3. Comparing to a noise-free RL would be nice in the simulated images section.\nResponse:\nThank you for your valuable suggestion. We have now included a comparison with noise-free\nRL deconvolution in Fig. 1 of the revised manuscript.\n4. The math in the Abstract is confusing because the numbers seem to suggest a factor of 4\nimprovement compared what is stated as 6.\nResponse:\nThank you for identifying this error. We have corrected it in the revised manuscript. According\nto Fig. 5h, the averaged resolution was improved from 346 nm to 64 nm following\n3Snet-CLID processing, improved 5.4 folds.\n5. There are very minor grammatical issues.\nResponse:\nThank you for your comment. We have carefully reviewed the manuscript's grammar and\nmade the necessary corrections.\nPOINT-BY-POINT RESPONSE TO REVIEWER’S COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors have responded sincerely to all comments with extensive additional experiments and\ndetailed theoretical explanations. The technical quality of the work is high, and the comprehensive\ndata disclosure demonstrates scientific integrity.\nResponse:\nWe appreciate your encouraging assessment of our work, as well as the time you devoted to\nreviewing this manuscript.\nAs pointed out in our initial Major Issues 1 and 2, the term \"super-resolution\" in the manuscript was\nunclear and misleading. Through the authors' earnest response to comments from all three reviewers,\nthe essential nature of the method has been clarified: CLID is not an optical super-resolution\nmicroscopy technique but rather a computational super-resolution image processing method. This\nclarification of the paper's scope is highly valuable, and we commend the authors' sincere efforts in\nthis regard. However, the title, abstract, and various sections of the main text still contain\nexpressions and discussions that may mislead readers into confusing it with optical super-resolution\nmicroscopy. For example, phrases such as \"surpasses the theoretical resolution threshold\" and\n\"recover lost details\" suggest the measurement of new physical information beyond the diffraction\nlimit, when in reality CLID performs computational estimation from existing measurements without\nhardware modifications.\nWe would like to suggest that rather than merely making superficial corrections to avoid\nmisunderstandings, reorganizing the manuscript to clearly position it as a paper on \"computational\nsuper-resolution image estimation/generation\" would not only clarify its scope but also make it more\ncompelling. The technical innovations—such as per-pixel denoising strategy, signal distribution\npreservation, and hybrid supervised/self-supervised learning—are currently scattered throughout\nthe text. By integrating these elements and explicitly presenting the novelty and advantages as an\nimage processing method, the paper's contribution would become clearer and more appealing to the\nbroad readership of Nature Communications.\nResponse:\nWe greatly appreciate your valuable suggestions. We have now explicitly defined CLID as a\ncomputational super-resolution method, underscoring its advantages through key features such as\nthe per-pixel denoising strategy, signal distribution preservation, and hybrid supervised/self-\nsupervised learning. Additionally, we have revised the title, abstract, and discussion as you\nrecommended to ensure that the manuscript consistently adopts the perspective of computational\nsuper-resolution throughout.\nSpecific comments to the authors' revisions/rebuttals follow:\n1. Major Issues 1 & 2: Contextualization and theoretical framework\nThe authors have provided extensive theoretical clarifications. We suggest this be reflected\nthroughout the manuscript as discussed above.\nResponse:\nThank you for your valuable suggestion. To ensure the theoretical clarifications are thoroughly\nreflected in the manuscript, we have carefully revised the text throughout, including the\nIntroduction, Methods, and Discussion sections, to integrate these points more seamlessly.\n2. Major Issue 3: Image upsampling validation\nWe appreciate the comprehensive validation with systematic testing and complete data\nregeneration.\nHere, the manuscript reads that the synthetic ground truth has 65 nm pixel sampling (Lines 472-480).\nThe validation showed 65 nm resolution achievement. The results can be interpreted in two ways:\nnegatively, as circular validation where the information limit is predetermined; or positively, as\nevidence that CLID appropriately stops at the data's inherent limit without generating spurious\ninformation (avoiding hallucination). Given the importance of this point for interpreting CLID's\ncapabilities, we suggest either more thorough discussion of this issue. More preferably,\nadditional validation approaches if feasible.\nResponse:\nWe sincerely thank you for this exceptionally insightful comment, which raises a critical point\nregarding the interpretation of CLID's resolution capabilities. We fully agree that a thorough\ndiscussion is essential.\nAs you astutely noted, the validation results can be interpreted positively: CLID appropriately\nstops at the data's inherent resolution limit without generating spurious information, thereby\navoiding \"hallucination.\" We agree with this interpretation, and our existing data strongly\nsupport it. Below, we elaborate further and provide additional evidence to reinforce our\nconclusions:\n1) The measured resolution is not predetermined by pixel sampling. The 65 nm value refers to\nthe pixel sampling when 1× upsampling is applied. In the original manuscript, we used 2×\nupsampling, which resulted in a pixel size of 32.5 nm and a corresponding theoretical Nyquist\nlimit of 65 nm. In our first revision, we switched to 3× Lanczos upsampling, yielding a pixel\nsize of 21.7 nm and a Nyquist limit of approximately 43.4 nm.\nIf the resolution were circularly predetermined by the upsampling step (the first, negative\ninterpretation), one would expect a measured resolution around 43 nm under 3× upsampling.\nHowever, our actual measurements on various samples consistently yielded values larger than\nthe camera's pixel sampling limit (~43.4 nm): Fig. 1c: ~65 nm (minimum distance between two\nbeads); Fig. 2c & 2e: ~65 nm (close to designed distance between fluorophores); Fig. 1g: ~58\nnm (cytoskeleton, measured by decorrelation analysis).\n2) CLID faithfully reports the true structural dimensions. Quantitative validation on two\nreference samples confirms accuracy without significant artifact: i) DNA origami tiles with a\ndesigned 60-nm fluorophore spacing (Fig. 2e), yielded ~65 nm with CLID, matching STORM\nmeasurements. ii) Nup96 rings (Fig. 5a-c) gave an average diameter of ~103 nm, in close\nagreement with electron microscopy data. These results demonstrate that CLID resolves\ngenuine geometry rather than introducing spurious features.\n3) Direct evidence from dual-camera experiments. Following your excellent suggestion, we\nperformed additional validation by imaging the same cellular structure using two cameras with\ndifferent native pixel sizes (65 nm and 110 nm after optical magnification). The results (below)\nshowed that with 2× Lanczos upsampling, CLID achieved resolutions of 70 nm and 113 nm,\nvery close to the respective pixel sampling limits. With 3× upsampling, the resolutions values\nimproved to~60 nm and ~90 nm—still fundamentally limited by the Nyquist limit. This data\nprovides direct evidence that CLID's resolving capability, like those of other RL deconvolution\nmethods, is practically constrained by SNR and the pixel sampling, and that CLID algorithm\ncorrectly halts before reaching this boundary.\nAssesment of CLID resolution with cameras of different pixel sizes. a, Comparison of SD and CLID-resolved images acquired using\ncameras with different pixel sizes. b and c, Fourier ring correlation (FRC) and corresponding decorrelation analysis are used to\nquantify the resolution of the denoised images by the 2 × upsampling (b) and the 3 × upsampling (c). For the box-and-whisker plots,\nthe center line represents the median, the box spans the interquartile range (IQR; 25th to 75th percentiles), and whiskers extend to\n1.5× IQR. Outliers are plotted as individual points.