Zero-Shot Blind-Spot Image Denoising via Cross-Scale Non-Local Pixel Refilling
Authors: Qilong Guo
Tianjing Zhang
Zhiyuan Ma
Hui Ji
Venue: NeurIPS 2025 poster ()
Keywords: self-supervision
image denoising
low-level vision
Primary area: applications

Abstract: Blind-spot denoising (BSD) method is a powerful paradigm for zero-shot image denoising by training models to predict masked target pixels from their neighbors. However, they struggle with real-world noise exhibiting strong local correlations, where efforts to suppress noise correlation often weaken  pixel-value  dependencies,  adversely affecting denoising performance. This paper presents a theoretical analysis quantifying the impact of replacing masked pixels with observations exhibiting weaker noise correlation but potentially reduced similarity, revealing a trade-off that impacts the statistical risk of the estimation.  Guided by this insight, we propose a computational scheme that replaces masked pixels with distant ones of similar appearance and lower noise correlation. This strategy improves the prediction by balancing noise suppression and structural consistency. Experiments confirm the effectiveness of our method, outperforming existing zero-shot BSD methods.

Zero-Shot Blind-Spot Image Denoising via Cross-Scale Non-Local Pixel Refilling
Qilong Guo
Tianjing Zhang Zhiyuan Ma Hui Ji
Department of Mathematics, National University of Singapore, 119076, Singapore (qilong guo, tinghang,,,,,, e0983565) @u. nus edu, mat jhenus. eduss.edduu... sg
Abstract
Blind-spot denoising (BSD) method is a powerful paradigm for zero-shot image denoising by training models to predict masked target pixels from their neighbors. However, they struggle with real-world noise exhibiting strong local correlations, where efforts to suppress noise correlation often weaken pixel-value dependencies, adversely affecting denoising performance. This paper presents a theoretical analysis quantifying the impact of replacing masked pixels with observations exhibiting weaker noise correlation but potentially reduced similarity, revealing a trade-off that impacts the statistical risk of the estimation. Guided by this insight, we propose a computational scheme that replaces masked pixels with distant ones of similar appearance and lower noise correlation. This strategy improves the prediction by balancing noise suppression and structural consistency. Experiments confirm the effectiveness of our method, outperforming existing zero-shot BSD methods.
Introduction
Image denoising, which aims to restore clean images from their noisy observations, is basic problem in image processing. Deep learning, particularly supervised methods, has become a popular approach, achieving impressive performance are trained using synthetic noise, such as additive white Gaussian noise (AWGN). Consequently, their generalization to real-world noise is limited 7 3. such noise is often spatially correlated. To address this domain gap, several real-world datasets have been constructed, such as SIDD 9 and FMDD [10]. However, these datasets cover only limited range of the diverse noise patterns encountered in practice. Alternative approaches, including the use of unpaired noisy-clean image collections [1] 13 multiple noisy observations [14 15), still rely clean images, which challenging to obtain in many domains, such as scientific and medical imaging.
synthetic noise [ 2 3 5 6.. These models
unsupervised denoising, enables training directly from noisy observations, bypassing the need for clean images. One common strategy constructs pseudo pairs to define self-supervised losses [16
Self-supervised image denoising, sometimes also referred
17 18]
Another popular
strategy is the BSD method, which trains neural networks (NNs) to predict each target pixel from its 26 These methods show promising performance on real-world images. However, they depend on large external noisy datasets, which may be unavailable misaligned with the target domain. This limitation has motivated zero-shot denoising methods, which avoid external data by adapting a model to each noisy image at test time.
neighboring pixels, excluding itself [19 20 21
22
23
24
25
Zero-shot denoising at testing time: Zero-shot methods adapt untrained model directly noisy image at test time. The pioneering Deep Image Prior (DIP) [27) demonstrates that convolutional neural networks (CNNs) inherently favor structured patterns over noise, enabling zero-shot denoising
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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via early stopping. The blind-spot approach is also effective in this setting, training model from scratch test time predict masked pixels from their unmasked neighbors [28] 29 30 Blind-spot methods have shown strong performance in the setting of zero-shot denoising.
Overview of BSD paradigm:
The practical relevance of zero-shot denoising and the effectiveness of BSD techniques motivate our investigation into further refinement of BSD to meet the demand for a powerful zero-shot solution for denoising real-world images.
Let y = a + n be a noisy image, where æ denotes truth image and n is noise. For a target pixel I; with noisy observation yt. let Ω2 denote the index set of the pixels within its receptive field. In supervised learning, a denoising NN D& + x is trained to minimize the following loss:
Σ Do Po (eu))en.) - 1 (Supervised),
(1)
which measures the discrepancy between the prediction and truth for all pixels.
In zero-shot denoising, as truth 2, is unknown, BSD methods train the NN to approximate the loss ① There are two BSD implementations:
Architecture-based BSD: The NN is designed to enforce a blind spot so that the receptive field
never contains the target pixel [3] 22
23
24
25
26
32].
Mask-based BSD: standard backbone is kept, but a random mask removes selected pixels from the input and the loss is computed only those masked pixels 200 19 28
21
29
30)
Overall, mask-based BSD is more appealing than architecture-based BSD in practical usage. imposes no architectural changes: A simple input mask and modified loss suffice, so any off-the-shelf NN model can be used. Moreover, mask ratio can be flexibly tuned. Specifically, let M f0, 1] #xW be a Bernoulii mask of probability p. Let Mo == {i: m = 0} be the index set of masked pixels and Mi := {i: m, 1} the index set of unmasked pixels. Then, its loss can be formed as:
Σ M
(Po(tshhen.mm) - y1l (BSD).
To maximize the effectiveness of BSD, the mask-based loss ② should be good approximation to the supervised loss [ By comparing the two losses, we can see that the BSD loss 2 is good approximation to the supervised loss (I if the following conditions are satisfied:
Key challenges in BSD:
Mask Ratio: The ratio of masked pixels in image, r Mo]+]MM] must be large enough;
MMal
otherwise, the loss (2) involves too few pixels, leading to high variance. Conversely, r must not be too large, as it will reduce the number of unmasked pixels in Mj n for prediction.
Noise Correlation: The noise of the unmasked pixels in Mi nΩ, should be nearly independent to that of the masked target pixels yı: otherwise, the loss 2 will ineur significant bias related to the supervised loss (T.
BSD enables self-supervised learning by predicting certain pixels from their surrounding pixels while excluding themselves, thus preventing over- over-fitting to their noisy counterparts. However, as shown in the discussion above, the performance of BSD faces two key challenges:
1. Local correlation of real-world noise: Real-world noise shows strong local spatial correlation. The noise of nearby pixels {v; hem,n,, is then correlated with that of the target pixel 2i, violating the independence assumption in BSD and introducing bias to the loss function (2).
2. Insufficient related pixels for prediction: As the ratio needs to be sufficiently large, the number of unmasked pixels in M1 N used to predict the target masked pixel x; is limited. This can lead to insufficient information for accurate prediction.
Most existing work addresses these challenges by removing more nearby pixels and including more distant ones 122 24.. However, while exhibiting weak noise correlation, distant pixels also have weaker value correlation with the target pixel, which can hinder accurate prediction.
Motivations and main idea: The challenges outlined above, limited predictive pixels due to masking and strong local noise correlation, highlight fundamental trade-off in BSD, the trade-off between

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noise decorrelation and pixel correlation. Existing approaches mitigate these issues by including spatially distant pixels, with lower noise correlation to the masked pixels. However, such pixels are likely less related to the target, reducing value correlation and impairing prediction accuracy. Such trade-off between noise decorrelation and structural similarity remains a challenge existing works. Moreover, the reduced predictive context caused by masking is not fully addressed.
Motivated by these observations, we propose tackle such a challenge by pixel refilling, that is all masked pixels are replaced by other noisy pixels from the same image when being passed to the NN as the input. The question is then how to select the pixels to be used for refilling. In this paper, we analyze the trade-off between noise decorrelation and value correlation for linear denoising NNs.
Briefly, for masked target pixel 2g with noisy observation yo Zo + no, suppose its receptive field contains a total of M pixels, partitioned into two disjoint subsets:
{uj = =, + n2 ) (un-masked pixels);
{ē/ = ã + u5 / (re-filled masked pixels).
The values and noise of both subsets are correlated to To and ng as follows:
Ti)) n2 An + VI- Mee, ūz= 5 + V ,
Jy 11-11)))) My) ž,
where random variables {リz}i. ورك} no. {ei}s and {āj}; are independent with zero mean, variance o², of and o² for three noises. Here, An measures noise correlation: smaller A, indicates weaker correlation between n. and no. same for An. J, and o, measure the pixel value correlation: Lower oy and o imply stronger correlation between the related predictive pixels and the target zi-
In this paper, we quantify the prediction risk of linear model under the above assumptions:
RS = [ ).
D ((y))a (ū,}) - =0
From the resulting Bayesian risk analysis for a linear model, we can draw several interesting conclusions which guide the design of our BSD method with pixel refilling. For example,
The noise correlation term Xm is amplified by M, while the value correlation o? is not. Thus, for refilled pixels, reducing noise correlation with the target ng is more critical than increasing value similarity (i.e., lowering a3)).
When the receptive field is sufficiently large (M is large). the prediction risk can still be reduced even if the refilldd pixels exhibit lower value correlation than the unmasked ones (i.e., of > a provided they have lower noise correlation with the target pixel (A,, < An)
These insights suggest more advantageous select pixels with lower noise correlation the target pixel, with a reasonable degree of pixel similarity. To achieve this, one must seek pixels that are spatially or statistically distant yet structurally related the target. Motivated by this idea, we design pixel refilling strategy that matches pixels to distant- with structural similarity ensured by the strong cross- scale self- sifiaiiily of natural images. property widely exploited by classic non-local methods [3 34 and super- super-resolution approaches [35] 36 37).
counterparts to reduce noise correlation,
This work addresses two central challenges in BSD: limited predictive pixels due to masking and biased loss caused by local noise correlation. Our contributions are twofold:
Main contributions:
Theoretical Analysis: We present a Bayesian-risk analysis of a linear BSD model, revealing a trade-off between noise decorrelation and pixel similarity. It shows replacing masked pixels with others of low noise correlation, despite weaker pixel similarity, can reduce prediction risk.
Practical algorithur: Motivated by this insight, we propose a novel pixel refilling strategy for BSD method that fills masked pixels with carefully selected noisy pixels from the same image across scales, ensuring lower noise correlation and sufficient pixel correlation.
Extensive experiments on real and synthetic noisy images demonstrate the effectiveness of our approach, which in general outperforms existing zero-shot BSD methods.
2 Related Work
Supervised denoising: Supervised denoising methods learn to directly map noisy images to clean ones on many paired images. Popular architectures include CNN-based models (c.g., DnCNN [I]
3

