Recover Cell Tensor: Diffusion-Equivalent Tensor Completion for Fluorescence Microscopy Imaging
Authors: Chenwei Wang
Zhaoke Huang
Zelin Li
Wenqi Zhu
Venue: ICLR 2026 Poster (2026)
Keywords: Fluorescence microscopy
Cell recovery
Tensor completion
Conditional diffusion
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Fluorescence microscopy (FM) imaging is a fundamental technique for observing live cell division—one of the most essential processes in the cycle of life and death. Observing 3D live cells requires scanning through the cell volume while minimizing lethal phototoxicity. That limits acquisition time and results in sparsely sampled volumes with anisotropic resolution and high noise. Existing image restoration methods, primarily based on inverse problem modeling, assume known and stable degradation processes and struggle under such conditions, especially in the absence of high-quality reference volumes. In this paper, from a new perspective, we propose a novel tensor completion framework tailored to the nature of FM imaging, which inherently involves nonlinear signal degradation and incomplete observations. Specifically, FM imaging with equidistant Z-axis sampling is essentially a tensor completion task under a uniformly random sampling condition. On one hand, we derive the theoretical lower bound for exact cell tensor completion, validating the feasibility of accurately recovering 3D cell tensor. On the other hand, we reformulate the tensor completion problem as a mathematically equivalent score-based generative model. By incorporating structural consistency priors, the generative trajectory is effectively guided toward denoised and geometrically coherent reconstructions. Our method demonstrates state-of-the-art performance on SR-CACO-2 and four real \textit{in vivo} cellular datasets, showing substantial improvements in both signal-to-noise ratio and structural fidelity.

Published as a conference paper at ICLR 2026
RECOVER CELL TENSOR: DIFFUSION-EQUIVALENT TENSOR COMPLETION FOR FLUORESCENCE MI- CROSCOPY IMAGING
Chenwei Wang*
Zhaoke Huang*
Laboratory for Artificial Intelligence in Design
City University of Hong Kong
Hong Kong Now181101@gmai11 com
Hong Kong
huangzhaoke@126.com com
Zelin Li
Wenqi Zhu
City University of Hong Kong Hong Kong
University of Oxford
United Kingdom
zelinli6-cem cityu. edu. hk
wenqi zww.mathummmtss.mmmmmmm ox ac
A ABSTRACT
Fluorescence microscopy (FM) imaging is fundamental technique for ob- serving live cell division, one of the most essential processes the cycle of life and death. Observing 3D live cells requires scanning through the cell volume while minimizing lethal phototoxicity, That limits acquisition time and results in sparsely sampled volumes with anisotropic resolution and high noise. Existing image restoration methods, primarily based on inverse problem modeling, assume known and stable degradation processes and struggle under such conditions, especially in the absence of high-quality reference volumes. In this paper, from new perspective, we propose a novel lensor completion framework tailored to the nature of FM imaging, which inherently involves nonlinear signal degradation and incomplete ob- servations. Specifically, FM imaging with equidistant Z-axis sampling is essentially tensor completion task under a uniformly random sampling condition. On one hand, we derive the theorctical lower bound for exact cell tensor completion, validating the fcasibility of accurately recovering 3D cell tensor. On the other hand, reformulate the tensor completion prob- lem as a mathematically equivalent score-based generative model. By in- corporating structural consistency priors, the generative trajectory is effec- tively guided toward denoised and geometrically coherent reconstructions. Our method demonstrates state-of-the-art performance on SR-CACO-2 and three real in vivo cellular datasets, showing substantial improvements in both signal-to-noise ratio and structural fidelity.
INTRODUCTION
Cell division is one of the most fundamental processes of life-it drives growth and repro- duction, yet also sets the stage for aging and death Sheldrake (1992)); Winter all (2023)). Observing the 3D membrane structure of cells during live cell division is essential for ad- vancing biological research Chung et all (2m1), which requires scanning through cell volume alone Z-axis with the aid of fluorescent dyes. To minimize lethal phototoxicity, the scanning time is strictly limited by XY-plane imaging at at equidistant intervals along the Z-axis. As result, 3D live-cell volume faces challenges like anisotropic resolution, and spatially varying noise, as illustrated in Fig. M These constraints significantly compromise the
"Atthors contributed equally to this work.
"Correspndiigg author.

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Published as a conference paper at ICLR 2026
spatial-temporal resolution of live-cell volumetric imaging, thereby impeding fundamental insights in a wide range of biomedical fields Woleti all (2019); ei all (2022).
Current most of image recovery algorithms are based the inverse problem Wang et al (2020), which aims to model the degradation mapping even the the degradation process is unknown. As discussed in prior studies, many of these methods rely supervised learning with known degradation models, requiring large paired datascts of high- and low-quality images, such as SRCNN Dong al (211 FSRCNN Dong et al. (201665) and DDPM He alal (2020a). These approaches are less suited to 3D fluorescence microscopy, where high- quality references are not available. To mitigate the reliance on paired data, unsupervised methods like CycleGAN Zhn et all (2mZ)), CinCGAN Yuan all (2U1), and Deep Image Prior Ulvanov et all (2018) have been proposed. Additionally, recent. efforts using self- supervised learning Ning et al. (2023); Quu et all (2024); Park.et.al (2022) and transformer- based architectures Li of all (2023a); Wang et all (20244) have shown promise. A more detailed discussion of related work is provided in Appendix C
However, FM imaging involves a noulinear and complex imaging process influenced by excitation, fluorescence emission and sample heterogeneity Lichtman & Conchelld (2005); Xu al (20224). This process is further complicated by high noise levels and incomplete signal acquisition due to attenuation and scattering. Traditional inverse problem methods, which rely on linear models and known physical assumptions Sol et all (21Pa)); IMo el all (2023); Hmi ct all (2022), struggle to accurately capture the underlying core pattern of 3D live-cell with such complexity. Under noisy or incomplete conditions with equidistant Z- axis sampling, these methods often become ill-posed and produce unstable or ambiguous reconstructions Yu & Elmokadem (2UT)); Genzel et. all (2022), as shown in Fig. M, which limits their reliability for life science applications. The details are presented in Section Ø
In this paper, we first highlight that most image restoration approaches grounded in inverse problem formulations may adversely affect the accuracy and fidelity of 3D cell recovery. Then, we propose cell tensor completion model, derive the cell-recovery bound and uncover its equivalence to conditional diffusion framework counter the evil. Specifically, our contributions are summarized as follows.
From a new perspective, we introduce a lensor completion model targeted for 3D FM imaging. This model not only aligns with the nature of FM imaging, like nonlinearily and incompletion, but also offers a principled framework for capturing the underlying structural patterns of cell volumes, enabling accurate 3D cell recovery. Furthermore, we derive the lower bound for exact 3D cell completion based on the proposed cell tensor completion model.
Through solving the proposed cell tensor completion model, we derive a mathematically equivalent score-based diffusion model by reformulating the low-rank tensor recovery as conditional generative process. This model is further guided by structural consistency priors to steer the generative trajectory toward accurate and denoised 3D FM reconstruction.
Evaluations on SR-CACO-2 and three real in vivo cellular datasets confirm that our method outperforms existing approaches, with clear gains in both SNR and structural fi- delity.
PROBLEM FORMULATIONS
2.1
3D FM LIVE CELL IMAGING
FM imaging is complex process involving light excitation, fluorescence emission, and diffraction through optical components Lichtman & Conchelld (200)), all of which are non- linear and influenced by diverse optical and biological interactions Xu el all (2022)). is further challenged by high noise levels such as optical noise, background interference, and low SNR-csppcially under low-light or high-speed conditions oi (20236).. Additionally, due to sample heterogeneity and signal attenuation scattering, the captured data often incomplete Pinkard et all (2021). An illustration the FM imaging process shown in Fig. MI
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Detector
Row
Bicubic
DBPN
Pinbole
Flacossnee
erzeere
Pinhole lens
Laser
Heamsplitter
Cycle+IPG
VOUME
Objective
Cell
The FM Imaging Processing
Artifacts and Noise levere Prohlem-Raved Mutheds
Figure 1: Illusraaioon of the FM imaging process and comparison reconstructed results across different methods. The schematic (left) shows the fluorescence imaging pipeline, where excitation light passes through optical components and interacts with the specimen before being detected. Raw observations are corrupted by noise and optical degradation. Reconstructed images using leverse-pooblem-iee suffer from hallucinated structures and residual noise.
methods (e.g., IPG, CycleGAN) often
Most of image restoration methods based inverse problem modeling typically assume linearity and well-defined physical models Sol all (2124), which fail to capture the non- linearities and sample complexity inherent in FM imaging Hui all (20221). Under noisy conditions, these models often become unstable Antain ef all (2020).
where minor input
perturbations lead to large reconstruction errors Genzel et all (2022). Such limitations re-
sult in unreliable reconstructions, which are unacceptable in life science applications, as demonstrated in Fig. M.
F(2:
(1)
where Is denotes the low-resolution image, İy is the high-resolution estimate, and F() represents the restoration model, approximating the inverse of the degradation process ((.). Although D is typically unknown and influenced by various factors, is often simplified
as single downsampling operation: 5) = (7y) 4s, where C å and 4. denotes
downsampling with scale factor s, typically via bicubic interpolation with antialiasing Wang
et all (212T).
Compared to inverse problem-based methods, tensor completion offers key advantages for FM imaging. In 3D FM cell scenarios with the nature of nonlinearity and incompletion, tensor completion effectively leverages the low-rank structure multi-dimensional data to recover missing information Goldtarb & Qin (2UJE) with inherent robustness to noise Wang et al] (2025), where inverse methods often suffer from instability. As a result, tensor completion yield more consistent and reliable reconstructions for downstream life science applications. More details of the motivations and advantages are presented in Appendix [
2.2
TENSOR COMPLETION MODEL FOR 3D FM CELL RECOVERY
The observed tensor Va can be decomposed into a underlying clean tensor and a residnal representing stochastic deviations:
(2) where X represents the structurally consistent volumetric fluorescence signal. While the physical imaging process follows a Poisson model, for the purpose missing-slice recon- struction, the additive abstraction in Eq. A is sufficiently expressive to capture the decom- position into coherent structural content and non-idcal perturbations (sec Appendix for a detailed physical derivation).