\nWe have incorporated these points and the new dual-camera validation data into the revised\nmanuscript. Specifically, we now cite \"~60 nm\" as the achieved resolution wherever appropriate\nand have added the following paragraph to the Discussion (Line 439-448): \"The resolution of\n3Snet-CLID, like that of other computational SR methods, is fundamentally bounded by the\nNyquist limit of the pixel sampling and is practically constrained by the SNR. Under our current\nimaging conditions — 6.5 μm camera pixels, 100× objective, and 3× Lanczos upsampling —\n3Snet-CLID achieves ~60 nm resolution on biological specimens without introducing\nappreciable artifacts. Fourier Ring Correlation (FRC) analysis of sector test pattern\nsimulations (Supplementary Fig. 2) and of the same cellular structure imaged with two cameras\nwhose native pixel differed (65 nm vs. 110 nm after optical magnification) (Supplementary Fig.\n4) confirm that this gain arises from genuine high-frequency signal recovery rather than\ndeconvolution artifacts. In principle, with higher SNR and finer pixel sampling, 3Snet-CLID\ncan approach the corresponding Nyquist limit.\"\nWe believe these additions substantially strengthen the manuscript and provide a clearer, more\ncompelling assessment of CLID's performance. We sincerely appreciate your insightful\nfeedback, which has been instrumental in improving our work.\n3. Major Issue 4: Comprehensive comparison analysis\nWe appreciate the addition of MED(ON-OFF) comparison and the detailed parameter\nspecifications as requested. The results show CLID's advantages over alternative methods,\nwhich is encouraging.\nHowever, some numerical values in Fig. 1b, 1c are unexpected. For instance, MED(ON) shows\nSTD of 15.6 versus AVG(ON)'s 5.14, and the performance gap between AVG(ON-OFF) and\nMED(ON-OFF) is larger than typically expected for Poisson noise. We suggest double-checking\nthese values to ensure the comparison's reliability.\nResponse:\nThank you for this careful observation regarding the numerical values in Figures 1b and 1c. We\nhave double-checked the calculations and can confirm the values are accurate.\nWe agree that the performance gap between AVG(ON-OFF) and MED(ON-OFF) is larger than\nwould be expected for pure Poisson noise. We believe the explanation lies in the nature of our\nsimulated data. The images were designed to incorporate not only Poisson noise but also other\nrealistic noise types present in actual captured images. While MED(ON-OFF) is highly effective\nat suppressing Poisson noise, the superior performance of AVG(ON-OFF) in this case reflects\nits ability to more effectively mitigate these additional, non-Poisson noise components. This\nresult underscores the robustness of the AVG(ON-OFF) method in a more realistic noise\nenvironment.\n4. Major Issue 5: Demonstration of generalizability\nWe highly commend the authors' extensive efforts and sincere response. The comprehensive\ndemonstration across diverse conditions (as summarized inSupplementary Table 2) successfully\nestablishes CLID's excellent generalization capability, making its practical utility much clearer.\nThis is a valuable contribution.\nResponse:\nWe are deeply grateful for your generous and encouraging comments. We are delighted that our\nefforts to demonstrate CLID's generalization capability have successfully conveyed its practical\nutility, and we thank you for recognizing the value of this contribution.\n5. Minor Issues 1-5\nWe appreciate the authors' sincere and appropriate responses to all minor issues.\nResponse:\nThank you for this encouraging comment. We appreciate the acknowledgment and are glad our\nclarifications were satisfactory.\nReviewer #2 (Remarks to the Author):\nOverall, the authors have satisfactorily addressed most of the concerns raised in the initial review,\nand the methodology is now much better explained. I appreciate the additional clarifications and\nimprovements provided in this new version of the manuscript.\nResponse:\nWe are grateful to you for this encouraging feedback. We are delighted that the improved\nexplanations and clarifications have satisfactorily addressed the concerns and enhanced the\nmanuscript's methodology.\nHowever, a few important points still deserve clarification or refinement:\n1. It would be important to clearly state early in the manuscript (e.g., in the Introduction), that the\nproposed method is essentially two-dimensional and primarily suited for data with high optical\nsectioning, such as confocal spinning-disk, TIRF microscopy, or other flat samples. Since the\napproach relies on a 2D model of PSF blur, it does not account for 3D out-of-focus contributions,\nwhich inherently limits its applicability to thicker samples compared to standard 3D deblurring\napproaches. Explicitly stating this from the beginning would help readers understand the\nintended scope and limitations of the method.\nResponse:\nThank you for your suggestions. In response, we have now explicitly stated in the Introduction\nthat CLID is two-dimensional, suitable for imaging samples with a depth of less than 10 μm\nand works best for confocal spinning-disk and TIRF microscopy imaging modes (Line 99-103).\n2. I remain unconvinced by the choice of datasets, both simulated and experimental, used to\ndemonstrate the generalizability of the approach, as they mainly feature 1D filamentous or\nnetwork structures. I previously suggested, and still recommend, using simulated data that\ninclude objects of varying sizes (from micrometer to nanometer scale), such as sector test\npatterns. For the experimental part, data such as chromatin or lipid membrane staining would\nbetter represent more homogeneous 2D surfaces and could highlight that, once trained, the\nnetwork can handle structures of diverse morphologies. Such examples would also better\nillustrate the robustness of the method against artefacts in homogeneous regions.\nResponse:\nThank you for the suggestion. Following the advice, we have incorporated simulated data\ncontaining structures of varying sizes (from micrometers to nanometers) to evaluate the\nrecovery of fine detail resolution and to assess potential artifacts in homogeneous regions. Since\nthe specific code for the sector test pattern referenced was unavailable, we generated a similar\npattern covering a comparable range of spatial frequencies (shown below). The simulation\nresults demonstrate that CLID not only greatly enhances image contrast but also resolves\nstructures ranging from the micrometer to the nanometer scale, without introducing significant\nartifacts when imaging either homogeneous or heterogeneous structures.\nValidation of 3S-CLID using synthetic sector test pattern. a, Top row: ground-truth (GT) image and the pSNR (peak\nsignal-to-noise ratio) and SSIM (structural similarity) values for the raw (noisy) image and the Clear (3S-denoised)\nimage relative to GT_blur (blurred ground truth). Middle row: Data uncertainty results of top row images indicated by\nthe averaged standard deviation (STD). The color bar blue to red represents the STD value. Bottom row:\ndeconvolution of top row images. The Raw images were created by acquiring a blank region of a fixed cell under\nWF illumination, and further injection of 5% Poisson noise and 5% Gaussian noise. The resulting images were\nprocessed using Lanczos upsampling by a factor of 3, followed by RL deconvolution with a theoretically derived\nBessel PSF, using 500 iterations. b, FRC analysis of denoised images; the line marks the 1/7 threshold.\nFor the experimental part, we would like to clarify that, based on evidence from techniques like\nlabel-free imaging and electron microscopy, both chromatin and lipid membrane staining\nstructures are known to exhibit significant heterogeneity and are not perfectly homogeneous\n(PMID: 38306982; PMID: 27702891; PMID: 40645941; PMID: 28356571). Nevertheless, to\ndirectly address the valuable point about testing on diverse morphologies, we have applied\nCLID to image both chromatin and cell membranes. The results, presented below, successfully\nillustrate the method's capability on these biologically relevant structures. We have added both\nthe simulation and experimental results to the manuscript (Lines 429-432).\nSD and 3Snet-CLID images of chromatin or lipid membrane in fixed U-2 OS cells\nexpressing mSG-labeled H2B (a) and LactC2 (b), respectively, under spinning disc (SD)\nmicroscopy.