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complex-valued CNN 38 and NAFNet (39 and transformer- models (e.g. Restormer [6] and Swin-IR (5)). However, their performance often degrades on real- noise, as models trained on
synthetic noise do not generalize well. One approach to relax the need for paired data by training on
unpaired noisy-clean images 11
12
or using multiple noisy observations [14 15 but
these still require either clean references or precise alignment, limiting their practicality.
Self-supervised denoising: Self-supervised denoising methods train NNs using only noisy images, removing the need for clean references. A dominant paradigm is the blind-spot scheme, which prevents the network from seeing the center pixel during prediction via architectural designs such as
occluded receptive fields [42) senter-masked convolutions with dilated layers [3T], or directional self-
attention in transformers 22).. Alternatively, masking- based blind-spot methods like Noise2Void [19]
and Noise2Self [20] define losses only over masked pixels to avoid overfitting, with extensions to global-aware mask mapping [1]] While blind-spot schemes perform well for independent noise, their performance decreases for local correlated noise. Pixel-shuffle downsampling (PD) is introduced to access distant pixels with weaker noise correlation by rearranging pixels from different spatial locations into multiple channels. Although PD reduces noise correlation, it also weakens local value correlation. APBSN [22) refines this by using a large stride during training and a smaller one during testing. LG-BPN [X
in [1 4
extends this with dense sampling and global branch to improve texture recovery. PUCA 24 uses patch shuffle operations to enhance global context. SS-BSN (25) combines grid self self-attention with simplified D- D-BSN B1. TBSN [32] and SelfFormer [26] employ transformer-basee blind-spots. Beyond blind-spot models, other self-supervised strategies include recorruption-aasee based methods R2R [16] and its extension < to general noise, downsample-brsg based
pairing NBR2NBR 17). and cyclic noise decomposition CVF-SID
45
Zero-shot denoising methods adapt an untrained model to each input at test time, thereby eliminating the need for external training datasets required by self-supervised methods. The pioneer work is DIP [27], which exploits the inductive bias of CNNs to fit structured content faster than noise. Subsequent methods extend this idea: Self2Self (28) combines the blind-spot principle with dropout ensembling; Noise2Fast [46] and ZS-N2N 47 use downsample-baset pairing; and
Zero-shot denoising:
Pixel2Pixel [48] creates patch-level matches at the original scale. To better handle real-world noise, Zheng et al. [49] project noisy images into latent AWGN-like space for denoising. ScoreDVI [50] includes score priors into Bayesian inference, TTT-MIM [5T] adopts an AWGN prior and adapts to shifted domain, while MASH 229 uses adaptive masking ratio and local shuffling to reduce noise correlation. These methods replace masked pixels with zeros during training, which limits the number of predictive pixels. To address this, BSN-INS 30) employs implicit neural representation (INR) to resample noisy pixels, yielding more predictive pixels with lower noise correlation.
Image restoration using patch-wise self-similarity Patch-wise self-similarity is a well-known phenomenon natural images, where similar image structures can be found at different locations and scales. This property is first exploited by non-local mean (33 for image denoising, BM3D [34] extends it by grouping similar patches for collaborative filtering. In super-resolution. cross-scale self-similarity has been extensively studied; see, e.g. [35 36 37). However, the self-similarity property has not been fully utilized in BSD for better performance on real-world image denoising.
3 Method
We analyze prediction risk in linear BSD models and introduce mask-based zero-shot BSD method that addresses two challenges: correlated noise and scarce predictive pixels. Our solution is pixel refilligg strategy leveraging natural image self-similarity.
3.1 Risk Analysis for Linear BSD Models with Pixel Refilling
We consider typical mask-based BSD model trained using the loss function (2). with a random
mask M. Let zo denote one masked pixel to be predicted. Its receptive field 2g contains M pixels. of which MM n Pol are masked, leaving only [M n Rol unmasked pixels available for predicting To.. To alleviate the issue of insufficient predictive information [42], we propose to replace masked pixels with values denoted by {ū, ) |MnnBoll That is, the input for predicting xo is
ú m,y, + (1 mz)ūs,
for j = ,,...,,, M,
(3)

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where mys are independent random samples from Bernoull(p)), which takes the value with proba- bility p and 0 with probability p. Following the same notation as in See we assume that the unmasked pixels {リi}ı and the refilled pixels {ūj}i are correlated with the target pixel zo by
yj = (1 - Mú M3) m,j.
U3 (1 3 ny;
ū = X0 + V X3
(4)
7 = X n2 + V 2
where assumed, all the variables {mz}s. (Kyly. no. {ejty and { are i..d. random variables with zero mean, where o o and o² are variances for the latter three noises, respectively.
Remark (Interpretation of Parameters). The parameters An. Ans and o. quantify noise and value correlations for unmasked pixels and refilled pixels to no and To respectively. Smaller An An indicate weaker local noise correlation, while smaller Jv, Fy imply stronger similarity in pixel values.
Consider a linear model Da parametrized by a = {ay و/و ((ú ) = Σラ 4 Øj- When using such a linear model to predict To. the corresponding risk is then defined by:
Ra (m, }- (. mo..(ss)..()) (,, Il| (())), rol
(5)
Then, linear model Da is learned using the following sulf-supervised loss:
M
M
Da- ((0)))1))
Σa as. Ūj> with a" := argmin agR [|] aj Us - 801l))
> j=1
(6)
j=1
Then, we have
Proposition The risk of the linear estimator Da- defined by (6) is:
M(r
(pdn, + (1 - 11))))) 204
Ra- = Mx + (M - 1)o + (1 (1-p)Am) + 2d + (1 (1--))0,o) +
Proof. See Appendix B for the details.
can be seen that the risk Ra- decreases when the refilled pixels exhibit a lower noise correlation
with no (smaller X,,) and a stronger value correlation with xp (smaller aß). This observation is consistent with intuition. A natural follow-up question is: What if we must trade off between noise and value correlation? Should we prioritize reducing noise correlation, or favor higher value similarity? Suppose M is sufficiently large, then the risk Ra- in 7 is dominated by the term
= (p), (1 - )) o z 0² (p)n + +1 )) 0n + o²
2 + zz0²
2
23 0² (pd,
p)
This implies the risk is primarily influenced by the noise correlation term d, of the refilled pixels, not by the value correlation parameter ag. This suggests that, for refilled pixels, reducing their noise correlation (lowering An) is more important than increasing their value similarity (lowering oe)
There are some simple refilling techniques in practice, e.g.. randomly selecting neighboring pixels to fill the masked pixels. In such a case, the refilled values {ū,} satisfy An = Xn and σ². o.
Corollary 1. When {ūj} satisfy Xm An and o² = o²., the risk of Da. defined by (6) is:
M M - x²
Ra- 2 Mx + (M 1) R + + 0²
(9)
Proof. See Appendix B for details.
With sufficiently large M, two risks 7 and (9) for two refilling schemes roughly satisfy
z 2002
2á + 2z00
Ra- 2 (ag +2) 2 + x² (pλn + (1- ))
v.s. (a) (o²+
Ra. (10)
2 + o2 X2
Thus, as long as the refilled pixels exhibit lower noise correlation than the neighboring pixels, the risk in the linear model can still be reduced, even if their value correlation is weaker. This indicates that simple refilling techniques, such as randomly selecting neighboring pixels, are suboptimal. More understanding of the risk of pixel refilling can be found in Appendix C
5