Y/2 X2 En.
From the above discussion, the basic tensor completion formulation is shown as follows: Specifically, given tensor T R x with observed entries index set Ω the recovery
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FM Imaging Nature 3D Live-Cell
Tensor Completion-MModelin min
|z|. + 2 || 2
P2( x=0
with observed
Noalinear Degradation
Tucker-D based Solution
3D Live-Cell
Incomplete
xr1 no. | - - 201-1"1 a
Observation
proc (26 -mm--
Tensor Complction
Reverse
Modeling
g n 22,0000 gom
Stage
Missing
(x"" - gnin)
Strictual
Consistmncy
Observed
Equivalence with Conditional Ditlusion
Priori
Noise
Results
High SNR
Exact Recovery
Bound
Structure
Fidelitty
(x
log')
SR-CACD-224 real cellular datasets
Conditional
Diffusion
Reformalate Conditional Diffusion
Figure Overview of the proposed framework. We first model 3D fluorescence microscopy (FM) restoration tensor completion task, capturing the nonlinear degradation and partial observation inherent FM imaging. Then, we reformulate this task into a math- ematically equivalent score-based generative process, revealing principled connection to conditional diffusion modeling. Finally, we introduce structural consistency priors to guide the generative trajectory, enabling accurate and denoised 3D cell volume recovery.
is formulated as the solution to the following convex optimization problem to recover X' that adheres to both structural priors and natural image characteristics:
min ||] s.t. Pa(X) Pa(T),
(3)
As 3D FM cell volumes are typically incomplete due the nonlincar imaging process, the sampling of cell entries in the tensor completion formulation, Pn(X), with an appropriate sampling distribution, effectively captures the incompleteness roducedd by fast volumetric scanning in FM imaging. To address the noise inherent in the FM imaging process, the tensor completion model should exhibit robustness to noise. Thus, we further optimize the formulation:
min || + A1|1|11
(4)
s.l. Pa Va, X
where || denotes tensor nuclear norm (e.g., tubal muclear norm), enforcing low-rank structure, ||8|]] penalizes sparse noise or corruption, Ps is the projection operator onto the observed entries.
By modeling 3D cell recovery as a tensor completion problem, becomes possible to more effectively address both the issue of missing entries and inherent noise in the cell tensor, thereby achieving better alignment with the imaging nature 3D cellular structures. It is worth noting that this formulation still lacks the capacity to capture the underlying pattern of the cell volume, which will be introduced in Scction 3.
2.3 LOWER BOUND FOR EXACT CELL RECOVERY
In this subsection, we derive the lower bound for exact cell recovery under the formulation of Eq. H, based on a sampling distribution that aligns with the characteristics of FM imaging.
First, we present the lower bound for exact cell recovery under the formulation of Eq. R and further extend it to the more general formulation given in Eq. g The lower bound for exact cell recovery under Eq. B is shown as below. To conserve space, the proof is provided in Appendix E.
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Theorem 1 (Exact Recovery Lower Bound under Eq. 3) Let be uniformly sam-
pled subset of [T] x... [Tk] and T be the solution to (1) with ōj vx.r./Ij. The reason of the sampling of FM imaging serving as a uniformly sampling is shown in Appendir [.
There erists conslant > O depending on k only so that P( - 7 2 1 - 1 if
1 max (r)()))())),
X 2 T. 1SiSk
(5)
and
n n: 2
2 (1 + B) (ve, + a, -= 2 k-1 T(log 1)2
(6)
1/21 ()-1///// 3//2 (log 1)
where = maxx Iz. denotes the effective rank of the tensor, and X is normalized rank scaling factor. Thus, the requirements of eract cell tensor recovery under is (( + r log" I).
Theorem 2 (Exact Recovery Lower Bound under Eq. 3) Let T X E R be tensor consisting of low-rank component X and sparse corruption E, with observed entries given by index set Ω C [T1] x ......... x [Tx]- Suppose the support of & is uniformly distrituted within S2 and sparsity level is |[ Then there exists constant
C > O such that evact recovery & X,E holds with high probability provided the number of observed entries satisfies:
Ω 2 C. (r/3/2 (r13/2+ llgg
(7)
where denoles the lensor rank and max max(11,.... (/,,.... Tx).
In the experiment section, we estimate the rank of the cell tensor and observe that, under the sampling rate of confocal fluorescence microscopy, the number of observed entries in the 3D cell volume exceeds the derived lower bound. This indicates the possibility of exact recovery for 3D cell structures.
PROPOSED SOLUTION
As discussed above, the robust cell tensor completion in Eq. B is better suited for handling FM imaging with nonlinearity and incompletion. In this section, we further provide principled solution to this optimization problem with capturing the core pattern underlying 3D cell. Then, we derive the equivalence between this solution and a conditional diffusion process, elegantly reformulating low-rank tensor recovery conditional generative process. The details of the proposed method can seen in Fig.
3.1 TUCKER DECOMPOSITION-DASEE SOLUTION
For Eq. [ the Tucker decomposition is effective tool it models the 3D FM cell through a low-rank core tensor and modc-specific factor matrices Kolda & Badei (2009)) This allows it to extract global spatial correlations, reduce redundancy, and isolate the dominant structural components across different dimensions timensions-mmking it particularly suitable for recovering incomplete and noisy 3D biomedical images. Then, the Tucker decomposition is shown as:
X= = x (1)) X2 (22) X3 U(3))
(8)
where G Xraxaa and (1)) xlaxa are the core tensor and factor matrices, respectively. The reformulated optimization becomes:
min G.(U())),E
|| + A1| s.t. Pa(g x1 U()) x2 (22) X3 1733) + E) -V2-
(9)
We decompose the original problem into subproblems and apply alternating update scheme over the core tensor, factor matrices, and sparse error. The update steps itera- tively refine the recovered tensor, gradually denoising and completing the missing entries.
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However, due to challenges in modeling noise and handling sparse sampling, closed-form solution is difficult to obtain under minimal assumptions.
We address this using the strategy detailed in Appendix E, which decomposes the problem into tractable subproblems and solves via alternating updates. The key processes are summarized as follows:
Inmls the sparse noise estimate g(,) and the dual variable ( we update the core tensor G(++1) by solving a least squares problem:
Step 1:
Update the core tensorg(*+1), Given the factor matrices (U())) |
(l++1) = arg min 1991 + 2 Pa (gx, Ua) X2 U22 X3 U g(0 cl0 D' -' -)+ (10)
-
where ( is the dual variable. Step 2: Update the factor matrix U("), Fixing the newly updated core lensor g((+1), we sequentially update each factor matrix ((x) by minimixing the projection error with respect to observed entries:
( arg
man min Pa (g ( ....... Xn U.... xa U + + ->) 1,2,3.
(11)
Step 3: Update the sparse noise tensor g(++1), After reconstructing the current estimate of the clean tensor, we update the sparse noise tensor g(++)) via the soft-thresholding operation:
g(++)) = Soft Softhhresholld (yo x -
- A())
(12)
where soft-thresholding is applied element-wise: Soft Thresholddd) = sign(x) max([=] 0). Step 4: Update the dual variable A ((++), To enforce the equality constraint in Eq, equa- tion BI, we update the dual variable using the standard ADMM rule:
(++1) = (0) + Pa (x + (((4))
(13)
Step Reconstruct the low-rank tensor (e++)) Finally, we reconstruct the full tensor estimate ((++1) using the updated core tensor and factor matrices:
x(++1 g((+1) X1 U()) X2 (2)) X3 U3)
(14)
As this optimization lacks a closed-form solution, it relics on iterative refinement. Interest- ingly, this multi-step update process mirrors the reverse dynamics of diffusion models. Moti- vated by this connection, we next. formulate conditional diffusion model that. incorporates structural consistency priors to guide accurate and denoised 3D FM image reconstruction.
3.2 EQUIVALENCE WITH CONDITIONAL DIFFUSION FRAMEWORK
Interestingly, the multi-step refinement process above in our optimization closely resembles the reverse trajectory of a diffusion model. Motivated by this observation, we establish theoretical equivalence between our iterative solution and a conditional diffusion framework. Let the observed 3D FM image tensor be represented as Vn2 = Xg + Eg, where Ω C (T] x [T2] x [Ta] denotes the index set of known entries, and εn is additive sparse noisc. The solution to the robust low-rank tensor recovery problem:
min X.E
|X||- + A11 s.t. Pa(x + + =Yn, X X20
(15)
where Tucker projection ((++1) serves as score-guided denoising, Sparse corruption g() models forward noise, and Observation Va provides the conditioning signal. Let X = G 1 (1) (2) X3 (3) be the Tucker decomposition of the clean latent tensor. Consider the following itcrative updates in ADMM Bai et all (2016); firstly, Tucker Projection Step (Structure prior inference):
x(++1) arg min M
x- - g( -00 A3)
(16)
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where Tucker denotes the low-rank Tucker manifold. This is equivalent to a MAP inference step under a Gaussian prior over X, constrained by the current denoised observation Kress ner et all (201Z)). In the language of diffusion models, this mimics the learned score-function V Vlog po (2 (2)) Sich-Dikktten all (2 Let 0 denote the learnable parameters of the diffusion model. Then, Sparse Noise Estimation (Forward process inversion):
g(++ prox (Jo - x(++1) ()n-
- ( )
(17)
which corresponds to soft-thresholding the residual, and is equivalent to denoising Gaussian- like noise in DDPM Ho ct all (20200). finally, Dual Variable Update (Lagrangian residual accumulation):
A (t-1) A + Pa(x((+11) -0+1))-))
(18)
Together, these three steps define deterministie Markov transition:
(x(0,e0)) + (egtt)))((+))))
(19)
which approximates the reverse sampling trajectory:
2--1 po c) + ///22,
(20)
in the diffusion process conditioned on input c= Va, with the difference that our method
achieves this without learning the score model, instead using manifold projections and prox- imal operators.