\n3. As artefact management is central to this work and to deconvolution in general, it would be\nuseful to explicitly mention that, although artefacts are reduced compared to other algorithms\n(as illustrated in many comparative examples), residual texture artefacts may still occur, as\nvisible in some figures (e.g., Fig. 4, central region, and Supplementary Video 1). A short\ncomment on this point would guide readers to interpret results with appropriate caution. Such\ntypical textures seem to occur in regions with low spatial details or dominated by out-of-focus\nsignal.\nResponse:\nThank you for your valuable comment. We fully agree that open discussion of potential artifacts\nis essential. CLID raises pSNR from 8.2 to 47.5 and yields an SSIM of 0.98—performance that\nexceeds current denoising methods—yet it cannot remove every photon noise, and iterative\ndeconvolution can still magnify residual artifacts.\nFollowing your suggestion, we have inserted the following clarification into the revised\nmanuscript: \"Although 3Snet-CLID substantially improves image quality and suppresses\nartifacts relative to existing approaches (Figs. 2d, 3b, 3d, Extended Data Fig. 1), faint texture\nartifacts may occasionally persist, especially in low-SNR regions (e.g., the central area in Fig.\n4a).\" (Lines 437-439) and \" CLID is a 2D SR technique and, like any algorithm that uses a 2D\nPSFs, remains susceptible to out-of-focus blur \" (Lines 458-459)\nWe believe these statements give readers clear, balanced guidance on the capabilities and\nlimitations of the technique.\n4. Typical artefacts are also visible in the Argolight slide imaging for all methods tested (Fig. 2d).\nEven if 3Snet reconstructions outperform other tested methods, sometimes a single line is\nvisible, and sometimes two, independently of the line-pair distances, which is unexpected and\nwould require some explanations. It would be helpful to add a reference line above the figure\nshowing the true pattern (e.g., are the patterns 1-2-1 or 2-2-2 lines?) and to clarify whether the\nline thickness remains constant across line-pair distances. Another puzzling point is why line-\npairs larger than 120 nm are not properly resolved by any algorithms except 3Snet and sparse\ndeconv, and why 3Snet seems to perform better on 60 nm pattern images compared to 210 nm\nones. The poor performance of Noise2Self is somewhat surprising but can likely be explained\nby the fact that it was designed to denoise very noisy data. This suggests that evaluating the\nmethod’s performance as a function of SNR, particularly in low-SNR conditions, would provide\nvaluable insight into its limits.\nResponse:\nThank you for your valuable feedback. We have inserted a reference line above Figure 2d to\nindicate the expected line pattern (1-2-1). Because the artifacts appeared with every method in\nthe original and first revision manuscript, we suspected a manufacturing defect in the original\nArgolight slide. We therefore repeated the acquisition on a newly purchased slide; the revised\nfigure now shows these cleaner data, which fully address the anomalies you noted. Owing to\nspace constraints, only the 30–210 nm data were shown in the main figure.\nSeparation of two fluorescent lines with interline spacing down to 60 nm by 3Snet-CLID. Raw images were either reconstructed with the\nPURE, DnCNN, Noise2Self, N2V, Sparse or 3Snet-CLID followed by 3× Lanczos interpolation before reconstruction with RL deconvolution\nfor 1000 iterations. \nThank you for highlighting the Noise2Self comparison. Our systematic tests show that\nNoise2Self’s pixel-subset strategy distorts the photon distribution; when the resulting image is\npassed to RL deconvolution this distortion produces severe artifacts and consistently low SSIM\nvalues, irrespective of SNR. Consequently, Noise2Self–deconvolution performs poorly even\nunder high-SNR conditions, so the steep drop we observe is intrinsic to the method rather than\na noise-level effect. In contrast, CLID preserves the original distribution and therefore retains\na clear resolution advantage across the entire SNR range, including the lowest doses we tested.\nComparison of the resolving performance of 3Snet-CLID and noise2self using simulated microtubule structures with low and high\npSNR. a, ground truth (GT) and blured ground truth (GT_blur). b, Raw images with low and high pSNR. The Raw images were\ncreated by acquiring a blank region of a fixed cell under WF illumination, and further injection of 5% Poisson noise and 5%\nGaussian noise. The resulting images from noise2self (c) and 3Snet-CLID (d) denoised method were processed using Lanczos\nupsampling by a factor of 3, followed by RL deconvolution with a theoretically derived Bessel PSF, using 1000 iterations.\n5. Finally, I remain cautious regarding the reported absolute resolution value of 65 nm (stated\ndirectly in the title). This could reflect algorithmic convergence effects (i.e., texture artefacts)\nrather than true structural resolution. For example, decorrelation analysis of deconvolved\nimages such as those in Fig. 2d might yield similar or even smaller values, making it difficult\nto discriminate resolution improvement from artefact enhancement. I understand that it is not a\ntrivial task, and including sector test patterns simulations covering a broad range of spatial\nfrequencies could help clarify this point. Unless such analysis is provided, I would recommend\nmoderating or qualifying this claim.\nResponse:\nWe appreciate your caution regarding the 65 nm value and share your concern about\ndistinguishing genuine resolution from algorithmic artifacts. To address this, we now quantify\nresolution with Fourier-ring correlation (FRC), a metric specifically designed to separate\nreproducible signal from noise-based artifacts (Nieuwenhuizen et al., Nat. Methods 2013).\n1) Sector patterns simulations spanning a wide frequency range give an FRC resolution of ~55\nnm after CLID and show no visible texture artifacts (SSIM = 0.89 versus ground truth),\nconfirming that the gain comes from restored high-frequency signal, not noise amplification.\n2) Direct evidence from dual-camera experiments. We performed additional validation by\nimaging the same cellular structure using two cameras with different native pixel sizes (65 nm\nand 110 nm after optical magnification). The results (below) showed that with 2× Lanczos\nupsampling, CLID achieved resolutions of 70 nm and 113 nm, very close to the respective pixel\nsampling limits. With 3× upsampling, the resolutions values improved to~60 nm and ~90 nm—\nstill fundamentally limited by the Nyquist limit. This data provides direct evidence that CLID's\nAssesment of CLID resolution with cameras of different pixel sizes. a, Comparison of SD and CLID-resolved images acquired using\ncameras with different pixel sizes. b and c, Fourier ring correlation (FRC) and corresponding decorrelation analysis are used to\nquantify the resolution of the denoised images by the 2 × upsampling (b) and the 3 × upsampling (c). For the box-and-whisker plots,\nthe center line represents the median, the box spans the interquartile range (IQR; 25th to 75th percentiles), and whiskers extend to\n1.5× IQR. Outliers are plotted as individual points.\nresolving capability, like those of other RL deconvolution methods, is practically constrained\nby SNR and the pixel sampling, and that CLID algorithm correctly halts before reaching this\nboundary.\n3) CLID faithfully reports the true structural dimensions. Quantitative validation on two\nreference samples confirms accuracy without significant artifact: i) DNA origami tiles with a\ndesigned 60-nm fluorophore spacing (Fig. 2e), yielded ~65 nm with CLID, matching STORM\nmeasurements. ii) Nup96 rings (Fig. 5a-c) gave an average diameter of ~103 nm, in close\nagreement with electron microscopy data. These results demonstrate that CLID resolves\ngenuine geometry rather than introducing spurious features.\nIn the original manuscript and the first revision, we reported the resolution of CLID as ~65 nm,\nbased on the minimum resolvable distance measured between adjacent structures in standard\nsamples (Fig. 1c, 2c, 2e). However, due to the limited number of pixels, a two‑peak fitting could\nnot be reliably performed; the measured “minimum resolvable distance” (65 nm) actually\nrepresents the distance between the pixel positions of two intensity maxima, which does not\nstrictly equate to the actual distance between fluorophores after accounting for pixel\ndiscretization. Therefore, in this revision, we now use the FRC‑derived resolution from\nbiological samples to represent the resolution achievable by CLID. Furthermore, following\nyour suggestion, we have qualified the reported resolution by stating that under our current\nimaging conditions (6.5 μm pixel camera, 100× objective, 3× Lanczos upsampling), CLID\nachieves a resolution of approximately 60 nm for biological samples without introducing\nsignificant artifacts. Accordingly, we have also removed the specific “65 nm” reference from\nthe title.