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3.2 Non-local Pixel Refilling by Cross-scale Patch Matching
Our analysis shows that the benefit from noise decorrelation generally outweighs the drawback of weakened pixel-value correlations. PD fits this principle very well: by reshufiling pixels from different spatial locations, it prioritizes noise decorrelation at the cost of reducing pixel-value correlation. This trade-off explains why PD remains effective, but also reveals its performance bottleneck. To fully exploit its potential, we propose pixel refilling scheme that constructs an image which compensates the loss of pixel-value correlation caused by PD while further improving noise decorrelation.
Our pixel refilling strategy is inspired by the classic non-local methods (e.g.. non-local means BB and BM3D (34). which exploit the self- self-similarity property natural images to enrich pixel information. Slightly different from those patch-level denoising methods, our approach operates at the pixel level: for each masked pixel, we search for the patch most similar to the one centering this pixel while ensuring sufficient spatial distance. Then, use the center pixel of the best match for replacement. Such pixels are likely to have high value correlation with the target while maintaining weak noise correlation. To further improve robustness, we leverage cross-scale self-similarity [35 37 of natural images. Specifically, the patches used for matching are extracted from a down-sampled version input image. This cross-scale refilling produces more desired replacements, yielding improved noise independence together with stronger pixel-value correlation.
Since masked pixels are randomly selected across many instances in mask-based BSD. we construct an auxiliary noisy image y from the original noisy image y to refill the masked pixels. The construction of such an auxiliary image improves computational efficiency, as patch matching only needs to be performed once. For each instance, pixel is selected as masked, it is replaced by the corresponding pixel from at the same location. The construction of y is based on the following steps:
1. Patch extraction at coarse scale: The noisy image y is down-sampled with average pooling to construct y 4s. Then, y and y la are partitioned into overlapping patches of same size N N. The patches are extracted with a stride N/4 along the width and height. Let Y and Y denote the sets of patches from y and ylu.
2. Patch matching and replacement: For each patch P. Y. we identify the patch P, E Ý with the smallest fg-distance |P, - PP among all patches in Y. Then, P. is replaced with Pj.
3. Construction of ÿ: After replacement, with a patch size of N N and stride of N/4, each pixel in ÿ. the auxiliary image used for refilling, is covered by 16 overlapping patches. The final pixel value is obtained by averaging its values across all overlapping patches.
Noisy image
Auxiliary image ÿ
Noisy image ya
Auxiliary image J
Figure 1: Sample images and their auxiliary images.
The auxiliary image ÿ. constructed via the proposed procedure, used refill the masked pixels in the original noisy image y. Each refilldd pixel is selected from a different patch with high similarity the target. The possible distant origin and down-sand sampling involved in the patches for matching ensure a lower noise correlation compared to neighboring pixels, while its high similarity to the target pixel Tig suggests strong value correlation. In implementation, the down-sampling rate k is set to 2, and the down-sampling is generated by applying average pooling on the original noisy image with window size and a stride See Figure T for the illustration of sample images and their auxiliary images. We also provide the illustration for patch matching in Appendix D

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Refill Pixels from y
Predict
Denoising NN
(1 (1-M) の
y
M + (1- 4
(1 M) Oy
Figure 2: Demonstration of BSD with pixel refilling, where M a random mask. The NN is trained by using both unmasked and refilled pixels predict masked pixels (1 M) øy.
3.3 BSD with Pixel Refilling and Training
The patch-based strategy first constructs auxiliary image ý by aggregating highly similar but distant patches, thereby reducing local noise correlation while preserving value correlation. Each masked pixel in the original noisy image y then refilled using the corresponding pixel from ÿ. The resulting image, combining refilled and unmasked pixels, is used as input to the denoising network.
Given random binary mask M, construct the input to the denoising NN Da by combining unmasked noisy pixels with refilled pixels from the auxiliary image. The NN is trained to predict the masked noisy pixels in self- self-supervised manner. Specifically, the BSD-based loss is defined as:
LBSN ||(1 M) (Do 2n -y)
(11)
where 9 = M (1 and M ~ Bernoulli(p). The parameter p controls the ratio between masked and unmasked pixels. PD with stride 2 symmetrically in both training and testing, denoted as 1/2 IP and 1-2 tP,, is implemented in our loss function. To further alleviate possible overfitting caused by the lack of the guidance of truth image during training, introduce consistency regularization term 47 52
Lcwn (0 -D
(12)
weighted by scalar A. The overall training objective combines the blind-spot reconstruction loss and the consistency regularization term:
- LASN + XLcons
(13)
where À is hyperparameter that balances the two terms.
4 Experiments
4.1 Experiment Setting
Five datasets, including both real and synthetic ones, are used for benchmarking. (1) SIDD 99. which contains real noisy-clean image pairs captured by smartphone cameras under diverse lighting conditions. We use both the validation set (1,280 images of 256 256) and the benchmark set (1,280 noisy-only images) for evaluation. (2) DND (53) consists of 50 pairs of noisy clean images, formed by capturing the same scenes twice with different ISO settings. The high-ISO images serve as noisy inputs, while the corresponding low-ISO images serve as ground-trute truth references. We use provided 512 x 512 images for evaluation on their website. (3) FMDD [10], contains real grayscale fluorescence images of biological samples acquired using widefield, confocal, and two-photon microscopes. Image size 512 x 512. (4) Kodak24 and McMaster18 [54), two synthetic denoising datasets of color images. We add i.idd. Gaussian noise with a 25, 50 and follow Pixel2Pixel 48 to crop them into patches of size 256 x 256 for evaluation. (5) fastMRI (55), dataset of MRI images. Following TTT-MIM (5T), we use its subset, add i.i.d. Gaussian noise with
Dataset:
o 18, and crop the images to 224 x 224.
Implementation details: The proposed model is implemented using PyTorch 2.4.1, CUDA 12.4, and an NVIDIA A6000 GPU. The model trained using Adam optimizer with an initial learning rate of 10-4, and other parameters of Adam are set to default. The auxiliary image is constructed with patch

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size N = 8. Two metrics, peak signal-to -o-niet ratio (PSNR) and structural similarity index measure (SSIM), are used for quantitative evaluation. Details of the network are provided in Appendix A The code of the proposed method is available on Githul
Table 1:
Quantitative comparisons (PSNR(dB) / SSIM) of different denoising methods on real
datasets. The best zero-shot methods bolded and the second underlined.
Category
Method
SIDD Val
SIDD Ben
DND
FMDD
Non-learnig
BM3D
34
30.83/.657
34.07/.662
34.51/.851
31.80/878
Supervised
DrCNN
37.73//943
37.61/991
37.90/.943
Noide2Void
19
27.06/.651
26.99/.652
NBR2NBR
77.94/.604
27.90/.679
CVF-SID 45
34.81/.944
34.71//917
36.50/924
32.73/.843
R2R [66
35.04/.844
35.88/.863
APBSN [22
36.73/.878
36.91//931
38.09/937
31.99/.836
Self-supervised
LG-BPN 23
37.32/.886
37.28/.936
38.43/9922
PUCA 24
37.54/.96
38.83/.942
SS-BSN 25
37.42/.977
38.46/990
ATBSN 56
37.88/9966
37.78/944
38.68/9942
SelfFormer
[26
37.69/937
38.92/9943
TBSN 32
37.78/940
39.08/.945
DIP 27
32.11/.740
32.90/.854
PD-denoising
43
33.97/.820
33.01/.856
Self2Self 28
29.46/.595
29.51/.551
30.76/.695
APBSN-single
22
30.90/8818
30.71/.869
28.43/.804
ZS-N2N 47
25.59/.565
30.19/428
30.671.737
31,65/.767
Zero-shot
ScoreDVI [50
34.75/.856
35.39//859
36.19/929
33.10/ 865
TTT-MIM [51
33.22/.638
34.91/.805
36.91/-
31.41/.819
MASH 29
35.06/.851
34.80/.814
34.751.910
33.71/.882
Pixel2Pixel 48
30.29/-
31.87/.631
34.16/836
33.26/.830
BSN-INS 30
35.31/.868
35.05/.922
33.55/8892
33.95/.885
Ours
36.32/.874
36.81//874
36.79/9944
33.47/.822
4.2 Performance evaluation
Real dataset: As a zero-shot method, our method is benchmarked against a comprehensive selection of cxisting zero-shot techniques. In addition, we also include representative methods from other categories. We use the authors' official code for generating the results or quote published results when available. Table I shows that method achieves the best overall performance among zero-shot approaches, ranking first on two datasets. Notably, the performance gaps to the top performer (0.12 dB and 0.48 dB, respectively) other two datasets (1.01 dB and 1.42 dB, respectively). Refer to Appendix F for visual comparisons of the results. Additional validation results more datasets are provided in Appendix E.2
much smaller than the margins by which method leads on the
Synthetic dataset:
The noise in the synthetic dataset not locally correlated, therefore, PD is not applied. This setting be regarded refilling strategy in addressing the insufficiency of predictive pixels. We only compare our method with the zero-shot methods that perform well on real- world noise. As shown in Table 2 our method achieves competitive performance in terms of PSNR and SSIM. Refer to Appendix for visual comparisons of the results.
evaluation of the effectiveness of the proposed pixel
Runtime and computational overhead by patch matching: The denoising process for each 256 x 256 image from the SIDD dataset takes approximately 60 seconds, with the construction of the cross-scale auxiliary image requiring less than second. This demonstrates that the auxiliary image introduces negligible computational overhead to the overall inference pipeline.