When solved via an ADMM framework using Tucker decomposition of X, yields an iterative sequence {x(0) that mathematically equivalent to a discrete-time conditional diffusion reverse process, i.., the Tucker-ber based iterative recovery process constitutes deterministic, optimization-driien analog of the conditional diffusion reverse chain:
1 1-
az co((2)))) + 012, Cee
21-1
It
(21)
Voi
V
where a 1- 81, and Bg is the noise variance added step t; ãe id defined the cumu- lative product: 0ę II. 0'si or is the variance of the Gaussian noise added back in the reverse process. This equivalence not only provides thcoretical insight into the optimization procedure but also motivates a principled generative framework for 3D FM cell reconstruc- tion. In the supplementary materials, we present the details of the conditional diffusion model with structural consistency priors.
4 EXPERIMENTS
We evaluate method three 3D fluorescence microscopy datasets, including SR-CACO- 2 Belbarb of all (2022)) and other in vivo collular volumes. We focus on two tasks: 3D super- resolution from sparse Z-axis sampling and denoising under low SNR conditions. Each of the three C. elegans embryonic datasets was characterized by a distinct trade-off between axial resolution, imaging speed, and biological viability. (1) C. elegans-1 features fast Z-axis scanning with only 30 axial planes and high laser intensity. This configuration is tailored for rapid volumetric acquisition in live-cell imaging, resulting in low axial resolu- tion but relatively clean lateral membranes due to strong excitation. (2) C. elegans-2 represents standard confocal acquisition protocol with 94 axial planes and medium laser intensity. It provides a balanced benchmark for morphological fidelity and phototoxicity, offering sufficient axial density for reliable 3D membrane geometry reconstruction. (3) C. elegans-3 employs high-density axial sampling with 200 planes. While it delivers the high- est axial resolution and cleanest volumetric membranes, its extreme phototoxicity makes it unsuitable for long-term full-lineage tracking, serving here near-ground -rutud- reference for volumetric consistency. Due to space limitations, a more detailed analysis provided in Appendix A
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4.1 MAIN RESULTS
We compare our method with state-of-the-art baselines SR-CACO-2 and two in vivo datasets using multiple metrics. The benchmarks include FM-specific and general restora- tion methods. We also provide visual results and analyze temporal consistency and perfor- mance distributions across datasets.
Table 1: Benchmark datasets used for fluorescence microscopy image processing.
Dataset
Volumes
Axial Res. (2)
Laser Intensity
Imaging Scenario
C. elegans-1
120
30
High
Fast live-cell tracking
C. elegans-2
220
94
Middle
Standard development
C. elegans-3
60
200
High
High-fidelity morphology
Table 2: Performance comparison of our method and other methods under SR-CACO-2 and two datasets in vivo cellular volumes.
Model
PSNR SSIMI LPIPSI
NIQEL
PIQEI
NRQM
C. elegons evaluation dataset 1
DBPN
31.89
0.6122
0.3941
19.05
44.43
4.23
Neuroclear
30.56
0.5798
0.6122
20.87
40.17
2.49
Cycle HAT
32.97
0.6236
0.4069
18.95
42.98
4.38
CyCle+IPG
32.17
0.6338
0.4640
19.97
41.50
4.36
DDPM (Baseline)
31.49
0.6157
0.4221
19.06
41.01
4.65
Ours
33.18
0.6682
0.3773
17.89
46.27
4.51
C. elegans cvaluation datasct 2
DBPN
37.91
0.9631
0.3872
19.11
46.11
3.95
Neuroclear
36.75
0.8405
0.5654
19.51
53.00
3.59
CIAT
39.86
0.9726
0.3648
20.53
48.64
4.51
Cycle + +IPG
37.92
0.9519
0.3138
19.37
46.46
4.69
(DPM(Buseline)
36.96
0.9766
0.3708
18.93
44.78
4.59
Ours
40.95
0.9868
0.2674
18.74
44.28
4.83
SR-CACO-2
DBPN
37.34
0.7871
0.5071
10.13
69.23
1.34
Neuroclear
33.93
0.7236
0.6182
11.78
88.30
2.74
Cycle+IAA
39.35
0.9313
0.3036
8.56
65.71
3.70
Cycle+IIPe +PG
39.82
0.9428
0.3369
8.85
66.27
3.87
(DPM(Daseline)
40.24
0.9447
0.3679
8.83
78.98
3.97
Ours
40.30
0.9476
0.2305
8.66
70.27
4.09
Rank Selection Strategy. Unlike samplc-spoeific tuning, we adopt a fixed multilincar rank (r),72,73) for each Z-axis downsampling configuration. The ranks are predetermined using truncated HOSVD on the training set to retain 95% of the energy. This ensures that the model exploits consistent structural redundancy patterns of the specific FM acquisition protocol without introducing test-time hyperparameter search or data leakage.
4.1.1 QUANTITATIVE COMPARISON WITH STATE-OF-THE-ARE METHODS
Table M compares our method with baseline models SR-CACO-2 and two in vivo cellular datasets. On all three dataset, our method achieves the best overall performance, with the highest PSNR, SSIM, and NRQM, indicating superior fidelity and perceptual quality. Compared to DDPM, we show clear improvements LPIPS and NRQM while maintain- ing comparable distortion-hased metrics. Specifically, C. elegans dataset 1, our method

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achieves the best PSNR/SSIM and strong LPIPS, offering good balance between percep- tual quality and structural accuracy. In C. elegans dataset 2, our method again achieves the top PSNR and SSIM, and outperforms all baselines in LPIPS, NIQE, and PIQE, confirming its robustness under real biological conditions.
Overall, the rosults highlight the strong generalization and reconstruction capabilities of our diffusion-guided framework across both synthetic and real-world microscopy data.
4.1.2 QUALITATIVE COMPARISON WITH STATE-OF-THIEARII METHONS
3D 3D/Slice ID/Slice/Zoommin /Zoom-in Visual Comparison. To evaluate structural fidelity and robust- ness, we compare reconstruction results at two representative time points (Fig. B). Un- der low-SNR conditions, raw inputs show heavy noise and blurred membranes. Bicubic fails to restore details, while DBPN introduces over-smoothing. Unsupervised methods like Cycle+IPG and Cycle+HAT often distort structures. Although Neuroclear improves sharpness, it lacks consistency. In contrast, our method reliably recovers continuous and biologically plausible membranes, preserving fine details and suppressing noise. These re- sults highlight the temporal generalization and structural accuracy of our diffusion-guided reconstruction.
Performance Statistics Analysis. We assess reconstruction quality on SR-CACO-2 and three C. elegans datasets using PSNR and LPIPS. As shown in Fig. B (a), our method yields high and stable PSNR, espocially SR-CACO-2 Fig. E (b) shows consistently low LPIPS across XY and YZ plancs, indicating strong perceptual quality. SR-CACO-2 achieves the lowest LPIPS, while C. elegans scores remain slightly higher due to structural complexity. The consistent, performance across planes highlights our methods robustness on anisotropic data and real biological volumes.
Temporal Robustness Analysis. We also evaluate the temporal robustness of our method on sequence of in vivo FM images from 2700s 5400s. Due low-SNR condi- tions, raw observations show severe noise and structural degradation. As shown in Fig. B our method consistently enhances structural fidelity and suppresses noise over time, demon- strating stable and reliable performance across extended temporal sequences.
Suppression of Artifacts and Hallucinations As illustrated in the 3D renderings (Fig. 3) and zoom-in comparisons (Fig. 5), texture- GAN methods like Cycle+IPG tend to create visually sharp but biologically implausible internal bright spots and artificial edges. These structures do not correspond to any known membrane organelle in the ground truth.
In contrast, method produces significantly fewer artificial details. By enforcing global cross-plane structural redundancy via the low-rank prior, our model ensures cross-slice geo- metric coherence. This is particularly evident in the YZ/XZ plane visualizations (Fig. 4 & 6), where our method maintains membrane integrity and topological consistency along the downsampled Z-axis, whereas baseline methods like DBPN and Cycle+HHA HAT often suffer from oversmoothing or broken structures.
Table 3: Performance comparison under in vivo cellular dataset with various noise levels and downsampling factors (C. elegans evaluation dataset 1).
Setting
PSNR
SSIM
LPIPSI
NIQE,
PIQE.
NRQM
Original (Clean)
33.18
0.6682
0.3773
17.89
46.27
4.51
+ Gaussian noise (o 0.01)
32.58
0.6427
0.3953
18.44
50.42
4.34
+ Gaussian noise (a 0.05)
31.26
0.6257
0.4253
19.86
57.58
4.01
Gaussian noise (r 0.1)
29.34
0.5921
0.4606
21.22
65.05
3.65
Downsampling x2
31.53
0.6354
0.4051
18.87
52.57
4.28
Downsampling
29.67
0.6102
0.4443
19.92
58.33
3.91
Downsampling
29.01
0.5955
0.4755
21.07
63.51
3.69

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Raw
DBPN
Neuroclear
Cycle+HAT
Cycle+IPG
Ours
qualitative denoising comparison of different methods on live 3D fluorescence microscopy volumes at the 2700s time point. Appendix A show the performance comparison at the 4950s time point.
Figure 3:
4.2 DISCUSSION
In this section, we further validate the effectiveness and rationality our model and meth- ods from multiple perspectives. First, analyze the distribution of cell volume ranks in the SR-CACO-2 dataset, showing that the number of observed entries slightly exceeds the theo- retical recovery bound we derived. Then, we evaluate the performance of our method under varying downsampling rates and noise levels, demonstrating its robustness to noise. As the downsampling rate increases, the number of observations falls below the exact recovery threshold, leading to noticeable drop in performance.