\nWe have incorporated these points and the new dual-camera validation data into the revised\nmanuscript. Specifically, we have updated the description of CLID's achieved resolution to \"~60\nnm\" throughout the manuscript where appropriate. And the Discussion has been expanded to\ninclude a clear paragraph stating (Line 439-448): \" The resolution of 3Snet-CLID, like that of\nother computational SR methods, is fundamentally bounded by the Nyquist limit of the pixel\nsampling and is practically constrained by the SNR. Under our current imaging conditions —\n6.5 μm camera pixels, 100× objective, and 3× Lanczos upsampling — 3Snet-CLID achieves\n~60 nm resolution on biological specimens without introducing appreciable artifacts. Fourier\nRing Correlation (FRC) analysis of sector test pattern simulations (Supplementary Fig. 2) and\nof the same cellular structure imaged with two cameras whose native pixel differed (65 nm vs.\n110 nm after optical magnification) (Supplementary Fig. 4) confirm that this gain arises from\ngenuine high-frequency signal recovery rather than deconvolution artifacts. In principle, with\nhigher SNR and finer pixel sampling, 3Snet-CLID can approach the corresponding Nyquist\nlimit.\"\nWe believe these additions substantially strengthen the manuscript and provide a clearer, more\nconvincing interpretation of CLID's performance. We are deeply grateful for your valuable\nfeedback, which has been instrumental in improving our work.\nReviewer #3 (Remarks to the Author):\n1. The authors have provided a thorough response to the reviewers. The comparison of the results\nof this method to deconvolution of a blurry, but noise free image are nearly identical (fig 2b).\nIf this is truly the performance of the method, than this case should be made even more strongly\nby the authors.\nResponse:\nWe thank you for highlighting this key observation. We agree that the near-identical\nperformance between 3S-CLID applied to the noisy measurement and deconvolution applied to\na noise-free blurred image (Fig. 1b，we believe you are referring to Fig. 1b) is an important\nresult and should be emphasized more strongly in the manuscript.\nOur CLID pipeline consists of (i) 3S denoising applied to the noisy image, followed by (ii) RL\ndeconvolution applied to the denoised output. The main reason CLID approaches the “noise-\nfree blurred” deconvolution baseline is that our 3S method is a single-pixel-based denoiser that\ncan remove strong noise efficiently while faithfully preserving the per-pixel signal distribution\n(i.e., without introducing spatial hallucination or structural distortions). Consequently, the\ndenoised image is a highly accurate estimate of the underlying blurred signal, enabling the\nsubsequent RL step to behave almost the same as it would on a truly noise-free blurred input.\nWe have strengthened the manuscript accordingly by explicitly stating this result in the Results\nsection around Fig. 1b and by adding the corresponding quantitative comparison. Specifically,\nfor the example in Fig. 1b, the raw noisy image has pSNR/SSIM = 8.2/0.15; after 3S denoising\nthe image reaches 47.5/0.98; after applying RL (i.e., 3S-CLID) we obtain a super-resolved\nreconstruction of 24.5/0.93, which is essentially indistinguishable from RL deconvolution of a\nblurry but noise-free image (23.9/0.94). This substantiates that CLID can deliver high-fidelity\nsuper-resolution under severe noise by first producing a denoised image that preserves the true\nsignal distribution required for stable deconvolution.\nWe have added this part into the Results section: “Notably, Figure 1b highlights an important\nproperty of 3S-CLID: the 3S-CLID reconstruction obtained from a strongly noisy measurement\nis nearly identical to the reconstruction obtained by deconvolving a blurry but noise-free image.\nStarting from the raw noisy input (pSNR/SSIM = 8.2/0.15), 3S denoising step substantially\nsuppresses noise while preserving the per-pixel signal distribution, resulting in a denoised\nestimate with pSNR/SSIM = 47.5/0.98. Applying RL deconvolution to this denoised image (i.e.,\n3S-CLID) yields a super-resolved reconstruction with pSNR/SSIM = 24.5/0.93, which closely\nmatches the result of deconvolution applied to a blurry, noise-free image (pSNR/SSIM =\n23.9/0.94). This near-equivalence indicates that 3S effectively recovers an accurate blurred\nsignal estimate under severe noise, enabling the downstream deconvolution to operate in a\nregime comparable to the ideal noise-free case. Overall, 3S-CLID combines (i) efficient single-\npixel-based denoising, (ii) faithful preservation of the signal distribution, and (iii) high-fidelity\nSR reconstruction.” (Lines 219-230)\n2. A few critical issues remain - please explain exactly how the decorrelation analysis was done.\nThis should be by comparing FRC between two completely different data sets on the same\nsample, otherwise the high frequency info could just be a high-resolution, but wrong.\nResponse:\nThank you for your insightful comments. In our study, all SR images subjected to decorrelation\nanalysis were first inspected visually at an appropriate iteration number to ensure no obvious\ntexture artifacts were present before the analysis was performed. Consequently, the resolution\nvalues obtained from the decorrelation analysis correspond directly to the images shown in the\nfigures.\nWe have cited the original method reference (Nature Methods, 2019, 16, 918–924) in the\nmanuscript. In the revised version, we have also provided a detailed, step‑by‑step description\nof the decorrelation analysis procedure in the legend of Figure 1e (where it first appears),\nas follows: “We used the plugin ‘ImageDecorrelationAnalysis_plugin.jar’ to perform the\ndecorrelation analysis. All SR images subjected to decorrelation analysis were first inspected\nvisually at an appropriate iteration number to ensure no obvious texture artifacts were present\nbefore the analysis was performed.” (See Line 685-691)\nIn our revised manuscript (Line 444-448), we have performed additional validation by imaging\nthe same cellular structure using two cameras with different pixel sizes (65 nm and 110 nm after\nAssesment of CLID resolution with cameras of different pixel sizes. a, Comparison of SD and CLID-resolved images acquired using\ncameras with different pixel sizes. b and c, Fourier ring correlation (FRC) and corresponding decorrelation analysis are used to\nquantify the resolution of the denoised images by the 2 × upsampling (b) and the 3 × upsampling (c). For the box-and-whisker plots,\nthe center line represents the median, the box spans the interquartile range (IQR; 25th to 75th percentiles), and whiskers extend to\n1.5× IQR. Outliers are plotted as individual points.\noptical magnification). For each camera, we applied 3Snet denoising followed by RL\ndeconvolution with both 2× and 3× Lanczos upsampling. At the appropriately chosen iteration\nnumbers—where no obvious visual artifacts were present—FRC analysis was conducted on the\nindependently acquired datasets. The results show that the resolutions determined by FRC and\nby decorrelation analysis are in close agreement under both upsampling conditions.\nWe believe this additional validation strengthens the methodological rigor of our work and\naddresses your concern regarding the interpretation of high‑frequency information.\n3. Please also clarify lambda in the loss model.\nResponse:\nWe thank the reviewer for pointing out the insufficient clarification of Lambda. We have added\na comprehensive explanation in Methods (Line 511-518, highlighted in yellow): “λ>0 denotes\nthe weighting factor between the self-supervised term and the supervised term in the loss\nfunction. A larger λ indicates a higher weight assigned to the supervised term. When λ=0, the\nsupervised term becomes zero and the DL model reduces to a self-supervised model; when λ\n=∞, the self-supervised term becomes zero and the DL model reduces to a fully supervised\nmodel. To determine the optimal λ, we set λ to 0/1/2/4/8/16/∞ and trained the model on\nthe same dataset for each setting. The dataset consists of two parts: an image set for training\nthe denoising network (train) and an image set for evaluating the denoising performance (test).