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Table Quantitative comparisons (PSNR(dB)/ SSIM) different zero-shot methods for removing AWGN noise. For natural images, AWGN with 25, 50 is added. For fastMRI, noise level is a (i.e., x² = 0.005 [0,1]) Best results are bolded and the second are underlined.
Kodak24
McMaster18
fas (a 18)
Method
25
50
25
50
DIP 127
27.38 /
23.95
27.61 /-
23.03 --
31.32
Self2Self [28
28.39 /-
26.22
28.71 /-
25.03 -
31.99 /
TTT-MIM [51
29.67 /
23.97
29.80
24.01 /-
29.87 /
Pixel2Pixel
[8
29.31 /-
26.26
29.50
25.28 /-
32.25/
PD-Denoising
28.98 / .801
26.40/.704
28.16 .784
25.96
26.79/ .550
ScoreDVI
500
29.31 / .796
24.89
/.633
29.20 .788
24.78
.641
31.10/
MASH
24.29 / .593
23.63
/579
25.89
/.738
25.47 /.703
31.35/ .738
BSN-INS 300
23.55 / .592
2 /.551
24.27
.676
23.43 / .634
29.83
9713
Ours
29.12 / 1.100
26.58 / .712
30.12
,853
27.41/.7766
32.61 .783
4.3 Ablation Study
Contribution of different components: There are two techniques involved in the proposed approach:
PD [T 43 [22] and the proposed pixel refilling technique. We evaluate their performance contribution the SIDD validation dataset with the parameters À 0.1 and p 0.5. As shown in Table 3 when applied individually, the performance improvement from the proposed refilling technique is
more modest compared to that from PD, which aligns with theoretical analysis. However, their improvements arise from different perspectives: PD improves denoising by decorrelating noise but weakening pixel-value correlations, whereas pixel refilling restores pixel-value correlations without introducing additional noise dependence. When combined, they complement each other and achieve the best overall performance.
Table 3: Ablation study of two components.
PD
Refilling
SIDD (PSNR dB)
31.27 (Plain)
X
V
31.85 (1 0.58)
34.01 (1 2.74)
35.65 (1 4.38)
Impact of hyperparameter in loss [3 : In this study, we evaluate the performance impact of the hyperparameter À with the SIDD validation dataset at a mask ratio of O.5. As reported in Table 4 the optimal result is achieved at À 0.2, whereas other values cause noticeable performance degradation. Note that pixel-shuffle downsampling is not implemented when applying the proposed method for spatially independent AWGN.
Table Effect of À on SIDD Val.
Table 5: Effect of p on SIDD Val.
A
0.1
0.2
0.5
0.1
0.3
0.5
PSNR
34.95
35.65
36.11
35.72
PSNR
36.24
36.32
36.11
Impact of mask ratio p: The impact of varying the mask ratio p. which determines the proportion of masked pixels, is examined the SIDD validation dataset. As shown in Table [ performance remains relatively stable across different values of p. For AWGN, the ablation study on the effect of the mask ratio is provided in Appendix E.I
Ablation on patch matching: We further study the effectiveness different scales and patch sizes for patch matching. We fix X 0.2,p = 0.3 and test on SIDD validation dataset for the experiments. For the source of scales, we compare the following settings: same-scale matching, downsampled matching scales J2 and L,. As shown in Table 6 downsampled 12 achieves the best

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result, demonstrating its ability to balance noise reduction and structure preservation. To evaluate the performance impact of different patch sizes, we use scale 22 and adopt three patch sizes: 4 x and 16 x 16. As shown in Table 7 patch size 8 x 8 achieves the best performance, demonstrating good trade-off between preserving the pixel correlation and noise decorrelation. More analysis of pixel refilling can be found in Appendix E
Table 6: Ablation for patches from different scales.
Table 7: Ablation for different patch sizes.
Choice
Same
42
41
Patch Size
8
16
PSNR
35.73
36.32
36,21
PSNR
35.88
36.32
36.14
Inference time comparison: Table reports the inference time per 256 x 256 image, the number of parameters and the FLOPs of several representative zero-shot denoising methods evaluated on the SIDD validation and benchmark datasets. Overall, our method has smaller model size compared to most methods, while achieving moderate inference time and FLOPs.
Table 8: Inference time, parameter count, and FLOPs comparison.
Method
Inference Time (s)
Params (M)
FLOPs (G)
DIP [27
89.0
13.4
31.06
Self2Self 228
1273.4
1.0
9.55
ZS-N2N 47
12.5
0.02
1.45
ScoreDVI [50
66.2
13.5
37.87
Pixel2Pixel
48
15.8
0.2
2.72
MASH 29
39.2
1.0
11.44
BSN-INS
30
48.3
1.0
11.82
Ours
65.4
0.5
32.97
Impact of different refilling schemes: Table 9 examines how different refilling choices affect denoising performance. Our refilling scheme, which both suppresses noise correlation owing to its spatial distance and preserves pixel similarity via cross-scale self-similarity matching, achieves the best results, outperforming both zero- zero-filling (Vanilla BSD) and local smoothing (Mean Filter).
Table Performance with different pixel refilling schemes
Choice
Vanilla
Mean Filter
Ours
PSNR
34.01
35.82
36.32
4.4 Limitation
One key limitation lies in the patch matching process. To serve its purpose of identifying similar patches at a coarser scale, cross-scale similarity needs to hold true, which is the case for natural images, but not for images in specific domain. As shown in experiments, the performance gain on FMDD, a microscopy image dataset, is less significant than that on SIDD, a natural image dataset. In addition, zero-shot requires training sample-specific models, which is computationally expensive when processing a large amount of data.
Conclusion
In summary, we present theoretical analysis of the trade-off between noise correlation and pixel correlation in blind-spot denoising, and propose a pixel refilling strategy that effectively balances the two. By leveraging distant but similar pixels with lower noise correlation, our approach addresses both the negative effect of local correlated noise and the issue of insufficient predictive pixels with a large mask ratio. Our method consistently outperforms existing zero-shot BSD methods across multiple benchmarks. In the future, we plan to explore different paradigms for zero-shot denoising, such leveraging pre- pre-trained models to reduce inference time while maintaining its flexibility.
10

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Acknowledgments
Hui Ji would like to acknowledge the support from Singapore MOE Academic Research Fund (AcRF)
Tier I Research Grant A- 4-8000981-00-000
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Appendix
This appendix provides additional material that supports and complements the main paper. Although some of the content may not appear the main manuscript, it serves enhance clarity and provide more complete picture of our method. Specifically, it includes:
Appendix A: Network Architecture Details
Appendix B: Proof of Proposition and Corollary 1
Appendix C:
Discussion on the Trade-off for the Proposed Linear Model
Appendix D: Visualization of Patch Matching
Appendix E:
More Analysis on Pixel Refilling
Appendix F:
Visual Comparisons for Real-World Denoising Experiments
Appendix G:
Visual Comparisons for Synthetic Denoising Experiments
A Network Architecture Details
3x3
input
s=2
Concat,
output
Central Masked Convolution
32
Dilated Convolution Module
3x3 Convolution with dilation
s=3
s=3
5=3
1x1 Convolution
5x5
Figure 3: Visualization of DBSN Architecture. The architecture is derived from the 3 x 3 and 5 x 5 central masked convolutional designs introduced in (31), but we adopt simplified version as proposed in APBSN 222. Each Dilated Convolution (DC) module consists of single 3 dilated convolution with a stride where network. We stack DC modules along each path. The number of output channels indicated below each convolutional layer, with 64 channels used by default. In contrast, the original APBSN (2 configuration uses DC modules and 128 channels by default.
is used for the upper path and
for the lower path of the
We adopt the simplified D-BSN architecture from APBSN [22]. as illustrated in Figure 3 The network is shallow and lightweight, comprising only 0.5M parameters, significantly fewer than the 3.7M parameters by default in APBSN [22].
Table 10: Ablation on DBSN model size and computational comparisons on a randomly selected 200-image subset of the SIDD validation.
PSNR (dB)
[Channels, Blocks]
#Params (M)
FLOPs (G)
Runtime (s)
36.56
[64, 4]
0.50
32.97
65.4
36.55
[64, 8]
0.83
54.44
110.2
36.58
[128, 4]
2.02
131.84
253,6
36.65
[128, 8]
3.33
217.74
420.1
In addition, Table 10
compares the performance differences among different configurations of DBSN, terms model size and computational efficiency. Overall, the performance difference is quite marginal.
22