Rank Distribution of FM Cell. Figure shows that cell volumes exhibit a bimodal rank distribution, with dominant modes around 15 and 30. The average rank is 20.83, indicating varying structural complexity across samples. This highlights the need for adaptive low- rank modeling. Figure D displays the distribution of the lower observed bound for exact recovery. Most samples lic well above the theoretical bound for rank 10, suggesting sufficient observations for recovery in practice. However, the multimodal pattern implics that some samples may still challenge fixed recovery thresholds.
Performance Under Different Sampling Densities and Noise. As shown in Ta- ble 3 our method maintains stable performance under increasing noise and downsampling. PSNR and SSIM gradually decrease with higher noise levels and downsampling factors, while LPIPS, NIQE, and PIQE increase as expected. Despite these degradations, the qual- ity drops remain smooth and moderate, demonstrating the robustness of our approach in handling low-SNR and low-resolution conditions.
5 CONCLUSION
We propose a structuro-aware unsupervised method for 3D FM reconstruction, which refor- mulates lensor completion as conditional diffusion process. It improves denoising and axial resolution while preserving fine cellular structures, demonstrating strong performance across diverse in vivo datasets. Our method provides clearer observations, helping reveal biolog- ical patterns and support discoveries in developmental biology and disease understanding.
ACKNOWLEDGMENTS
This research is funded by the Laboratory for Artificial Intelligence Design (Project Code: RP2-2), Innovation and Technology Fund, Hong Kong Special Administrative Region.
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A DETAILED EXPERIMENTAL ANALYSIS AND MORE EXPERIMENTAL VALIDATION
Quantitative Comparison with State-of-the-Art Methods.
Table and Table Eprrseent a comprehensive comparison of our method against several baselines SR-CACO-2 and three in vivo cellular datasets. On SR-CACO-2, our method achieves the highest PSNR (40.30) and SSIM (0.9476), along with the lowest LPIPS (0.2305), indicating strong pixel-level and perceptual fidelity. Compared to DDPM, which shares similar generative backbone, our method yields improved perceptual quality (lower LPIPS and higher NRQM) and slightly better structural preservation.
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Raw
DBPN
Neuroclear
Cycl++HAT
Cycle+IPG
Ours
Figure 4: YZ (Yellow) and XZ (Blue) slice qualitative super-resolution comparison of dif- ferent methods on live 3D fluorescence microscopy volumes at the 2700s time point.
On the more challenging C. elegans datasets, our method remains competitive. In dataset 1, while IPC achieves the highest NRQM (5.06), it suffers from worse LPIPS (0.3040) and SSIM (0.6338), suggesting potential over-enhancement or structural distortion. Our method provides the best balance between distortion and perceptual quality, with load- ing SSIM and strong LPIPS and PSNR. In dataset 2, our method again attains the best PSNR (40.95), SSIM (0.9868), and LPIPS (0.2674), outperforming DDPM and Cycle-based baselines by a clear margin.
These results demonstrate that diffusion-guided approach generalizes well across syn- thetic and real biological volumes, delivering consistent improvements in both low-level fidelity and perceptual quality.
3D //Slicc/Zoonnee fidelity and robustness of our method, we conduct visual comparisons across full 3D recon- structions, individual slices, and zoomed-in regions at two representative time points (2700s and 4950s), as illustrated in Figure R. Raw observations under low-SNR conditions exhibit severe background noise and blurred or incomplete membrane structures, which hinders morphological interpretation. Bicubic interpolation fails to restore high-frequency details, resulting in oversmoothed textures and edge ambiguity. DBPN, despite leveraging deep residual learning, tends introduce over-smoothing artifacts and axial distortion due to cycles. Unsupervised approaches like Cycle-IPG IPG
Visual Comparison. To comprehensively evaluate the structural
its reliance on downsampling-upsaale and Cycle+HAT) HAT, although trained without paired data, frequently hallucinate unrcalistic structures distort membrane continuity, especially in low-intensity regions. Neuroclear improves visual sharpness but shows inconsistent local fidelity and introduces background artifacts in some areas. In contrast, method consistently reconstruets continuous and biologically plausible membrane structures, effectively suppressing noise and restoring fine cellular boundaries. The zoomed-in comparisons clearly reveal models advantage in pre- serving edge integrity and subcellular continuity across time. These results demonstrate that our iiffusiin-guiiled framework generalizes well temporally and capable of maintaining high spatial fidelity even under challenging acquisition settings.
Performance Statistics Analysis. We further assess the reconstruction quality of our method using quantitative metrics across diverse datasets. Specifically, we evaluate both perceptual and distortion- based performance using LPIPS and PSNR on the SR- 2R-CACO-2 dataset and three C. elegans volumes. As shown in Figure (aa). PSNR values remain high and stable across both XY and YZ planes, with SR-CACO-2 showing the highest scores and lowest variance, reflecting relatively clean and uniform structure. The C. elegans datasots, which feature higher structural complexity and natural variability, exhibit moderately lower PSNR values but maintain consistent distributions across both spatial planes. Figure B(b) shows that LPIPS values are consistently low, indicating strong perceptual similarity to ground truth. SR-CACO-2 again achieves the lowest median LPIPS, while the C. elegans datasets show slightly higher scores, likely due to their more heterogeneous and detailed biological morphology. Notably, the similarity of performance between XY and YZ planes
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Raw
DBPN
Neuroclear
Cycle+HAT
Cycle+IPG
Ours
Figure 5: 3D/XXsslicezoom-in qualitative denoising comparison of different methods on live 3D fluorescence microscopy volumes the 4950s time point.
Raw
DBPN
Neuroclear
Cycle+HAT
Cycl++IPG
Ours
Figure 6: YZ (Yellow) and XZ (Blue) slice qualitative super-resolution comparison of dif- ferent methods on live 3D fluorescence microscopy volumes at the 4950s time point.
across all datasets suggests that our method handles anisotropic imaging characteristies elfectively. These quantitative results affirm the generalizability and robustness of our re- construction framework across both synthetic and real-world biological imaging data.
Temporal Robustness Analysis. To evaluate temporal consistency, we apply our method to reconstruct dynamic sequence of in vivo FM volumes captured between 2700s and 5400s. This time interval corresponds to prolonged imaging under low-SNR conditions, where pho- ton exposure is limited to preserve cell viability. As shown in Figure M, raw frames pro- gressively degrade in signal quality, with increasing noise and weakening structural clarity. Despite these challenges, our model consistently produces clean and high-fidelit recon- structions over time. Membrane structures remain continuous, and noise accumulation is effectively suppressed, even later frames with lower signal strength. This demonstrates methods robustness against temporal variations in image quality and confirms its ap- plicability in long-term live-cell imaging scenarios where maintaining structural coherence time is critical.
Rank and Recovery Bound Analysis. We conduct a statistical analysis of tensor rank and observation sufficieccy across the dataset to validate the theoretical assumptions un- derlying our model. Figure Ø(a) presents the rank distribution of cell volumes, revealing bimodal pattern with peaks around ranks 15 and 30. The mean rank 20.83 with no-
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ieforedd ioe Cot,
Eound othe ran
(a) Distribution of Cell volume rank
(b) Distribution of lower observed bound
Figure 7: Distributions of cell tensor ranks and lower observed bound [ for exact cell recovery across the dataset.
table variance, reflecting the diverse structural complexity of cellular data. This variability underscores the importance of adaptive rank modeling rather than fixed-rank assumptions in volumetric restoration. Figure (bb)) shows the distribution of the lower observed bound [[] required for exact recovery. Most samples exceed the theoretical threshold for rank 10, suggesting that the empirical observation densities are sufficient to ensure theoretical recov- erability. However, the presence of a long-tailed, multimodal distribution also indicates that a subset of samples remains challenging, particularly those with higher rank or less complete obscrvations. These insights justify and diffusion framework that can adapt to the structural and observational diversity in real-world fluorescence microscopy data.
design of flexible, data-aware tensor completion
Robustness to Noise and Downsampling. Table & summarizes the performance of our method under various levels of Gaussian noise and downsampling factors, based on the C. elegans evaluation dataset. Starting from clean inputs, we observe a gradual degradation in reconstruction quality as noise intensity inercascs. PSNR drops from 33.18 (clcan) to 29.34 under a 0.1, while SSIM falls accordingly from 0.6682 to 0.5421, reflecting in- creased structural distortion. LPIPS also rises with noise, indicating reduced perceptual similarity. Meanwhile, NIQE and PIQE, as no-reference metrics, increase consistently, cap- turing the ual degradation introduced by noise. A similar trend is observed with increasing downsampling factors. PSNR and SSIM degrade from 30.53 and 0.6154 at x2 downsampling to 28.21 and 0.5255 at x4, respectively. Perceptual quality metrics such as LPIPS and NRQM also indicate reduced fidelity at higher compression levels. Despite these degradations, our mothod maintains relatively stable performance across all scttings, with smooth and interpretable declines. The results demonstrate the robustness of our model under practical imaging degradations, including low-SNR conditions and resolution loss.
Limitations and Future Work. While method demonstratts strong performance across multiple datasets, it has primarily been evaluated on fluorescence microscopy data. Further validation on other bio-image modalities would help assess generalizability. Additionally, although the current framework shows stable performance under noise and resolution degra- dation, integrating weak supervision or modality priors may further enhance adaptability. Future work will explore broader datasct coverage, improved robustness, and optimization for computational efficiency.
We also evaluate the temporal robustness of our method using a sequence of in vivo fluo- rescence microscopy images captured over time, from 2700s to 5400s. The raw observations suffer from high noise and degraded structural details due to prolonged imaging under low- SNR conditions. Our method is applied frame-by ba-eeby-frame frame to reconstruct the clean high-fidelig volume across this time scries.