\nThe λ used in the loss function is chosen as the value that yields the highest average pSNR on\nthe denoised images in the test set.”\n4. I share many of the concerns expressed by the other reviewers in the original reviews, in\nparticular the requirement of the PSF to be known exactly as deconvolution goes much beyond\nthe diffraction limit, otherwise artifacts can be produced. This should be discussed more\nstrongly - although I see there is now a figure comparing the result when using mismatched\nPSFs.\nResponse:\nWe thank you for this important comment and agree that RL deconvolution is highly sensitive\nto PSF mismatch. When the PSF used in the forward model does not match the true system\nresponse, RL can over-fit the mismatch and introduce non-physical structures (e.g.,\nringing/haloing or spurious fine details), particularly when attempting to recover high spatial\nfrequencies. We have therefore strengthened the manuscript text to emphasize this limitation\nexplicitly and to clarify that accurate, condition-matched PSF estimation and conservative\niteration stopping are essential to avoid artifacts; we also refer the reader to the mismatch\ncomparison now provided (Supplementary Fig.6).\nTo ensure a matched PSF in our experiments, we used two complementary approaches under\nthe same imaging configuration. First, we imaged sub-diffraction fluorescent beads on the same\nmicroscope and extracted the effective lateral/axial widths (e.g., FWHM) and sampling\nparameters; together with the known optical parameters (objective/NA, emission wavelength,\npixel size), we generated a condition-matched PSF for RL deconvolution (Methods, revised).\nSecond, we independently measured the PSF experimentally using recently reported single-\nchain ultrasmall fluorescent polymer dots (“suPdots”/polymerdots; <5 nm size and very high\nbrightness), which behave as quasi-point emitters and enable direct PSF measurement under\nidentical conditions (Yang et al., Nature Photonics 19, 1336–1344 (2025), doi:10.1038/s41566-\n025-01767-1). Importantly, RL deconvolution of the same denoised input image using (i) the\nbead-derived, condition-matched PSF and (ii) the experimentally measured polydot PSF\nComparison of 3Snet-CLID results with different PSF models. Left to right: SD image, 3Snet-CLID images with Gaussian,\nexperimental or Bessel PSFs. Scale bar: 5 μm.\nproduced nearly indistinguishable results (new Supplementary Fig. 6), supporting that our PSF\nconstruction is accurate enough for the conclusions drawn and that the observed structures are\nnot driven by an arbitrary PSF choice.\nFinally, to minimize over-iteration artifacts, we applied a conservative stopping criterion and\ntypically used appropriate RL iterations, terminating iterations before any visible onset of\nringing/haloing or other obvious non-physical features. We now state this explicitly in the\nMethods and point to Supplementary Fig. 6 for the PSF-validation comparison and the\nrobustness assessment.\nA POINT-BY-POINT RESPONSE TO THE REVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nGeneral Assessment\nThe revised manuscript represents a substantial improvement. The explicit positioning as\n\"computational super-resolution,\" the removal of the specific resolution figure from the title, and\nthe honest discussion of limitations (2D constraints, PSF sensitivity, residual artifacts, out-of-focus\nsusceptibility) set an appropriate standard for reporting computational SR methods. Aside from\none remaining concern discussed below, the revisions adequately address the reviewers'\ncomments.\nResponse:\nThank you very much for your thorough and constructive feedback throughout the review process.\nWe are delighted to hear that the revised manuscript represents a substantial improvement and\nthat the explicit positioning as \"computational super-resolution,\" along with our honest discussion\nof limitations, meets the appropriate standards for reporting computational SR methods.\nThe authors are particularly commended for conducting additional dual-camera validation\nexperiments—an effort that goes beyond mere textual revision.\nResponse:\nWe are particularly grateful for your recognition of our additional dual-camera validation\nexperiments. Your acknowledgment that this effort goes beyond mere textual revision is deeply\nappreciated, as we indeed invested significant time and resources to strengthen the experimental\nvalidation of our method.\nRemaining Concern\nThe use of decorrelation analysis for resolution estimation is understandable and not inappropriate\nper se. However, given that the authors have now explicitly framed this work as computational\nsuper-resolution, the limitations of this metric when applied to computational SR outputs should\nbe clearly discussed.\nDecorrelation analysis confirms the presence of high-frequency content but does not\nindependently verify its accuracy. Hou et al. (eLight 2024) demonstrated that deconvolved images\ncan show higher resolution by decorrelation analysis \"largely due to simple amplification of the\nhigh-frequency part\" while lacking fidelity. The 2020 Addendum to the original method\n(Descloux et al., Nature Methods) also acknowledges that image generation processes can influence\nresolution estimates.\nResponse:\nWe thank you for this important point. We agree that, when a method is framed as computational\nsuper-resolution, a single-image resolution metric such as decorrelation analysis should be\ninterpreted cautiously, because it primarily confirms the presence of high-frequency content rather\nthan independently proving its fidelity.\nFollowing your suggestion, we revised the manuscript to more clearly discuss these limitations in\nthe context of computational SR (Line 443-453, highlighted):\nIn the current study, we primarily employ decorrelation analysis to estimate image resolution;\nhowever, we acknowledge that this metric has limitations for computational super-resolution\noutputs. The 2020 Addendum to the original method notes that resolution estimates can be\ninfluenced by image-generation or post-processing steps (Descloux et al., Nature Methods, 2020),\nand Hou et al. (eLight, 2024) further demonstrated that deconvolution may yield artificially\nelevated decorrelation-based resolution largely through high-frequency amplification without a\ncorresponding improvement in fidelity. Thus, decorrelation analysis confirms the presence of high-\nfrequency content but does not independently verify its accuracy. To mitigate this risk, all SR images\nin our study were visually inspected at optimized iteration numbers to avoid artifacts prior to\ndecorrelation analysis; under these conditions, the resulting resolution estimates closely agreed\nwith FRC-based validation (Supplementary Fig. 4).\nSuggestion\nPart of this concern can be addressed using the authors' own dual-camera dataset. Cross-FRC\nanalysis between the CLID-processed outputs from the two cameras is strongly recommended.\nBecause the two cameras have different pixel sizes, algorithmically generated high-frequency\nartifacts would be pixel-grid-dependent and thus uncorrelated between the two outputs, whereas\ngenuine structural information would correlate. This provides more rigorous validation than\nindependent decorrelation analysis of each output and requires only re-analysis of existing data.\nIf the authors' claims are correct, cross-FRC should show correlation up to ~90 nm, corresponding\nto the resolution of the lower-resolution camera output. This would provide independent\nconfirmation that structural information in this frequency range is consistently recovered. The ~60\nnm claim, however, cannot be validated with this dataset. If the authors wish to further validate\nhigher frequencies, a dual-camera configuration with a smaller pixel size (e.g., using a 2× relay lens\nto achieve ~55 nm pixels) would be one possible approach.