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A.1 Ablation on Performance Impact of Network Architecture
Our proposed method is architecture-age agnostic and can theoretically enhance any vanilla (zero-filling) BSD framework regardless of the backbone. To verify this. we adopt the UNet architectures used in [4 29 as backbone models. As shown in Table [T equipping vanilla UNet-based BSD with our refilling strategy yields performance gain of more than 2dB, demonstrating the broad applicability of our approach.
Table 11: Ablation on UNet backbone.
SIDD Validation
Vanilla BSD (UNet backbone)
33.12
Ours (UNet backbone)
35.26
B Proof of Proposition 1 and Corollary 1
Lemma Let A +I BE, where > Then the inverse is given by
B and E ee with e [L..... 11" R.
1
B E.
-
a
a(a + 3M)
and A is symmetric positive definite (SPD).
Proof of lemma
We verify directly that the proposed inverse satisfies A-1A I. Define
A -- = I
B
E, A = +I+ E.
ala + BM)
Then.
1 I
3
A- A
E
(al + ΙE)
ala 3M)
3
3
I
E
E
E
a
3M
a1a + 3M)
8
8
I+
E.
a
a
3M
a(a BM)
Now observe:
8 3
8(a + 3M) 3a
3² M 0. a(a + BM)
+ BM a(a + 3M)
Therefore, A -1 -'A = I, confirming the claimed inverse.
To show A is symmetric positive definite:
symmetry is immediate since both I and E are symmetric. For positive definiteness, consider any nonzero RM
x A. al 2 B(x" e)².
The first term is strictly positive since a > 0 and æ + O; the second term is nonnegative since 3 2 0.
Hence x" Aæ for all x o so A is SPD.
Proposition 1. Consider two vectors for weights a = Maj TT and pixels ÿ [(ú, 1,TT" m2 Bernoullipp). Then with refilled already, Úi could be rewritten as
IT.
"1 m,y; (1 15mmm) -m,)0n
(14)
The linear denoiser is denoted as Da and self-supervised loss is denoted as f(a),
Dalū) a" g. with a" argmin f(a),
(15)
23

---

where
(16)
The prediction risk is defined:
Ra = Rm= (ih (0) - zol12-
(00))xollé.
(17)
Then the prediction risk of optimal denoiser w.r.t. self-supervised loss is:
M(a (ndn, (1-
Ra- Mxî + +M - (p) + (1- 11 + 1)0220 + + +
Mag + M-T 1o (1 p)o +2
Mo²
Mo²
M - + +
Mxğ + (M - 1)00 (pdn +
p) p) + prpa (1 - -p) + t
z (pdn + (1 (1- (1-p) p))m)) 00
2-
+ xb
o + (pdn + (1 p) p)
1/ 0 on
1 + 0²
10 + 0 + (1 (1-p)ha p2
(18)
Proof of proposition 1. Ma) could be rewritten and further simplified (expectation E will omit the variables {m,}. (e { no: Ro):
f(a) = EE I[a" exo - a² proo + a" ń x0 - =0
E [aa" la"ee" anj + a" pp ang a" e'' T a + 20 + n - -2a ex1 -2a" nna
a" C'Ean + (po + (1 a"
+a" (IDn + (1 - ()- + (a2 (pdn + +1 (1-2)\n)P0211) a
(19)
+10 2a ex 2a T e(p\n + (1 - p)nn)0?
= =² (pdn (1 p) )
+ (po + (1-p)o + 0² 1² ,, 0" (1 - 2)22300 -1- I
- 2(22 + (pdn + (1 p) e 2 +o
where
nT Kigho b3 = mylty + (1 - m)
(20)
nT = [m]b. n== myny + (1 - -m,)ū
Then
E A p0) = (po + (1 1)o
(21)
E Bn. = (p\n + (1 - p)),)) 'E (0² - (pdn + (1 - p))nn)200)1
(22)
Thus
f(a) = a" Aa - 221222(10-1 + (pt, + (1 - p)))))))))))) ee
e +22 2/.
(23)
where
A = + 2
(24)
We can derive
a" = =0g + (pdn + - (1=
2/ + ph,, + (1- p),,
(25)
Ma + (M - 1p) + +1 - + p (1
24

---

Then we calculate the risk of the optimal linear denoiser and derive
Ra. =E a (10g
(10g) 1/ xo _2] = E (a
exo -h p.o + a nz x0)²
=aaAAa' -21aa" T z
Aaa"
M - (pd, (1-
Mag + - (p) (1 91 0² +
Ma + Md² p12
M-1 +
Mo²
+
+ 2
Maj + (M 1)02 +1 2) (1-
p) 2 02
M 1
1 (pdn + +11 (1111))p P0
2 op (1 p)2n)² 2
1 + o 2r
2 -02 0²
In + o2 (p\n + (1 - p) )m
(26)
Corollary 1. When {ūg} satisfies Xn An and 0² oz. the risk Dà defined by 115 is:
M M(ag x²)
Ra- = a
(27)
Mxă + (M - 1)02 + 0. -Z20
Proof of corollary 1. Simply replace the in An and o, = o. in Proposition 1, then we could immediately get the result.
25

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C Discussion on the Trade-off for the Proposed Linear Model
The effectiveness of the refilling strategy in our linear model depends on the trade-off between noise correlation and pixel-value correlation of the refilled pixels. When the refilled pixels exhibit weaker noise correlation (Ax) and reasonably good pixel correlation (ē.). the strategy effectively reduces the prediction risk compared to using original pixels alone (the red dash as the baseline from Corallory
1.). This scenario is illustrated in Figure 4 where the optimal ratio p lies within (0, 1). demonstrating a meaningful balance between original and refilled pixels.
mine
Pa U.A. Optimalp" -0 tard, 075
baseline
Optina -0.00 00.000000.0.....0 600
optina -0 for 6r75
RG-00
Figure 4: With reasonable parameter settings: M = 127, 30 100, An 0.3, o. 0.04, Xn = 0.1, the left subfigure illustrates one example of our linear model. In this plot, the rainbow-colored histogram corresponds to the optimal resampling ratio p" for each value of o.. The right subfigure shows a special case, highlighting how the ratio p influences the prediction risk when the pixel correlation is reduced, i.e., dv < o. = 0.75.
(b) Good noise decorrelation but pixel correla- tion too weak, right subfigure suggests no refill- ing;
(a) No noise decorrelation and pixel correlation too weak, right subfigure suggests refilling;
Octee 2000
(c) No noise decorrelation and stronger pixel correlation, right subfigure suggests refilling all pixels;
(d) Slightly larger noise correlation dominates, requiring strong pixel correlation to make refill- ing strategy work.
Figure 5: Prediction risk curves under different bad noise or signal correlation settings.
However, when the refilled pixels fail to suppress noise correlation or badly suffer from poor signal correlation, the strategy becomes ineffective, and the optimal solution degenerates to p Rs 1, meaning the model relies entirely on original pixels. The failure modes are shown in Figure (a) (b) and (c). As we have stated that the noise correlation dominates when M is quiet large, if the noise correlation is slightly larger in the refilled pixels, only when the refilling pixels exhibit terribly strong pixel
26

---

correlation could the refilling strategy work, see Figure 5 (d). These findings support our theoretical analysis and emphasize the importance of matching refilled pixels with both low noise correlation and adequate signal fidelity.
D Visualization of Patch Matching
See how patch matching works on different scales in Figure 6 Note that when patch matching within the same scale, the patch P. is replaced by Py with the smallest lg-distance I| ll among all patches except the one with the same center as P; in Y, i... second smallest fz-distance.
1
Figure 6: (a) Clean image with reference patch highlighted in orange. (b) The corresponding noisy image patch (red) at the same spatial location, together with its most similar patch (blue) found within the same noisy image. (c) The noisy image coarser scale (obtained by 2 2 average pooling), where the most similar patch (yellow) corresponds to the noisy reference patch (red).
E More Analysis on Pixel Refilling
In this section, we first ablate the mask ratio for the AWGN case, followed by additional experiments to further verify the robustness of our strategy. Specifically, we evaluate performance on additional real-world datasets, and examine the robustness under various noise levels against vanilla BSD (zero-filling). All experiments use the lightweight DBSN model with channel configuration of [64, 4] as the backbone.
Table 12: Ablation of mask ratio on McMaster18 8 with AWGN = 50.
0.3
0.5
0.7
0.9
PSNR 27.37
27.39
27.37
27.19
27

---

E.1
Ablation on Mask Ratio for AWGN
We examine the performance impact of varying the mask ratio p, which controls the proportion of masked pixels, under AWGN with 50. As shown in Table [2] performance remains stable across different values of p, and we adopt p 0.5.
E.2 Evaluation More Real Datasets
PolyU (57 contains 40 pairs of noisy-clean images captured at various ISO levels. These datasets span wide range of noise levels. NIND (58] another real-world dataset consisting of clean-noisy image pairs captured at ISO levels of 3200, 4000, 5000, and 6400, with 22, 14, 13, and 79 pairs, respectively. We selected two sub-datasets ISO5000, for comparison. It can be seen that, on the PolyU dataset which features relatively low noise level, our method still achieves the best performance. This suggests that the proposed pixel refilling strategy remains effective even when the noise level is low. Note that the results on PolyU are quoted from Pixel2Pixel
represent two types of noise level, ISO3200 and
[8
Table 13: Comparison of zero-shot denoising methods on PolyU and NIND datasets. Results are reported PSNR(dB) SSIM.
Method
PolyU
NIND ISO3200
NIND IS05000
ZS-N2N
35.17/-
29.40/0.642
26.58/0.546
Pixel2Pixel
36.11/-
32.30/0.783
30.18/0.744 745
ScOreDVI
34.00/-
34.12/0.845
31.64/0.80 803
MASH
31.97/-
33.32/0.834
31.34/0.800
Ours
36.29/0.942
34.40/0.860
32.58/0.835
E.3 Robustness w.r.t. Different Noise Levels
To evaluate the robustness of the proposed pixel refilling strategy with respect to different noise levels, we conduct experiments under different levels of AWGN, including low (a 10), moderate (a = 25), and extreme (o = 100), using the same backbone and mask ratio as vanilla BSD. The results show that under extreme noise conditions, the effectiveness of pixel refilling becomes weaker, as severe corruption makes reliable texture matching more difficult. Nevertheless, all cases, the pixel refilling strategy consistently outperforms its vanilla counterpart.
Table 14: Comparison on Kodak24 under different noise levels (a 10, 25, 100).
Method
10 (Low)
25 (Moderate)
100 (Extreme)
Ratio of masked pixels
0.5
0.1
0.5
0.1
0.1
Vanilla BSD
29.75
30.96
27.91
28.77
23.26
Ours
30.98
31.39
29.03
29.12
23.36
28