As illustrated in Fig. 9. our method consistently improves structural fidelity and effectively suppresses noise throughout the sequence. Notable enhancements observed across all frames, with particularly clear improvements from 2700s to 5400s. This demonstrates the model's ability to maintain stable and reliable reconstruction performance under challeng-
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1.-
MICD COOO O Go CO
50
14-
45
1,0
1985
40-
0.8
35
30
0.2
25
xy
Coelegass
c.llegnns:
Bleggans
SP-CACO-2
C. Celegans Dataset Name
Celegans 2
elegans 3
(b) LPIPS distributions across XY and YZ
(a) Violin plots of PSNR values for SR- planes for SR-CACO-2 and three C. elegans CACO-2 and three C. elegans datasets.
datasets.
Figure 8: Performance statistics analysis across XY and YZ planes for SR-CACO-2 and three elegons datasets.
Table 4: Performance comparison of our method and other methods under SR-CACO-2 and two datasets of in vivo cellular volumes.
Model
PSNR SSIM1 LPIPSI
NIQE
PIQEI
NRQM
C. elegans evaluation dataset 3
DBPN
32.84
0.6984
0.3956
16.85
52.91
2.60
Neuroclear
31.51
0.7339
0.3665
16.23
54.00
1.88
Cycle+HAT
33.96
0.8053
0.2077
16.06
48.97
2.09
Cycle+IPG
33.22
0.7881
0.1995
15.36
48.68
2.50
(BPselaslline)
33.43
0.8037
0.1986
15.94
53.48
2.24
Ours
34.81
0.8174
0.1168
12.11
47.53
2.97
ing conditions and extended temporal acquisition periods. The results validate the temporal consistency and robustncss our diffusion-guidedd reconstruction framework.
B MOTIVATION
Cell division is of the most fundamental processes of life-it drives growth and repro- duction, yet also sets the stage for aging and death Shelrakd I); Winter et all (202a)). Understanding this process at the structural level crucial for advancing research in areas such as developmental biology, oncology, and regenerative medicine. Observing the 3D mem- brane structure of cells during live cell division especially important, the membrane plays a central role in maintaining cellular integrity and mediating dynamic interactions Chung et all (2 This observation typically involves volumetric scanning along the Z- axis, where high-resolution XY-plane images are acquired al equidistant depths with the help of fluorescent. dyes.
To minimize lethal phototoxicity during this process, the scanning time must be strictly limited, reducing the number of axial slices and the overall imaging intensity. As a result, 3D live-cell imaging often suffers from anisotropic resolution and spatially varying noise, particularly in deeper or faster-acquired slices, as illustrated Fig. MI These constraints significantly limit the spatial-temporal fidelity of the captured volumes, making it difficult to reconstruct fine membrane structures or dynamic changes. This, in turn, impedes fun- damental insights in wide range of biomedical fields Volefi all (2mTg); Li et all (2025).
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Table 5: Superresolution performance on the SR-CACO-2 test set (full image).
PSNR (1)
NRMSE (1)
SSIM (1)
SISR Method
CELLO
CELLI
CELL2
Mean
CELLO
CELLI
CELL2
Moan
CELLO
CELLI
CELL2
Moan
Bicubic
41.76
38.22
37.07
39.02
0.0383
0.0286
0.0337
0.0335
0,9470
0.9233
0.9128
0.9277
Preupsampling SR
SRCNN Dong
37.50
37.39
36.99
37.33
0.0650
0.0319
0.0340
0.0436
0.7103
0.8137
0.8419
0.7893
VDSR
43.14
39.08
38.53
40.25
0.0812
0.0251
0.0279
0.0281
0.9611
0.9118
0,9381
0.9470
10
DRRN
1m
43.14
39.03
38. 13
40.20
0.0810
0.0253
0.0282
0.0282
0.9623
0.9108
0,9361
0.9465
12:111
MemNel
41.39
36.23
36.89
38.17
0.0390
0.0374
0.0345
0.0370
0.9463
0.7588
0.9096
0.8716
(A13
Postupssmplligg SR
NLSN
39.58
138.12
37.40
38.37
0.0505
0.0286
0.0324
0.0372
0.7986
0.8816
0.8756
0.8519
10 (412241)
DFCAN Aipc
43.19
39.12
38. 26
40.19
0.0307
0.0260
0.0287
0.0281
0.9641
0.9422
0.9194
0.9419
(MTAATT
Swin1R Lrans
42.00
33873
38. 23
39.65
0.0347
0.0263
0.0291
0.0300
0.9257
0.9238
0,9266
0.9253
(
37.48
36.80
37.81
37.38
0.0856
0.0335
0.0289
0.0427
0.7034
0.8008
0,9323
0.8122
KNI.CN
40.03
38.33
37.74
38.70
0.0476
0.0278
0.0309
0.0054
0.8221
0.8929
0,9946
0.9699
13:
41.74
36.18
37.80
38.50
0.0370
0.0374
0.0311
0.0051
0.9115
0.7372
0.9681
0.8389
[co13
39.07
36.76
35.36
37.07
0.0542
0.0345
0.0120
0.0436
0.7717
0.7813
0.7411
0.7647
8:111
42.14
38.63
37.94
39.57
0.0352
0.0265
0.0301
0.0306
0.9488
0.9813
0.9209
0.9337
2-1119
(442463
Herratvv upanddown sampling SR.
37.87
36.19
35.96
37.34
0.0634
0.0284
0.0386
0.0435
0.7108
0.8772
0.7735
0.7871
20
SRFEN
42.24
38.20
37.07
39.17
0.0358
0.0286
0.0339
0.0328
0.9498
0.8993
0.8802
0.9098
Progressive upsampling SR
41.65
36.61
38.08
39.45
0.0376
0.0267
0.0295
0.0813
0.9050
0.9044
0.9095
0.9063
11
MSL MSN
30.99
31.81
33.69
32.16
0.1277
0.0657
0.0193
0.0809
0.4628
0.5500
0.6905
0.5678
11
O Ous
41.59
38.47
10.98
40.30
0.0228
0.0276
0.0198
0.0254
0,9581
0.9348
0,9562
0.9475
Time=2700s
Time=3150s
Time=3600s
4050=4050s
4500=
T95o=4950s
T4me=5400s
Raw
Ours
<>
Figure 9: Temporal comparison of raw observations and our reconstructed results at mul- tiple time points. The proposed method consistently enhances structural fidelity and sup- presses noise over time, particularly under challenging low-SNR conditions. Improvements are evident from 2700s 5400s, demonstrating the robustness of diffusion-guidee construction across the temporal sequence.
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FM imaging involves sophisticated and multi-stage imaging process that includes light source excitation, fluorescent signal emission from labeled samples, and diffraction and de- tection through optical elements such as objective lenses and detectors Lichtman & Conchella (200)); k et all (200m). Fach stage introduces its own set of nonlinearities and complex- ities, which are further compounded by intricate interactions between light and biologi- cal tissue such as multiphoton absorption, scattering, and refractive index mismatches Xui et al (2122). These interactions distort the original signal in ways that are difficult to model analytically. In addition, practical imaging conditions introduce significant noisc sources, including optical noise from detectors, autofluorescence from surrounding tissues, and background interference from out-of-focur regions. Particularly in live-cell imaging, low excilation power required to minimize pholotoxicilyy, resulting in low signal-to-noise ratios (SNR), especially under fast. volumetric scanning or time-lapse acquisition Li all (202817); Mandhacdhiaa et al (212M). Compounding these challenges, the biological structures being imaged are often highly heterogeneous and dynamic, leading to signal attenuation, scatter- ing, and partial transmission that result in spatially incomplete or missing data Piinkadd al (2IZT). These issues collectively render the fluorescence microscopy (FM) imaging process highly nonlinear, noisy, and partially observable. An overview of this process is illustrated in Fig. M
Inverse problem-based methods have been widely adopted to restore degraded images by mathematically modeling the imaging process as forward degradation operator and esti- mating its inverse. However, such methods typically rely on simplified assumptions most often that the degradation is linear, spatially invariant, and governed by known and stable physical models Mo ct all (2023); Sol_ct all (2023). These assumptions may hold in well- controlled synthetic scttings, but they fall short in the context of FM imaging. The nonlincar optical transfer functions, sample-dependent variability, and the unpredictable effects of bi- ological environments render inverse formulations insulficient to capture the true complexity of FM imaging. Moreover, under realistic conditions characterized by low SNR and sparse observations, these inverse problems become severely ill-posed: small variations or noise in the input can lead to disproportionately large errors in the output, making the recon- struction process unstable and unreliable. As a result, obtaining high-quality, artifact-free reconstructions using traditional inverse approaches is extremely difficult-an issue partic- ularly critical for life science applications, where precise structural fidelity is essential for downstream analysis and biological interpretation, as highlighted in Fig.
C RELATED WORK
C.1 DEEP LEARNING DRIVEN IMAGE RESTORATION
Deep learning has revolutionized single-image super-resolution (SR) by introducing architec- tures that jointly improve image fidelity and computational throughput. Early convolutional neural network (CNN) approaches such as SRCNN demonstrated that end-to-end feature learning can outperform traditional interpolation Dong et all (2016)) while deeper architec- tures like VDSR showed that residual learning facilitates faster convergence and higher peak signal-to-noise ratios Kim et all (20T6))) Subsequent models, for instance EDSR, removed unnecessary components to streamline performance on high-resolution (HR) reconstruction tasks Lim (2017a).
Building on these foundations, attertion-augmeented CNNs learned to prioritize salient im- age regions, refining perceptual details and structural consistency Zhang et al. (2MT)); Dai al (2u1). Generative adversarial networks (GANs) further advanced SR by introduc- ing a discriminative component that drives the generator to synthesize realistic textures and finoscale details, leading to more visually convincing outputs Ledig et al] (2017); Wang ef all (20115: 2112T).. More recently, Transformers have introduced long-range dependency modeling, improving feature representation and global context learning Chen al. (2021; 2023: 2022);: (Choi et all (2022); Liang et all (2021a);; Zhon et. all (2022). IPT IChen et all
(2021) showcased the potential of large-scale pre-trained Transformers, while SwinIR, Liang
(2021a) leveraged hierarchical Swin Transformers [Lu et all (202T) for multi-scale
processing.