\nResponse:\nWe thank you for the suggestion to perform cross-FRC between the CLID outputs from the two\ncameras. We agree with the underlying intent (to test whether high-frequency information is\nconsistently recovered across independent measurements). However, we believe that cross-FRC is\nnot a rigorous or interpretable validation in our current dual-camera configuration, because the\ntwo cameras differ substantially in pixel pitch (65 µm vs 110 µm) and consequently produce images\nwith different sampling grids and different fields of view. Standard two-image FRC assumes that\nthe two images represent the same region of interest on a common sampling grid, with\nindependent noise realizations (Koho, S., et al. Nature Communications 10, 3103 (2019).). In our\ncase, to compute cross-FRC one would first need (i) geometric registration (translation/rotation and\npotentially distortion correction due to different effective magnification and FOV), and (ii)\nresampling of one image onto the other’s pixel grid (or onto a third common grid). Both steps are\nknown to affect the FRC frequency axis and correlation values because FRC computed from\ndiscretized images depends on the sampling step/pixel size and the numerical handling of the\ndiscrete Fourier domain.\nConcretely, Koho et al. demonstrate that if one plots FRC curves while incorrectly assuming the\nsame pixel size, the curves show an apparent frequency shift, and they explicitly state that the\ncalibration is needed to correct for different pixel pitch. This is directly relevant here: any cross-FRC\nbetween two differently sampled outputs is not “plug-and-play” and requires a careful\ncalibration/transform pipeline. Moreover, Pham et al. (closed-form FRC analysis) emphasize that\ndiscrete FRC depends on experimental/numerical parameters such as pixel size, and that the\naccuracy of discrete FRC is tied to the spatial sampling step and interpolation/aliasing behavior.\nImportantly, after resampling and registration, the resulting cross-FRC would no longer measure\nthe agreement of the native CLID outputs from each camera, but rather the agreement between\none native output and a geometrically transformed/interpolated version of the other. In such a\nsituation, cross-FRC becomes strongly confounded by (a) interpolation-induced\ncorrelations/spectral smoothing, and (b) residual registration errors, both of which can dominate\nthe high-frequency correlation decay and lead to under- or over-estimation that is not attributable\nto true optical/super-resolved structural information.\nFor these reasons, in our view the dual-camera dataset is well-suited for independent within-\ncamera validations (as we already performed: decorrelation analysis and FRC validation per\ncamera, Supplementary Fig. 4), but it is not ideally suited for cross-FRC as a decisive fidelity test\ngiven the large pixel-pitch mismatch and different FOV requiring nontrivial resampling/registration.\nFinally, we agree with the reviewer that, if one aims to validate frequencies beyond the lower-\nsampling channel, an improved dual-camera configuration with a smaller effective pixel size (e.g.,\nusing a relay to reach ~55 nm sampling at the specimen plane) would be a more appropriate\nexperimental design, because it would reduce the need for aggressive resampling and extend the\ninterpretable frequency range.\nRecommendation Regarding Resolution Claims\nGiven these validation limitations, stating a specific resolution figure in prominent locations is\npotentially misleading. The authors' decision to remove the specific number from the title reflects\nappropriate caution and is commendable. However, the claim of \"~60 nm resolution\" still appears\nin the Abstract. Consistent with the reasoning behind the title revision, I recommend removing this\nfigure from the Abstract.\nResponse:\nThank you for this valuable suggestion. We have removed the claim of \"~60 nm resolution\" from\nthe Abstract to maintain consistency with the title revision.\nReviewer #1 (Remarks on code availability):\nThe repository was not accessible at the time of review.\nResponse:\nThank you for bringing this to our attention. We have corrected the link, and the repository is now\nfully accessible.\nReviewer #2 (Remarks to the Author):\nAfter carefully reviewing the final revised version of the manuscript, I am pleased to note that the\nauthors have thoroughly addressed all the concerns raised during the previous rounds of review.\nThe revisions have substantially strengthened the manuscript, both in terms of methodological\nclarity and in the discussion of limitations and validation. I appreciate the authors’ careful and\nconstructive responses throughout the review process.\nResponse:\nThank you very much for your thorough and constructive feedback throughout the review process.\nWe greatly appreciate your time and effort in carefully evaluating our manuscript across multiple\nrounds of revision.\nWe are delighted to hear that the revisions have successfully addressed your concerns and that the\nmanuscript has been strengthened in terms of methodological clarity as well as the discussion of\nlimitations and validation. Your insightful comments and suggestions have been invaluable in\nhelping us improve the quality of our work.\nBefore final publication, I would kindly ask the authors to verify that the newly added\nsupplementary figures mentioned in the point-by-point response to the reviewers are properly\nincluded in the merged final document, as they do not seem to appear in the current. In addition,\nit would be beneficial to include zoomed-in views of selected images to better visualize the\nreported improvements as well as potential artefact-prone regions. Such magnified views would\nhelp readers more clearly appreciate both the gains and the limitations of the approach.\nResponse:\nWe have verified that the newly added supplementary figures mentioned in the point-by-point\nresponse to the reviewers are properly included in the merged final document. And as suggested,\nwe also included zoomed-in views of selected images to better visualize the reported improvements\nas well as potential artefact-prone regions.\nReviewer #3 (Remarks to the Author):\nThe authors have satisfactorily responded to my criticisms.\nResponse:\nWe greatly appreciate your thorough review and constructive feedback throughout the revision\nprocess. We are pleased that our responses and revisions have satisfactorily addressed your\ncriticisms. Thank you for your valuable time and effort in helping us improve the quality of our\nmanuscript."}, {"round": 2, "reviewer_comments": {"reviewer_1": "General Assessment\nThe revised manuscript represents a substantial improvement. The explicit positioning as \"computational super-resolution,\" the removal of the specific resolution figure from the title, and the honest discussion of limitations (2D constraints, PSF sensitivity, residual artifacts, out-of-focus susceptibility) set an appropriate standard for reporting computational SR methods. Aside from one remaining concern discussed below, the revisions adequately address the reviewers' comments.\nThe authors are particularly commended for conducting additional dual-camera validation experiments—an effort that goes beyond mere textual revision.\nRemaining Concern\nThe use of decorrelation analysis for resolution estimation is understandable and not inappropriate per se. However, given that the authors have now explicitly framed this work as computational super-resolution, the limitations of this metric when applied to computational SR outputs should be clearly discussed.\nDecorrelation analysis confirms the presence of high-frequency content but does not independently verify its accuracy. Hou et al. (eLight 2024) demonstrated that deconvolved images can show higher resolution by decorrelation analysis \"largely due to simple amplification of the high-frequency part\" while lacking fidelity. The 2020 Addendum to the original method (Descloux et al., Nature Methods) also acknowledges that image generation processes can influence resolution estimates.\nSuggestion\nPart of this concern can be addressed using the authors' own dual-camera dataset. Cross-FRC analysis between the CLID-processed outputs from the two cameras is strongly recommended. Because the two cameras have different pixel sizes, algorithmically generated high-frequency artifacts would be pixel-grid-dependent and thus uncorrelated between the two outputs, whereas genuine structural information would correlate. This provides more rigorous validation than independent decorrelation analysis of each output and requires only re-analysis of existing data.