---

Visual Comparisons for World Denoising Experiments
CLASSIC
CLASSIC
CLASSIC
CLASSIC
CLASSIC
CLASSIC
xxrite
x-rite
x-rite
x-rite
x-rite
x-rite
DRY ERASE
DRY ERASE
tos DRY ERASE
DAY ERASE
k DRY ERASE
R DRY ERASE
LOP
Lop
LOP
Forward
Forward
Forward
FecHard
Forward
Forward
Park
Park
Park
Park
Noisy PD 4
ScoreDVI 50
MASH 29
Ours
Clean
Figure Qualitative comparisons on SIDD Validation images. Each row corresponds to dif- ferent noisy input, and columns show outputs from different denoising methods: noisy input, PD- denoising (43), ScoreDVI (50), MASH 22), our method, and the clean reference. Our method consistently preserves more fine details and recovers textures more faithfully compared to other approaches.
29

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colorch
colorch
colorch
colorch
colorch
colorch
R
R
K
R
GOLD co
DOLD
SOLD
SOLD
BOLD
RY ERAS
RY ERASH
RY RY ERASH
ERAS
RY ERASE
GOLD GOLD COLOR
FOLD COLOR
GOLD COLOR
GOLD COLOR
R
FOLD COLOR
GOLD COLOR
Noisy
BM3D +-
BSN-INS
30
ScoreDVI 50
MASH 29
Ours
Figure 8: Qualitative comparisons SIDD Benchmark images. Each row corresponds different noisy input, and columns show outputs from different denoising methods: noisy input, BM3D (34,, BSN-INS G0), ScoreDVI [50], MASH 22), method. Our method maintains visual fidelity and reduces noise more effectively than other zero-shot methods.
30

---

RoveAAmer
Rove
RoceAAmer
RoseAAmer
RoseAAmer
RoceAAmor
Ours
ScoreDVI 50
MASH 29
Pixel2Pixel
48 TTT-MIM 51
BSN-INS 30
Figure 9: Qualitative comparisons DND Benchmark images. Each row corresponds to different noisy input, and columns show outputs from different denoising methods: Ours, ScoreDVI [50], MASH 29), Pixel2Pixel (48), TTT-MIM [51] and BSN-INS (30). Our method maintains visual fidelity and reduces noise more effectively than other zero-shot methods.
31

---

Noisy
ScoreDVI 50
ZS-N2N
MASH
Ours
Clean
Figure 10: Qualitative comparison on the FMDD.
Noisy
ScoreDVI 50
ZS N2N
4
MASH
Ours
Clean
Figure 11: Qualitative comparison on the FMDD.
32

---

G Visual Comparisons for Synthetic Denoising Experiments
Noisy
ScoreDVI 50
MASH 29
Pixel2Pixel
48
Ours
Clean
Figure 12: Qualitative comparisons on Kodak with AWGN 50. Each row corresponds different noisy input, and columns show outputs from different denoising methods: Noisy input, ScoreDVI (50), MASH (29), Pixel2Pixel [48), our method, and the clean reference. Our method consistently preserves more fine details and recovers textures more faithfully compared to other approaches.
33

---

2
SV
Noisy
ScoreDVI 50
MASH
Pixel2Pixel
Ours
Clean
Figure 13: Qualitative comparisons McM with AWGN 50. Each row corresponds
different noisy input, and columns show outputs from different denoising methods: Noisy input,
ScoreDVI (50), MASH (29), Pixel2Pixel [48), method, and the clean reference. Our method consistently preserves more fine details and recovers textures more faithfully compared to other approaches.
34

---

Noisy
ScoreDVI
MASH
Pixe12Pixel 48
Ours
Clean
Figure 14: Qualitative comparison on one slice from the fastMRI Dataset with AWGN a 18. Our
result shows more consistent textures than other zero-shot denoising methods.
Noisy
ScoreDVI
MASH
Pixe12Pixel 48
Ours
Clean
Figure 15: Qualitative comparison on one slice from the fastMRI Dataset with AWGN a 18. Our
result shows more consistent textures than other zero-shot denoising methods.
35