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Beyond these architectures, emerging directions in SR research include graph-based methods that encode pixel relationships as graph structures Tian et all (2024)), diffusion probabilistic models that iteratively refine noisy estimations Zheng et all (20221); Lee et all (2024)); Wang el all (2022r) and settionar-llarinng approaches that learn sparse representations for re- construction [Wang al] (20ZE)). While these techniques offer promising gains, they often demand extensive paired datasets or encounter stability challenges during training. As the field advances, ongoing work aims to enhance data efficiency, robustness to diverse degrada- tions, and runtime efficiency to bridge the gap between rescarch prototypes and deployable SR systems.
C.2 SR OF 3D FLUORESCENCE MICROSCOPY
Achieving superresolution in 3D fluorescence microscopy remains challenging due to anisotropic optical blurring and low signaltonoise ratios. A range of deep learning approaches has been proposed to tackle these issues by exploiting both spatial and frequencydomain priors. For instance, DFCAN Qiao all (2021a) employs a multiscale frequency extraction module to recover fine structural details, while OTCycleGAN [Park aLal (2022) integrates 3D optimaltransport objectives into an adversarial framework lo enforce rsot resolution restoration. SelfNet Ning et. al. (2023) takes advantage of inherent highresolution lateral views by learning a crossaxis mapping that refines axial detail. In parallel, TCAN Huan al ((IZk) introduces dualchannel attention mechanism that selectively emphasizes in- formative features from both spatial and channel dimensions. More recently, SN2N Qu al (2022) adopts selfsupervised Noisc2Noise strategy to denoise and upsample without ground-truth highresolution volumes, improving robustness across imaging modalities.
Despite these advances, many methods underuse the rich structural priors present in 3D cellular data. A notable example is the SimCLIR-inspired model by Qiao et al. Qiao et all (2122)), which jointly learns denoising and superresolution objectives but falls short in fully leveraging volumetric context, leading to occasional instability and less accurate reconstruc- tions. A detailed comparison provided in the experimental soction.
C.3 TENSOR COMPLETION AND TUCKER DECOMPOSITION
In recent years, recovering high-dimensional data from incomplete or damaged observations has become key challenge. Tensor completion generalizes the matrix completion problem to higher-order arrays by exploiting low-rank structure across multiple modes. The field was catalyzed by the success of low-rank matrix complction via muclear-norm minimiza- tion, which proved that one can exactly recover low-rank matrix from a small subset of its entrics. Building on this foundation, carly work extended convex relaxation to tensors. Lin Limeet al (2012) introduced the early definition of a tensor trace norm (as the sun of nuclear norms of matricizations) and formulated lensor completion as a convex program. They developed effective algorithms e.g. Simple, Fast, and High-accuracy Low-Rank Ten- sor Completion (SiLRTC, FaLRTC, HaLRTC) to solve tensor trace-norm minimization in visual data. Gandy et. all (2IlT) likewise proposed recovering low-n-rank tensor (low rank in every mode) via convex optimization, treating the multi-dimennional case as a nat- ural extension of matrix completion. These seminal methods demonstrated that missing entries in multi-way data (images, videos, etc.) can be accurately imputed by enforcing low multilinear rank. Beyond convex approaches, researchers explored direct factorization strategies. For example, Jain &r Of (20114) proposed an alternating least-squares scheme (analogous to CP decomposition) with provable guarantees, showing that Under the stan- dard p=incoherence assumption, we prove that through the alternating minimization algo- random observations are needed to uniquely and exactly
rithm, only ((fFr"n3/2(log reconstruct rank-r orthogonal third-order tensor. Such developments spanning convex relaxations and nonconvex alternating optimization have established tensor completion as rich rescarch area.
The Tucker decomposition provides a foundational model for multi-way low-rank struc- ture, essentially serving higher-order form of PCA. First introduced by [ucker (19966) as three-mode factor analysis and later formalized as the higher-order SVD (HOSVD) by De Lathauwer el. all (200)). Tucker decompasition expresses tensor as a small core tensor
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multiplied by orthogonal factor matrices along each mode. This multilinear factorization was soon leveraged in tensor completion to enforce low Tucker rank. Early convex ap- proaches implicitly used Tuckers idea by minimizing the muclear norms of unfolded tensors the closest, convex proxy to Tucker rank Lu et all (2019). While such relaxations are theoretically appealing, an alternate line of work directly applied Tucker factorization to incomplete tensors. For instance, Filipovie & Jukid (2 proposed an ALS-based Tucker decomposition algorithm for tensor completion, showing it can recover tensors even when the assumed ranks are higher or lower than the true ranks. Their tncker-based method was demonstrated small fraction of entries is observed, underscoring Tuckers praclical efficacy in extremely sparse settings. In parallel, optimization on the manifold of fixed multilinear rank tensors has been developed to handle Tucker models efficiently. Kressner et all (2mTl introduced a Riemannian conjugate gradient scheme on the manifold of tensors of fixed Tucker rank, achieving scalable performance and accurate recovery even when the vast majority of en- tries are missing. The Tucker decompasitions solid theoretical basis capturing multi-mode interactions via core tensor and its strong empirical performance (e.g. in image in- painting and hyperspectral data recovery) have made it cornerstone in tensor completion research. By combining Tuckers multi-linear algebra principles with modern optimization techniques, these works have significantly advanced the state-of-ther the---rrtt offering methods with both deep theoretical guarantees and high practical impact in multi-dimensional data reconstruction.
outperform nuclear-norm minimization approaches when only very
D GENERALIZATION VS SPECIFICITY
In this section, we provide detailed discussion clarify the motivation, scope, and im- plications of adopting structural priors in our model, in response to concerns about the generality and applicability of our approach.
Motivation for Structural Priors in Biological Imaging. Unlike general-purpose im- age restoration tasks where input data may exhibit highly diverse and unstructurod content, our work focuses on fluorescence microscopy (FM) imaging of model cellular systems, partic- ularly epithelial cell lines like Caco-2. These cells are known to exhibit strong morphological regularities, such rounded membrane contours and consistent spatial organization across samples. These regularities are not incidental, but instead rooted in biological mechanisms such as cell polarity and tissue architecture.
Given this domain-speciffi consistency, incorporating a structural prior is not only reason- able but also scientifically motivated. It enables the model to leverage biologically meaning- ful constraints, reducing noisc-induced ambiguity and promoting faithful recovery of collular morphologycritieal for downstream tasks such as segmentation, tracking, and mitotic spindle orientation analysis.
Trade- Off Between Generality and Reliability. We acknowledge that structural priors learned from the training data may not generalize well to arbitrarily structured images outside the cellular domain. However, our design intentionally sacrifices some degree of generality in favor of domain-specific reliability. In cellular imaging, even minor geometric distortions can compromisc biological interpretation. Therefore, we prioritize structural fidelity over universal applicability.
Moreover, general models that assume arbitrary structures often introduce randomness or deformation in the restored outputs, particularly under heavy noise or undersampling. This can severely limit their utility biomedical contexts, where precision and reproducibility are essential.
Domain-Scoped Applicability and Broader Value. It is important to emphasize that our method is designed for specific yet widely relevant domain: long-term FM inaging of model organisms in biomedical research. While it may not apply to all imaging domains, it holds significant value within its intended scope. For example, Caco-2 and similar epithe- lial cell lines are broadly used in drug testing, cell biology, and tissue engineering, where consistent structural modeling is highly advantageous.
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of structural priors is principled design choice aligned with the charac- teristics and needs of this domain, rather than an arbitrary or overly narrow constraint. Future extensions may explore ways to adaptively relax the prior or incorporate uncertainty modeling to broaden applicability.
Thus,
E
PROOF OF EXACT TENSOR COMPLETION REQUIREMENT
E.1 EXACT RECOVERY GUARANTEE FOR INCOHERENT TENSOR COMPLETION
We restate the recovery problem
min
s.t. Pa(x) PP(()) ||*
X
and prove that uniform sampling with
[|] ((1 + 1)
is sufficient for exact recovery with high probability.
Let T be the tangent space T in Tucker format and Qr, Q the orthogonal projections onto T and T-. Define
dh
k
1/(k-1
max [Qr(e,, .... ... @ &eiss r. H. kr d Frrey
kd
and (d. 122 max: where Wo is sub-gradiens of [| The incoherence straint requires μa, = O(1), a2 = O(1). Here, h is the tensor order, I = max, I is the maximal mode dimension, r = max, (T( the maximal Tucker rank, = 1o Σ, L is the arithmetic mean and d. (II, 1,) is the geometric mean.
Lemma (sufficient condition) If there exists 9 E Range(Pa) such that
Vn/(2d,)
11Qr Wo)llss -
(A1)
k:k
10+-11 <1 kik 1)²
1
(A2)
1Qr ( Ps lHss-ss 1
(A3)
then the minimiser of equation g is unique and equals T.
The proof is a direct adaptation of Lemma D in Yuan & Zhang (2016) which proceeds in three key steps.
Step 1: Sampling Operator Concentration
For Ω sampled without replacement,
72/2
P(11Qr ( Pn - IIlrrllss--- -Hs 27) r} < 2k -
+ 27/3 kpwr k- -ld
Setting 7= and demanding the RHS < T- yiclds
n 2 cx + nr, k- log
(B)
Step 2: Golfing-Scheme Construction
Split Ω Jن U2 with |22 ni (so n nin2) and define
R₂ = I df Pu, Wo Wo. W, QTR,QrW,---
n1 WE
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The candidate dual certificate is 9 Σ}= R Tangent-space contraction. By matrix Bernstein,
|W & W'lloollss with 7 kuur k-1 dlog I
R1
Choose n1 r I 1.4 Taking n2 c2 log ensures Eq. equation A
Orthogonal-space leakage, For the max-norm we invoke Lemma 3.3 of Yuan & Zhhan (20T0): with 2 p(k-1)/2 f3/2 I and log J, condition Eq. equation A2 is satisfied with high probability.