\nIf the authors' claims are correct, cross-FRC should show correlation up to ~90 nm, corresponding to the resolution of the lower-resolution camera output. This would provide independent confirmation that structural information in this frequency range is consistently recovered. The ~60 nm claim, however, cannot be validated with this dataset. If the authors wish to further validate higher frequencies, a dual-camera configuration with a smaller pixel size (e.g., using a 2× relay lens to achieve ~55 nm pixels) would be one possible approach.\nRecommendation Regarding Resolution Claims\nGiven these validation limitations, stating a specific resolution figure in prominent locations is potentially misleading. The authors' decision to remove the specific number from the title reflects appropriate caution and is commendable. However, the claim of \"~60 nm resolution\" still appears in the Abstract. Consistent with the reasoning behind the title revision, I recommend removing this figure from the Abstract.\n(Remarks on code availability)\nThe repository was not accessible at the time of review.", "reviewer_2": "Overall, the authors have satisfactorily addressed most of the concerns raised in the initial review, and the methodology is now much better explained. I appreciate the additional clarifications and improvements provided in this new version of the manuscript.\nHowever, a few important points still deserve clarification or refinement:\nIt would be important to clearly state early in the manuscript (e.g., in the Introduction), that the proposed method is essentially two-dimensional and primarily suited for data with high optical sectioning, such as confocal spinning-disk, TIRF microscopy, or other flat samples. Since the approach relies on a 2D model of PSF blur, it does not account for 3D out-of-focus contributions, which inherently limits its applicability to thicker samples compared to standard 3D deblurring approaches.\nExplicitly stating this from the beginning would help readers understand the intended scope and limitations of the method.\nI remain unconvinced by the choice of datasets, both simulated and experimental, used to demonstrate the generalizability of the approach, as they mainly feature 1D filamentous or network structures. I previously suggested, and still recommend, using simulated data that include objects of varying sizes (from micrometer to nanometer scale), such as sector test patterns. For the experimental part, data such as chromatin or lipid membrane staining would better represent more homogeneous 2D surfaces and could highlight that, once trained, the network can handle structures of diverse morphologies. Such examples would also better illustrate the robustness of the method against artefacts in homogeneous regions.\nAs artefact management is central to this work and to deconvolution in general, it would be useful to explicitly mention that, although artefacts are reduced compared to other algorithms (as illustrated in many comparative examples), residual texture artefacts may still occur, as visible in some figures (e.g., Fig. 4, central region, and Supplementary Video 1). A short comment on this point would guide readers to interpret results with appropriate caution. Such typical textures seem to occur in regions with low spatial details or dominated by out-of-focus signal.\nTypical artefacts are also visible in the Argolight slide imaging for all methods tested (Fig. 2d). Even if 3Snet reconstructions outperform other tested methods, sometimes a single line is visible, and sometimes two, independently of the line-pair distances, which is unexpected and would require some explanations. It would be helpful to add a reference line above the figure showing the true pattern (e.g., are the patterns 1-2-1 or 2-2-2 lines?) and to clarify whether the line thickness remains constant across line-pair distances. Another puzzling point is why line-pairs larger than 120 nm are not properly resolved by any algorithms except 3Snet and sparse deconv, and why 3Snet seems to perform better on 60 nm pattern images compared to 210 nm ones.\nThe poor performance of Noise2Self is somewhat surprising but can likely be explained by the fact that it was designed to denoise very noisy data. This suggests that evaluating the method’s performance as a function of SNR, particularly in low-SNR conditions, would provide valuable insight into its limits.\nFinally, I remain cautious regarding the reported absolute resolution value of 65 nm (stated directly in the title). This could reflect algorithmic convergence effects (i.e., texture artefacts) rather than true structural resolution. For example, decorrelation analysis of deconvolved images such as those in Fig. 2d might yield similar or even smaller values, making it difficult to discriminate resolution improvement from artefact enhancement. I understand that it is not a trivial task, and including sector test patterns simulations covering a broad range of spatial frequencies could help clarify this point. Unless such analysis is provided, I would recommend moderating or qualifying this claim.\n(Remarks on code availability)", "reviewer_3": "The authors have satisfactorily responded to my criticisms.\n(Remarks on code availability)"}, "author_response": "A POINT-BY-POINT RESPONSE TO THE REVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nGeneral Assessment\nThe revised manuscript represents a substantial improvement. The explicit positioning as\n\"computational super-resolution,\" the removal of the specific resolution figure from the title, and\nthe honest discussion of limitations (2D constraints, PSF sensitivity, residual artifacts, out-of-focus\nsusceptibility) set an appropriate standard for reporting computational SR methods. Aside from\none remaining concern discussed below, the revisions adequately address the reviewers'\ncomments.\nResponse:\nThank you very much for your thorough and constructive feedback throughout the review process.\nWe are delighted to hear that the revised manuscript represents a substantial improvement and\nthat the explicit positioning as \"computational super-resolution,\" along with our honest discussion\nof limitations, meets the appropriate standards for reporting computational SR methods.\nThe authors are particularly commended for conducting additional dual-camera validation\nexperiments—an effort that goes beyond mere textual revision.\nResponse:\nWe are particularly grateful for your recognition of our additional dual-camera validation\nexperiments. Your acknowledgment that this effort goes beyond mere textual revision is deeply\nappreciated, as we indeed invested significant time and resources to strengthen the experimental\nvalidation of our method.\nRemaining Concern\nThe use of decorrelation analysis for resolution estimation is understandable and not inappropriate\nper se. However, given that the authors have now explicitly framed this work as computational\nsuper-resolution, the limitations of this metric when applied to computational SR outputs should\nbe clearly discussed.\nDecorrelation analysis confirms the presence of high-frequency content but does not\nindependently verify its accuracy. Hou et al. (eLight 2024) demonstrated that deconvolved images\ncan show higher resolution by decorrelation analysis \"largely due to simple amplification of the\nhigh-frequency part\" while lacking fidelity. The 2020 Addendum to the original method\n(Descloux et al., Nature Methods) also acknowledges that image generation processes can influence\nresolution estimates.\nResponse:\nWe thank you for this important point. We agree that, when a method is framed as computational\nsuper-resolution, a single-image resolution metric such as decorrelation analysis should be\ninterpreted cautiously, because it primarily confirms the presence of high-frequency content rather\nthan independently proving its fidelity.