Reviews:
[{"review_id": "diPhVZGP35", "reviewer": "Reviewer_gdnC", "summary": "The paper proposes a self-supervised image denoising method applied at test time (test-time training). The approach enhances the vanilla Blind-Spot Denoising (BSD) framework by refilling masked pixels with pixels from similar patches within the same image, or its downsampled version. The method achieves competitive results compared to other self-supervised single-image denoising methods.", "questions": "See weaknesses.", "limitations": "See weaknesses.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths:**\n\n1. The paper tackles the interesting problem of unsupervised image denoising.\n\n2. Although the theoretical analysis is based on simplistic assumptions and does not seem to lead to novel findings, I found it overall insightful.\n\n3. The method shows good improvement over the baselines on the SSID dataset.\n\n\n**Weaknesses:**\n\n1. The central idea and claimed contribution focus on improving the BSD framework. However, the authors train their model using a combination of the BSD loss and the pixel shuffle downsampling loss with $\\lambda=0.1$. The contribution of each component should be investigated, particularly the case of $\\lambda=0$, which would clearly highlight the contribution of the proposed method.\n\n2. The only significant improvement over the baselines in case of the real data is observed on the SIDD dataset, which is generally characterized by (i) a high noise level and (ii) high noise correlation. I suspect that the noise level is an important factor in the success of the method, and I believe investigating this aspect is crucial. In particular, I think that the proposed pixel refilling strategy might be suboptimal in cases of low noise levels, and that a vanilla BSD with a low masking ratio could lead to better results.", "was_revised": true, "final_justification": "The paper achieves state-of-the-art results across multiple datasets with a consistent hyperparameter configuration, as claimed by the authors, and introduces a novel pixel-refilling approach for blind-spot denoising. However, an ablation study on the chosen network/backbone is necessary to determine whether pixel refilling and pixel-shuffle downsampling alone are sufficient to achieve these results (if not, the architecture itself should be highlighted as a third component of the method). A more thorough robustness analysis of the pixel-shuffling idea in various scenarios (e.g., high noise levels, textured regions) is also needed. If a heavy architecture is crucial to the state-of-the-art performance, the authors should acknowledge that the improvement comes at the cost of increased computational requirements\n\nOverall, I have a mixed opinion and lean toward borderline acceptance, based on the authors’ efforts during the discussion, and I recommend incorporating the above suggestions in their revision.", "rebuttal": "Thank you for the feedback. We emphasize that our method introduces a novel pixel refilling strategy for blind-spot denoising (BSD), grounded in our solid theoretical framework. Unlike typical zero-shot BSD approaches, e.g., the current SOTA zero-shot method MASH [1], which rely solely on zero-masking, our approach replaces the masked pixels with meaningful candidates from the same image or its downsampled version. While it incorporates standard techniques such as pixel shuffle downsampling (commonly asymmetrically used due to its limitations in BSD variants like APBSN[2], LGBPN[3] and PUCA[4], as we have discussed in Sec. 2 of our manuscript), the main contribution lies in the refilling strategy, which not only drives significant performance gains but also addresses the limitations of shuffling. In response to your comments, we have conducted ablation studies and additional experiments, which will be included in the revised manuscript. Please see our detailed responses below.\n\n[1] *Chihaoui, H., et al. (2024). Masked and shuffled blind spot denoising for real-world images. CVPR.*\n\n[2] *Lee et al. (2022). AP-BSN: Self-supervised denoising for real-world images via asymmetric PD and blind-spot network. CVPR.*\n\n[3] *Wang et al. (2023). LG-BPN: Local and global blind-patch network for self-supervised real-world denoising. CVPR.*\n\n[4] *Jang et al. (2023). PUCA: Patch-unshuffle and channel attention for enhanced self-supervised image denoising. NeurIPS.*\n\n---\n\n**[W1]** *The authors train their model using a combination of the BSD loss and the pixel shuffle downsampling loss with $\\lambda = 0.1$. The contribution of each component should be investigated, particularly the case of $\\lambda = 0$*\n\nThanks for the insightful suggestion. Please refer to Table A.1.1 below for the ablation study. We validate the contribution of pixel refilling on two real-world datasets, SIDD validation and NIND[5] subset, where NIND is a real-world dataset consisting of clean-noisy image pairs captured at ISO levels of 3200, 4000, 5000, and 6400, with 22, 14, 13, and 79 pairs, respectively and we pick up the smallest subset.\n\nPixel shuffle downsampling alone slightly degrades performance ($34.12\\rightarrow 34.01$ on SIDD and $29.90\\rightarrow 29.83$ on NIND subset), as it breaks local noise correlation but also weakens pixel correlation. In contrast, our proposed pixel refilling significantly improves performance ($34.12\\rightarrow 34.95$ on SIDD and $29.90\\rightarrow 32.10$ on NIND subset) by introducing distant pixels with strong pixel correlation and low noise correlation. When combined, the two strategies complement each other: pixel reshuffle helps decorrelate local noise, while pixel refilling restores meaningful pixel correlations without compromising noise independence. Together, they yield the best performance ($35.65$ on SIDD and $32.58$ on NIND subset). These empirical observations are consistent with our theoretical analysis.\n\n\n*Table A.1.1. Ablation study of two components.*\n| PD Loss |  Pixel Refilling in BSD|SIDD (PSNR dB) | NIND (PSNR dB)|\n|-|-|-|-|\n| $\\times$|$\\times$|34.12 (Baseline)| 29.90(Baseline)|\n| $\\times$|$\\checkmark$|34.95 ($\\uparrow$ 0.83)|32.10 ($\\uparrow$ 2.20)|\n| $\\checkmark$|$\\times$|34.01 ($\\downarrow$ 0.11)|29.83 ($\\downarrow$ 0.07)|\n| $\\checkmark$|$\\checkmark$|35.65 ($\\uparrow$ 1.53)|32.58 ($\\uparrow$ 2.68)|\n\n\n---\n\n\n**[W2]** *The only significant improvement over the baselines in case of the real data is observed on the SIDD dataset. The proposed method might be sub-optimal in cases of low noise levels, and that a vanilla BSD with a low masking ratio could lead to better results.*\n\nWe thank the reviewer for this insightful comment. In response, we conducted the experiments under various noise conditions. Please see Table A.2.1. for the results across multiple real-world datasets, including DND[6], PolyU[7], NIND[5] subsets ISO3200, and ISO5000. DND consists of 50 noisy-clean pairs, formed by shooting the same scene twice with different ISO values. PolyU contains 40 pairs of noisy-clean images captured at various ISO levels. These datasets span a wide range of noise levels. In particular, on the PolyU dataset, which features the lowest noise level, our method still achieves the best performance. This suggests that the proposed pixel refilling strategy remains effective even when the noise level is low.\n\n*Table A.2.1. Comparison of zero-shot denoising methods on different real denoising datasets.*\n\n|Method|DND|PolyU|NIND ISO3200|NIND ISO5000|SIDD Val|SIDD Ben|\n|-|-|-|-|-|-|-|\n|ZS-N2N| 30.67/0.737| 35.17/--|29.40/0.642|26.58/0.546|25.59/0.565|30.19/0.428|\n|Pixel2Pixel|34.16/0.836|*36.11*/--|32.30/0.783|30.18/0.745|30.29/--|31.87/0.631|\n|ScoreDVI|*36.19/0.929*|34.00/--|34.12/0.845|31.64/0.803|34.75/0.857|*35.39/0.859*|\n|MASH|34.75/0.910|31.97/--|*33.32/0.834*|*31.34/0.802*|*35.06/0.851*|34.80/0.814|\n|Ours|**36.79/0.924**|**36.29/0.942**|**34.40/0.860**|**32.58/0.835**|**36.32/0.874**|**36.81/0.874**|\n\n\nTo further examine our method's performance under low noise levels, we conduct experiments on the Kodak dataset with AWGN $\\sigma=10$ and $\\sigma=25$. We compare our method against vanilla BSD with low (0.1) and moderate (0.5) mask ratios to evaluate its effectiveness without relying on high noise levels or strong noise correlation. The results, presented in Tables A.2.2 and A.2.3, show that our method consistently outperforms the vanilla BSD baseline across both noise settings.\n\n*Table A.2.2. Comparison on Kodak with $\\sigma = 10$ (low noise).*\n\n| Method                         | Mask Ratio = 0.5 | Mask Ratio = 0.1 |\n|--------------------------------|------------------|------------------|\n| Vanilla BSD                    | 29.75            | 30.96            |\n| Ours                           | *30.98*          | **31.39**        |\n\n*Table A.2.3. Comparison on Kodak with $\\sigma = 25$ (moderate noise).*\n\n| Method                         | Mask Ratio = 0.5 | Mask Ratio = 0.1 |\n|--------------------------------|------------------|------------------|\n| Vanilla BSD                    | 27.91            | 28.77            |\n| Ours                           | *29.03*          | **29.12**        |\n\n\n\n[5] *Brummer et al. (2019). Natural image noise dataset. (CVPRW).*\n\n[6] *Plotz et al. (2017). Benchmarking denoising algorithms with real photographs. (CVPR).*\n\n[7] *Xu et al. (2018). Real-world noisy image denoising: A new benchmark. (arXiv).*\n\n---\n\nWe welcome any further questions and thank the reviewer again for the valuable and constructive feedback."}, {"review_id": "bYUqUPy6D4", "reviewer": "Reviewer_esC5", "summary": "This paper presents a quantitative Bayesian-risk analysis of a linear blind spot denoising model, and reveal a trade-off between noise decorrelation and pixel similarity. It shows that replacing masked pixels with those with low noise correlation can effectively reduce prediction risk. Built on the insight, a novel pixel refilling strategy is proposed, and extensive experiments on both real and synthetic datasets demonstrate its effectiveness.", "questions": "Questions:\n\n1. What is the runtime and model complexity?\n2. There is no ablation regarding network structure. I wonder how does the network structure affects the denoising performance? Is it possible that other methods could still achieve similar performance when using your NN architecture?", "limitations": "yes", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The idea of pixel refilling is interesting and novel. The idea also has solid theoretical analysis and support.\n2. The proposed method achieves state-of-the-art denoising performance among the zero-shot denoising approaches with a clear margin on both synthetic and real benchmark datasets.\n3. The paper is well organized. The presentation of the idea, methodology, and experimental details are clear. Also, the supplementary material supplements enough technical details for the readers.\n\nWeaknesses:\n\n1. It could be better if the runtime and parameter complexity can be provided and compared.", "was_revised": true, "final_justification": "I would like to lower my rating, based on the following reasons:\n(1) Missing important ablation: The authors do not provide comparison on the same network structure, which is an important experiment that could show the real potential of the proposed methodology. Also, the updated FLOPs information show that the adopted network takes more FLOPs and has double inference time compared to MASH. It implies that the achieved SoTA performance could partly attribute to the bigger network.\n(2) I also refer to the comments from other reviewers, and their concerns have not been well addressed yet.", "rebuttal": "We thank the reviewer for the encouraging comments and constructive feedback. We are  glad that the novelty of our pixel refilling strategy and the strength of our theoretical analysis were recognized. Please see below for the responses to the concerns.