Step 3: Sample-Size Consolidation
Combine the two requirements on 11, 712:
R1 Z (ux + - k-1 (log 1)2 + a, X 1/2-1
r* (/-1)/2 1)/2 13/2 (log 1)².
Under the mildincoherence regime F4, Cr. X. = 0(1) and r. ( this simplifies (for ( + I2 log I),
k = 3) to
completing the proof.
E.2 EXACT RECOVERY GUARANTEE FOR ROBUST TENSOR COMPLETION
We extend the dualcertificate argument of Yuan & Zhang (2016) to the robust setting where the observation T X' + contains lowrank component X' and an entrywise sparse component E.
Step 1: Dual Programme. The Lagrangian of equation B is
((X,E,9) = || + A A1||E11 + (G. with dual constraint Pn(G) = 9, |Pr(9))22 < 1, ||P (9) S d1- Exact recovery is guaranteed if we can find dual certificate 9 satisfying the above constraints and Prg Wo. Pağ = G.
-))),
Step 2: Golfing Scheme. Split the sample set Ω - 26 recursively
[Stll and define
Wo Wo, Wr Q I di EPu QTW--1. m
Set 9 Ete
(I-4)
d' Ewenn We-1.
Step 3: Control on the Tangent Space. MatrixBernstein gives
|[elllss - ( [Wolls m z ur
1log
With L, = O(lg 7) have || Wo)l T-9
Step 4: Control on the Orthogonal Space and Sparsity. For any fixed tensor 2 with and supp(2) 2) C Ω, Hoeffdingtype bounds yield
[[Pr 21 <
log = O(T (Pr ( S av
provided m 2 (k 1)/2 log I. Since the support of is uniformly random and size s,
a union bound ensures 1Pr_ < Y₁ as long as m 2 slog 1.
Step 5: RIP Sparse Part. Define Ps as the projection onto entries in S supp(E). Standard couponcollector arguments give
d n
P - -Pall----- = n n slog
Step 6: Collecting Bounds. Pick to satisfy simultaneously
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1. 2 pr
pr ko log I;
2. 2 (1k-1)/233/1 log 1;
3. m Z s llog I.
With L (log 1) the total sample size n mL obeys
Ω = O (r (k/1)/2 13/2//23///2_/ + 5) log log²1).
For the most common case k 3 this becomes [0]] 0(()2 +) 1). Absorbing
constants and taking max, rj gives
| 2 C(r13/2 + log" I,
completing the proof.
F PROPOSED SOLUTION: TUCKER DRCOMPOSITTON-BASEE) TENSOR COMPLETION
This section provides the alternating-directinn method of multipliers (ADMM) that use to tackle the robust censor-complette objective in Eq. equation g We first motivate why Tucker dccomposition and ADMM are natural partners for fluorescence volumes, then guide the reader through every mathematical stepsprinkling cach derivation. We close with a convergence theorem and fully annotated algorithm.
F.1 WHY TUCKER, AND WHY ADMM?
Fluorescence microscopy (FM) data contain two complementary structures:
1. a global, lowrank backbone that reflects optical blur and the smooth nature of bio- logical tissue; and
2. sporadic, high--mplllude oulliers triggered by photon shot noise and electronic glitches.
Tucker decomposition excels at capturing the backbone with a tiny core and three thin mode matrices (T(m). ADMM, in turn, lets peel the two structures apart by alternating between a lowrank projection (to refine the backbone) and a sparse shrinkage (to trap outliers). The result is solver that is both mathematically transparent and computationally light-
F.2 PROBLEM IN TUCKER COORDINATES
Denote by Ω the set of measured voxels and by Pa the projection that keeps only those entries. We assume
= X1 (1)) X2 (2) X3 U3))
((TT I,,;
where the ranks (r1, T2, 13) satisfy Tn < In. The compst-co objective becomes
min G.(U
|| A 11|1
(22)
s.t. Pr 2 + E) = Vn.
Z 320 0.
F.3 AUGMENTED LAGRANGIAN
To transform the hard equality constraint into something we can iterate on, introduce dual tensor A and penalty weight p > 0:
C = | + 11 + PA. -A 1)
(23)
The quadratic term an increasingly strict penalty fence driving the iterates toward data fidelity, while A records mismatch information for the next cycle.
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F.4 ADMM UPDATES
Initialize 2 = Pa()), g()) = 0, and A 0. Each outer loop then performs five conceptually clear acts.
Step 1: Core tensor g(++1), Fix {Ul"), ,00 , Using the mode-1 unfolding (11)
(1)( o U solve
[I (I+ ((t E
I UUT (ua o O00),
where == = Pn g(0 - Al)). Modes and 3 have identical structure; all systemss size
In x Tn-
Step 2: Factor matrices U(m), For each ne (1,2,3)
min U- [E() p p' Am))) U (n) (v ( o (10))
(24)
Let M = (E(m) - pー 11)
ou(l)) compute SVD(M) PEQT, and set U
PQ (orthogonal Procrustes).
Step 3: Sparse tensor g((+1)
g(++1) -Soft Soft.Threshod /d'' 2/ 2 A(1).
applicd only on observed entries.
Step 4: Dual tensor.
(1+1)= A +Po(2(+ g(++1) - -)).
Step 5: Reconstruction.
z = g(++1) U()) x2 (2) U3)
One full sweep costs core LS O(rirers + [2]), three Procrustes updates Σ., ((Tr))), and residual operations O((2))
F.5 CONVERGENCE
Theorem 3 (Global Convergence) If [S] > (r/33/2 + s) log" and the restricted- isometry conditions in Theorem E hold, then the ADMM sequence (Z()) (00 (())) converges to the unique global minimiser (X*,E*) of Eq. equation
Sketch. Each sub-problem is convex with a unique minimiser; two-block ADMM theory plus dual-certificate guarantees convergence.
F-6 IMPLEMENTATION
A Algorithm II translates the math into code-ready steps.
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Published as a conference paper at ICLR 2026
Algorithm 1 ADMM for Robust Tucker Completion
Require: Observation y, mask Ω2 ranks (r1, F2, rs), parameters p)
1: Warm start: U(m) +- TruncatedHOSVI((PG.
2: & E 0, 0
3: repeat
4:
Update 9 (three tiny ridge systems)
5: for n-=1 to do
6:
Update U()) (one thin SVD) end for
7:
8:
Z + 8+9 X1 (() X2 (122 X3 U(3)
9:
E SoftThresholdd///dl
Zn A) (-))
At A Po(Z
11:
until || Z 2prev || 1//12 F 10-3 or max iterations
12:
return (2,8)
G DATASETS AND SETTINGS
The datasets used in the experiments include SR-CACO-2 and three datasets of in vivo cellular volumes.
This SR-CACO-2 dataset contains large image tilcs 9k x 9k, each composed of 10 x 10 unique sub-images of Caco-2 epithelial cells. Caco-2 cells serve studying mitolic spindle orientation and epithelial polarity, and can be easily modified for fluorescence lagging. The dataset includes fixed-cell images labeled with three fluorescent markers: mCherry-Histonn
reliable model for
H2B (chromatin). GFP-tubulin or E-cadherin (cell structure and membrane), and Survivin (midbody during cell division). It provides over 9,000 real LR-HR patch pairs for each cell type, enabling comprehensive evaluation of SISR models across different magnification levels. The dataset sctup and experimental protocols are standardized and detailed in the original work, ensuring reproducibility and relevance to live-cell imaging tasks.
We constructed comprehensive experimental pipeline using three real-world in vivo cellular datasets, acquired from live-cell cultures with Zeiss LSM 980 and Nikon AIR confocal microscopy systems. 3D imaging volumes were processed using Zen Blue and Fiji (ImageJ). To minimize phototoxicity during 4D time-lapse imaging, scanning was performed at 7000 Hz with water immersion objective, which inevitably introduced challengos such high noise, low contrast, and anisotropic spatial resolution.
To support quantitative evaluation, collected three benchmark datasets under varied imaging conditions including standard acquisition, high-speed axial scanning, laser-induced damage, and low-frame-rate capture. These datasets were acquired at elevated laser inten- sities for observational validation but were excluded from model training. Each sequence was segmented into temporal intervals of 50 frames. Laser intensity compensation along the Z-axis ranged from 1-4% for the 405 nm channel and 15-85% for the 561 mm channel.
We also introduce new dataset comprising 500 annotated 3D fluorescence volumes (265 unique volumes, totaling 22,830 lateral 2D slices), referred to as UnpairedTrain. These volumes were collected independently from the benchmark datasets and do not include direct high-resolution supervision, making them suitable for weakly- self-supervised learning schemes in fluorescence microscopy.
For training, we used GFP-labeled membranc-stained fluorescent images input, excluding ground truth HR images from the optimization target to encourage model generalization. The original 4D image volumes have dimensions of 512x712x94, optimized for preserving cell viability during acquisition. Training was performed using the Adam optimizer with an initial learning rate of 0.0002 and exponential weight decay (decayed every 100 iterations). All models, including ours and baselines, were trained and evaluated on six NVIDIA A100 GPUs.
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Published as a conference paper at ICLR 2026
H LARGE LANGUAGE MODELS USAGE STATEMENT
Large Language Models were only used to aid or polish writing.