\nFollowing your suggestion, we revised the manuscript to more clearly discuss these limitations in\nthe context of computational SR (Line 443-453, highlighted):\nIn the current study, we primarily employ decorrelation analysis to estimate image resolution;\nhowever, we acknowledge that this metric has limitations for computational super-resolution\noutputs. The 2020 Addendum to the original method notes that resolution estimates can be\ninfluenced by image-generation or post-processing steps (Descloux et al., Nature Methods, 2020),\nand Hou et al. (eLight, 2024) further demonstrated that deconvolution may yield artificially\nelevated decorrelation-based resolution largely through high-frequency amplification without a\ncorresponding improvement in fidelity. Thus, decorrelation analysis confirms the presence of high-\nfrequency content but does not independently verify its accuracy. To mitigate this risk, all SR images\nin our study were visually inspected at optimized iteration numbers to avoid artifacts prior to\ndecorrelation analysis; under these conditions, the resulting resolution estimates closely agreed\nwith FRC-based validation (Supplementary Fig. 4).\nSuggestion\nPart of this concern can be addressed using the authors' own dual-camera dataset. Cross-FRC\nanalysis between the CLID-processed outputs from the two cameras is strongly recommended.\nBecause the two cameras have different pixel sizes, algorithmically generated high-frequency\nartifacts would be pixel-grid-dependent and thus uncorrelated between the two outputs, whereas\ngenuine structural information would correlate. This provides more rigorous validation than\nindependent decorrelation analysis of each output and requires only re-analysis of existing data.\nIf the authors' claims are correct, cross-FRC should show correlation up to ~90 nm, corresponding\nto the resolution of the lower-resolution camera output. This would provide independent\nconfirmation that structural information in this frequency range is consistently recovered. The ~60\nnm claim, however, cannot be validated with this dataset. If the authors wish to further validate\nhigher frequencies, a dual-camera configuration with a smaller pixel size (e.g., using a 2× relay lens\nto achieve ~55 nm pixels) would be one possible approach.\nResponse:\nWe thank you for the suggestion to perform cross-FRC between the CLID outputs from the two\ncameras. We agree with the underlying intent (to test whether high-frequency information is\nconsistently recovered across independent measurements). However, we believe that cross-FRC is\nnot a rigorous or interpretable validation in our current dual-camera configuration, because the\ntwo cameras differ substantially in pixel pitch (65 µm vs 110 µm) and consequently produce images\nwith different sampling grids and different fields of view. Standard two-image FRC assumes that\nthe two images represent the same region of interest on a common sampling grid, with\nindependent noise realizations (Koho, S., et al. Nature Communications 10, 3103 (2019).). In our\ncase, to compute cross-FRC one would first need (i) geometric registration (translation/rotation and\npotentially distortion correction due to different effective magnification and FOV), and (ii)\nresampling of one image onto the other’s pixel grid (or onto a third common grid). Both steps are\nknown to affect the FRC frequency axis and correlation values because FRC computed from\ndiscretized images depends on the sampling step/pixel size and the numerical handling of the\ndiscrete Fourier domain.\nConcretely, Koho et al. demonstrate that if one plots FRC curves while incorrectly assuming the\nsame pixel size, the curves show an apparent frequency shift, and they explicitly state that the\ncalibration is needed to correct for different pixel pitch. This is directly relevant here: any cross-FRC\nbetween two differently sampled outputs is not “plug-and-play” and requires a careful\ncalibration/transform pipeline. Moreover, Pham et al. (closed-form FRC analysis) emphasize that\ndiscrete FRC depends on experimental/numerical parameters such as pixel size, and that the\naccuracy of discrete FRC is tied to the spatial sampling step and interpolation/aliasing behavior.\nImportantly, after resampling and registration, the resulting cross-FRC would no longer measure\nthe agreement of the native CLID outputs from each camera, but rather the agreement between\none native output and a geometrically transformed/interpolated version of the other. In such a\nsituation, cross-FRC becomes strongly confounded by (a) interpolation-induced\ncorrelations/spectral smoothing, and (b) residual registration errors, both of which can dominate\nthe high-frequency correlation decay and lead to under- or over-estimation that is not attributable\nto true optical/super-resolved structural information.\nFor these reasons, in our view the dual-camera dataset is well-suited for independent within-\ncamera validations (as we already performed: decorrelation analysis and FRC validation per\ncamera, Supplementary Fig. 4), but it is not ideally suited for cross-FRC as a decisive fidelity test\ngiven the large pixel-pitch mismatch and different FOV requiring nontrivial resampling/registration.\nFinally, we agree with the reviewer that, if one aims to validate frequencies beyond the lower-\nsampling channel, an improved dual-camera configuration with a smaller effective pixel size (e.g.,\nusing a relay to reach ~55 nm sampling at the specimen plane) would be a more appropriate\nexperimental design, because it would reduce the need for aggressive resampling and extend the\ninterpretable frequency range.\nRecommendation Regarding Resolution Claims\nGiven these validation limitations, stating a specific resolution figure in prominent locations is\npotentially misleading. The authors' decision to remove the specific number from the title reflects\nappropriate caution and is commendable. However, the claim of \"~60 nm resolution\" still appears\nin the Abstract. Consistent with the reasoning behind the title revision, I recommend removing this\nfigure from the Abstract.\nResponse:\nThank you for this valuable suggestion. We have removed the claim of \"~60 nm resolution\" from\nthe Abstract to maintain consistency with the title revision.\nReviewer #1 (Remarks on code availability):\nThe repository was not accessible at the time of review.\nResponse:\nThank you for bringing this to our attention. We have corrected the link, and the repository is now\nfully accessible.\nReviewer #2 (Remarks to the Author):\nAfter carefully reviewing the final revised version of the manuscript, I am pleased to note that the\nauthors have thoroughly addressed all the concerns raised during the previous rounds of review.\nThe revisions have substantially strengthened the manuscript, both in terms of methodological\nclarity and in the discussion of limitations and validation. I appreciate the authors’ careful and\nconstructive responses throughout the review process.\nResponse:\nThank you very much for your thorough and constructive feedback throughout the review process.\nWe greatly appreciate your time and effort in carefully evaluating our manuscript across multiple\nrounds of revision.\nWe are delighted to hear that the revisions have successfully addressed your concerns and that the\nmanuscript has been strengthened in terms of methodological clarity as well as the discussion of\nlimitations and validation. Your insightful comments and suggestions have been invaluable in\nhelping us improve the quality of our work.\nBefore final publication, I would kindly ask the authors to verify that the newly added\nsupplementary figures mentioned in the point-by-point response to the reviewers are properly\nincluded in the merged final document, as they do not seem to appear in the current. In addition,\nit would be beneficial to include zoomed-in views of selected images to better visualize the\nreported improvements as well as potential artefact-prone regions. Such magnified views would\nhelp readers more clearly appreciate both the gains and the limitations of the approach.\nResponse:\nWe have verified that the newly added supplementary figures mentioned in the point-by-point\nresponse to the reviewers are properly included in the merged final document. And as suggested,\nwe also included zoomed-in views of selected images to better visualize the reported improvements\nas well as potential artefact-prone regions.\nReviewer #3 (Remarks to the Author):\nThe authors have satisfactorily responded to my criticisms.\nResponse:\nWe greatly appreciate your thorough review and constructive feedback throughout the revision\nprocess. We are pleased that our responses and revisions have satisfactorily addressed your\ncriticisms. Thank you for your valuable time and effort in helping us improve the quality of our\nmanuscript."}]

Decision letter