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Reviews:
[{"review_id": "R3vNV2SP8U", "reviewer": "Reviewer_b64G", "summary": "This paper proposes a novel tensor completion framework for 3D fluorescence microscopy imaging that overcomes the limitations of traditional inverse problem methods. The authors reformulate cell volume recovery as a robust low-rank tensor completion problem, establishing theoretical recovery guarantees and proving mathematical equivalence to conditional diffusion models. Using Tucker decomposition with structural consistency priors, the method effectively handles the inherent challenges of fluorescence imaging: nonlinear degradation, incomplete Z-axis observations due to phototoxicity constraints, and high spatially-varying noise. Experiments on SR-CACO-2 and live C. elegans datasets demonstrate state-of-the-art performance with superior noise robustness and temporal consistency, achieving significant improvements in both signal fidelity and structural preservation for biological applications.", "questions": "1. During testing, how do you determine the rank for a new unseen volume—do you estimate it per-sample or use a fixed value?\n\n2. For λ₁: What value(s) did you use? Does it change across datasets or noise levels? If I choose r = 15 instead of r = 25, or λ₁ = 0.05 instead of 0.5, how much does PSNR drop?\n\n3. Could you provide a unified notation table?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The paper establishes a novel mathematical equivalence between Tucker-based tensor completion and conditional diffusion models, providing rigorous theoretical guarantees with clear derivations for exact recovery under sparse sampling conditions inherent to fluorescence microscopy.\n2.The method achieves robust 3D cell reconstruction without requiring paired high-resolution ground truth data, instead leveraging low-rank structure and sparse noise decomposition directly from incomplete noisy observations.\n3.The approach demonstrates state-of-the-art quantitative results across multiple datasets while maintaining exceptional temporal consistency and structural fidelity throughout extended time-lapse sequences (2700s-5400s) under degrading signal conditions.", "weaknesses": "1. Since the paper focuses on biological image reconstruction, relying solely on visual quality metrics lacks sufficient persuasiveness—high PSNR does not guarantee biological correctness, as reconstructions may appear visually plausible yet contain biologically inaccurate structures. Based on Figure 3 and other renderings, the cycle+IPG method gives me a better overall impression, and it performs better in reproducing details compared to the method proposed in this paper.\n\n2. The paper lacks critical discussion on hyperparameter selection, particularly the Tucker ranks (r₁, r₂, r₃) and sparse regularization weight λ₁, providing neither specific values, selection strategies, nor sensitivity analysis, which severely compromises reproducibility and practical applicability.\n\n3. The paper suffers from notational inconsistencies and insufficient explanations—parameter θ in Equation 1 is undefined, the transition between Equations 2-3 lacks clear explanation of tensor relationships (T vs. Y), and similar issues with forward symbol references and inconsistent variable naming persist throughout.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "h4Ibi2mh5X", "reviewer": "Reviewer_AjRV", "summary": "This paper reframes 3D live-cell fluorescence microscopy reconstruction as a tensor completion problem rather than an ill-posed inverse imaging task. The authors show that sparse axial sampling can be modeled as missing tensor entries, enabling recovery via low-rank tensor priors and sparse-noise decomposition. They further prove a formal equivalence between the resulting alternating minimization algorithm and a structurally guided conditional diffusion process, linking classical low-rank projection with modern generative denoising dynamics. The method provides theoretical recovery guarantees and achieves state-of-the-art performance on multiple real biological datasets, producing cleaner, more faithful volumes than existing inverse-problem and deep learning baselines.", "questions": "- How the method behaves when the underlying cell volume exhibits high intrinsic complexity that is not well-approximated by a low-rank tensor (e.g., dense organelles, cytoskeletal networks, neurites)? \n\n- How sensitive is performance to the choice of Tucker ranks, regularization parameters, and sparse-noise thresholds? A small ablation or rule-of-thumb guideline would help practitioners avoid overfitting or texture loss.\n\n- While the method avoids GAN-like hallucinations, could low-rank priors oversmooth fine biological details? A controlled stress test—e.g., synthetic volumes with known thin filaments.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper reframes 3D fluorescence microscopy reconstruction as cell-tensor completion rather than a traditional inverse problem, and establishes a provable connection between low-rank tensor recovery (via ADMM) and conditional score-based diffusion dynamics. This theoretical bridge is genuinely novel and goes beyond heuristic model design, giving a principled interpretation of diffusion priors in biological imaging.\n\n- The paper provides clear recovery guarantees under missing-data and sparse-noise settings, and designs an interpretable ADMM solver with separated low-rank and sparse components—well aligned with actual microscopy noise physics (e.g., shot noise and acquisition sparsity). The algorithm is lightweight, transparent, and grounded in theory rather than black-box training.\n\n- Experiments on multiple live-cell datasets show state-of-the-art performance in PSNR/SSIM/LPIPS and visibly better membrane continuity and cellular morphology preservation compared to supervised GAN-based and reconstruction-based baselines. The method avoids hallucinations and preserves structural fidelity, particularly important for biological interpretation.", "weaknesses": "- The paper highlights the diffusion-equivalence result but does not compare against recent unsupervised or self-supervised generative FM restoration methods (e.g., score-based microscopy denoising, inverse-consistent diffusion models, diffusion-based deconvolution pipelines). Without such comparisons, it is hard to quantify whether the proposed tensor-based approach benefits primarily from low-rank structure or from the implicit generative prior interpretation. Adding baselines like self-supervised diffusion denoisers or Plug-and-Play diffusion priors would strengthen the empirical story.\n\n- The paper does not provide sufficient analysis of rank selection, regularization weights, and sparse-noise thresholding. Since these choices likely impact geometry fidelity and hallucination risk, a systematic study (e.g., effect of Tucker rank on membrane sharpness and artifact suppression.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pU8IfLuya8", "reviewer": "Reviewer_9jax", "summary": "The paper presents a novel tensor completion framework for fluorescence microscopy (FM) imaging, addressing nonlinear signal degradation and incomplete observations. FM imaging with equidistant Z-axis sampling is modeled as a tensor completion task under uniform random sampling. The framework establishes the theoretical lower bound for exact 3D cell tensor recovery and reformulates the problem as a score-based generative model. Structural consistency priors guide the generative process toward denoised and geometrically coherent 3D reconstructions.", "questions": "Please see the Weaknesses.", "limitations": "", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. Well-written and well-organized, with comprehensive supplementary material.\n2. Introduces a tensor completion approach specifically tailored to fluorescence microscopy imaging, addressing a novel research problem that has not been extensively explored in the literature.\n3. Derives the theoretical lower bound for exact 3D cell tensor recovery and reformulates tensor completion into a score-based generative modeling framework.", "weaknesses": "### Mismatch Between Noise Model and Physical Imaging Process\n\nIn the manuscript, the observation is formulated as  \nY_\\Omega = X_\\Omega + E_\\Omega\n\n(an additive sparse noise model), which is a convenient and commonly used formulation.  \nHowever, in fluorescence microscopy, the primary degradations typically involve **Poisson noise** (due to photon counting), **system PSF** (blur or convolution), **signal attenuation and scattering**, and even **multiplicative effects**.  \nTherefore, such a simple additive sparse model may not adequately capture the real imaging process.  \n\nIf the equivalence or performance analysis of the proposed method relies on the assumption of *additive Gaussian plus sparse noise*, the paper should **explicitly state this assumption** and **discuss its implications and robustness** when the actual noise deviates from it.  Otherwise, the **generalizability and practical applicability** of the method may be limited.\n\n\n### Insufficient Experimental Evaluation\nThe paper lacks analysis and comparison with the latest method **MicroDiffusion** : Implicit Representation-Guided Diffusion for 3D Reconstruction from Limited 2D Microscopy Projections.\n\nHow is the **Z-axis sampling rate**  determined, and how does the model perform under different sampling rates?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "N4OwjXN1kt", "reviewer": "Reviewer_cSNp", "summary": "This paper focuses on a particular imaging inverse problem in fluorescence microscopy, which is formulated as a tensor completion problem. The authors propose integrating Tucker decomposition into the ADMM framework and compare the ADMM iterations to a diffusion process. The efficacy of this method is guaranteed by recovery theory. The proposed method demonstrates superior performance in super-resolution and denoising tasks compared to other methods.", "questions": "1. The paper states that it approximates the complex, true degradation process using a combination of downsampling and noise. However, it is unclear whether the datasets used in the experiments were generated using this approximated degradation or a true degradation process. This point requires clarification.\n   \n 2. The paper mentions 'Structural Priors in Biological Imaging'. However, the only prior explicitly integrated into the model appears to be low-rankness. The authors should justify this choice and discuss whether other priors specific to biological imaging, or more general image priors (such as continuity or nonlocality [2]), were also considered.\n   \n3. Clarity is needed regarding the DDPM's training methodology. The paper should explicitly state in the main text whether the DDPM was pre-trained or trained from scratch using paired data.\n\n[2].Liu Y, Yang Y, Cui Z X, et al. Patch-based Reconstruction for Unsupervised Dynamic MRI using Learnable Tensor Function with Implicit Neural Representation[J]. arXiv preprint arXiv:2505.21894, 2025.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. By leveraging Tucker decomposition, the method effectively exploits the intrinsic low-rank property of the data, which largely accounts for the observed performance improvement.\n    \n2. The method is supported by theoretical guarantees and use of the ADMM framework enhances its interpretability.", "weaknesses": "1. The method appears to be incremental, as the integration of tensor decomposition within the ADMM framework has already been explored in several existing papers (e.g., [1]).\n   \n 2. While the comparison between the ADMM optimization process and diffusion-based denoising is intuitive given their shared iterative patterns, a key distinction lies in their underlying priors. Diffusion models utilize an implicit prior learned from datasets. In contrast, low-rankness serves as an explicit structural prior. These two types of priors have their own distinct advantages. Therefore, the paper requires a discussion on why simply swapping these priors is a reasonable approach, and why the chosen explicit prior is more suitable for this specific problem than an implicit diffusion-based one.\n\n[1].Yuan, L., Li, C., Mandic, D., Cao, J., & Zhao, Q. (2019). Tensor  Ring Decomposition with Rank Minimization on Latent Space: An Efficient  Approach for Tensor Completion. *Proceedings of the AAAI Conference on Artificial Intelligence*, *33*(01), 9151-9158.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)