\n\n---\n**[W1&Q1]** *What is the runtime and model complexity?*\n\n\nPlease refer to Table B.1.1. below for the comparison of inference time, parameter count, and FLOPs.. Our method achieves a favorable balance between performance and computational efficiency among zero-shot denoising methods. While ZS-N2N and Pixel2Pixel are faster, they suffer from a significant drop in performance. On the other hand, ScoreDVI and MASH have performance closer to ours but with comparable computational complexity.\n\n*Table B.1.1. Complexity comparison of zero-shot methods.*\n\n| Method                          | Infer. time (s) | Params (M) | FLOPs (G) |\n|--------------------------------|------------------|------------|-----------|\n| DIP                            | 146.2            | 13.4       | 31.06     |\n| PD-denoising                   | 0.1              | 0.7        | 46.94     |\n| ZS-N2N                         | 9.8              | 0.02        | 1.45    |\n| Pixel2Pixel                    | 24.3               | 0.2        | 2.72     |\n| Self2Self                      | 3546.5           | 1.0        | 9.55      |\n| ScoreDVI                       | 81.2             | 13.5       | 37.87     |\n| MASH                           | 75.3             | 1.0        | 11.44     |\n| **Ours**                       | 65.4        | 0.5    | 32.97 |\n\n\n\n\n---\n\n**[Q2]** *How does the network structure affects the denoising performance? Is it possible that other methods could still achieve similar performance when using your NN architecture?*\n\nWe thank the reviewer for highlighting the need for ablation studies on network structure. In response, we conducted a model ablation on the SIDD Validation set (200 randomly selected images due to time constraints), analyzing model size and computational cost using a DBSN-based architecture parameterized by the number of channels and blocks. Details of the architecture are provided in Appendix A of the supplemental material. As shown in Table B.2.1, we adopt the compact [64, 4] model in our final version to strike a balance between performance and efficiency.\n\n*Table B.2.1. Ablation on model size and computation comparisons*\n\n| PSNR (dB) | Model Size [Channels, Blocks] | #Params (M) | FLOPs (G) | Runtime (s) |\n|-----------|-------------------------------|-------------|-----------|-----------|\n| 36.56     | [64, 4]                        | 0.50        | 32.97     |65.4      |\n| 36.55     | [64, 8]                        | 0.83        | 54.44     |110.2     |\n| 36.58     | [128, 4]                       | 2.02        | 131.84    |253.6     |\n| 36.65     | [128, 8]                       | 3.33        | 217.74    |420.1     |\n\nWe also apply our method to a vanilla U-Net-based BSD model on the SIDD Validation set. Results are shown in Table B.2.2. It shows that our method can consistently enhance the performance of vanilla U-Net based BSD by 1.03 dB. \n\n*Table B.2.2. Pixel refilling on U-Net based BSD.*\n\n| Vanilla U-Net | U-Net with **Ours** |\n|---------|----------|\n| 32.72   | **33.75** |\n\n---\n\nWe will include these results in the revised manuscript. Thank you again for your positive comments and valuable suggestions."}, {"review_id": "oCONFiVtSx", "reviewer": "Reviewer_N84f", "summary": "This paper introduces a zero-shot blind-spot denoising (BSD) method via pixel-refilling. Existing mask-based real-world denoising methods could break noise correlation, but simultaneously damage the content. Instead, the authors theoretically analysis and address two major challenges in BSD: limited predictive pixels due to masking and biased loss caused by local noise correlation. Therefore, they propose a novel pixel refilling strategy for BSD method that filling masked pixels with carefully selected noisy pixels from the same image with lower noise correlation and sufficient pixel correlation. Experiments in real and synthetic noisy images demonstrate the effectiveness of proposed approach.", "questions": "Please see Weaknesses. If the questions are addressed well, I will increase the rating.", "limitations": "Yes.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\n1. The analysis of conflicting between mask ratio and correlation of noise is reasonable.\n2. The proposed pixel refilling strategy could improve the tradeoff between mask ratio and correlation of noise, which is practical to existing blind-spot denoising methods.\n3. The paper is well written and organized.\n\nWeaknesses\n1. The experiments on DND and PolyU dataset for real-world denoising are lacked.\n2. The DBSN network architecture used in this paper may be computation inefficient, what about use U-Net based BSN? How does the size of the network's parameters affect the results?\n3. There are lack of recent related works on self-supervised image denoising such as ZS-N2M[1], SASL[2], AT-BSN[3], TBSN[4], Pixel2Pixel[5]. In particular, adding more methods and results comparison with Pixel2Pixel and ZS-N2M would be better.\n4. There are lack of computation comparison in the paper, please compare the training time, inference time, parameter count, etc. with previous zero-shot BSD methods.\n\n[1]Zero-Shot Noise2Mean: Gap Minimization for Efficient Denoising from a Single Noisy Image, AAAI 2025.\n[2]Spatially adaptive self-supervised learning for real-world image denoising, CVPR 2023.\n[3]Exploring Efficient Asymmetric Blind-Spots for Self-Supervised Denoising in Real-World Scenarios, CVPR 2024.\n[4]Rethinking Transformer-Based Blind-Spot Network for Self-Supervised Image Denoising. AAAI 2025.\n[5]Pixel2Pixel: A Pixelwise Approach for Zero-Shot Single Image Denoising. TPAMI 2025.", "was_revised": true, "final_justification": "My concerns have been addressed. I have also read the other reviewers' questions and discussions. Overall, I am inclined to accept this paper and hope that the authors will incorporate these discussions, especially the additional experiments, into the revised version. I will increase my rating to \"borderline accept\".", "rebuttal": "Thank you for the detailed and constructive comments. The main weaknesses raised concern missing experiments. which will be included in the revision.  Please see below for the detailed response regarding the evaluations (DND, NIND, PolyU), recent method comparisons, and computational analysis. \n\n---\n\n**[W1]** *The experiments on DND and PolyU dataset for real-world denoising are lacked.*\n\nSee the table below for the requested comparisons. Results on PolyU are quoted from the Pixel2Pixel paper. Due to time constraints, we conducted evaluations on the DND dataset and two NIND subsets using the official code of only competing methods, where NIND[1] is a real-world dataset consisting of clean-noisy image pairs captured at ISO levels of 3200, 4000, 5000, and 6400, with 22, 14, 13, and 79 pairs, respectively. We selected two subsets, ISO3200 and ISO5000 for comparison.\n\n It can be seen that our method noticeably outperformed the competing methods.\n\n\n*Table C.1.1. Comparison of zero-shot denoising methods on different real denoising datasets.*\n\n|Method|DND|PolyU|NIND ISO3200|NIND ISO5000|SIDD Val|SIDD Ben|\n|-|-|-|-|-|-|-|\n|ZS-N2N| 30.67/0.737| 35.17/--|29.40/0.642|26.58/0.546|25.59/0.565|30.19/0.428|\n|Pixel2Pixel|34.16/0.836|*36.11*/--|32.30/0.783|30.18/0.745|30.29/--|31.87/0.631|\n|ScoreDVI|*36.19/0.929*|34.00/--|34.12/0.845|31.64/0.803|34.75/0.857|*35.39/0.859*|\n|MASH|34.75/0.910|31.97/--|*33.32/0.834*|*31.34/0.802*|*35.06/0.851*|34.80/0.814|\n|Ours|**36.79/0.924**|**36.29/0.942**|**34.40/0.860**|**32.58/0.835**|**36.32/0.874**|**36.81/0.874**|\n\n\n[1] *Brummer et al. (2019). Natural image noise dataset. (CVPRW).*\n\n---\n\n**[W2]** *The DBSN network architecture used in this paper may be computation inefficient, what about use U-Net based BSN? How does the size of the network's parameters affect the results?*\n\nFor the model size of our method, please refer to Appendix A of the supplemental materials for the details. Indeed, we use the small DBSN with [64, 4] channels and blocks as our final model, which has only 0.5M parameters. \n\nWe apply the proposed pixel refilling scheme to a vanilla U-Net-based BSD model. Please see Table below for the results on SIDD Validation set. It shows that our method also works for the vanilla U-Net based BSD, with 1.03 dB performance gain.\n\n\n\n*Table C.2.1. The Proposed Pixel refilling on U-Net based BSD.*\n\n| Vanilla U-Net| U-Net with **Ours** |\n|---------|----------|\n| 32.72   | **33.75** |\n\n\nRegarding the performance impact of model size, please see the table below for the ablation study on model size and computational efficiency. While larger models slightly improve PSNR (e.g., +0.09 dB from 0.5M to 3.33M parameters), the increase in FLOPs is substantial (32.97G to 217.74G). To balance performance and complexity, we adopt the compact 0.5M model.\n\n\n*Table C.2.2. Ablation on model size and computational efficiency*\n\n| PSNR (dB) | Model Size [Channels, Blocks] | #Params (M) | FLOPs (G) | Runtime (s) |\n|-----------|-------------------------------|-------------|-----------|-----------|\n| 36.56     | [64, 4]                        | 0.50        | 32.97     |65.4      |\n| 36.55     | [64, 8]                        | 0.83        | 54.44     |110.2     |\n| 36.58     | [128, 4]                       | 2.02        | 131.84    |253.6     |\n| 36.65     | [128, 8]                       | 3.33        | 217.74    |420.1     |\n\n---\n\n**[W3]** *There are lack of recent related works,  such as ZS-N2M[1], SASL[2], AT-BSN[3], TBSN[4], Pixel2Pixel[5]. In particular, Pixel2Pixel and ZS-N2M*\n\nWe thank the reviewer for highlighting these recent works. We will cite them appropriately in the revised manuscript. \n\nFor Pixel2Pixel, please refer to Table C.1.1 for the comparison. The results of Pixel2Pixel on SIDD Validation and PolyU are quoted from the paper and others are generated using the author's code.  It can be seen that our method noticeably outperformed Pixel2Pixel. \n\nFor ZS-N2M, the authors have not released their code (their GitHub states it will be available soon), and we have not received a response to our request. Moreover, the paper reports results only on randomly selected subsets of benchmark datasets, rather than on the full benchmarks. Therefore, a fair and complete comparison to ZS-N2M  is currently not feasible at current stage.\n\n\n---\n\n**[W4]** *Lack of computation comparison in the paper.*\n\nWe thank the reviewer for highlighting this point. Please refer to the table below for the requested comparison. Our method achieves a favorable balance between performance and computational efficiency among zero-shot denoising methods. While ZS-N2N and Pixel2Pixel are faster, they suffer from a significant drop in performance. On the other hand, ScoreDVI and MASH have performance closer to ours but with comparable computational complexity.\n\n\n*Table C.4.1. Complexity comparison of zero-shot methods.*\n\n| Method                          | Infer. time (s) | Params (M) | FLOPs (G) |\n|--------------------------------|------------------|------------|-----------|\n| DIP                            | 146.2            | 13.4       | 31.06     |\n| PD-denoising                   | 0.1              | 0.7        | 46.94     |\n| ZS-N2N                         | 9.8              | 0.02        | 1.45    |\n| Pixel2Pixel                    | 24.3               | 0.2        | 2.72     |\n| Self2Self                      | 3546.5           | 1.0        | 9.55      |\n| ScoreDVI                       | 81.2             | 13.5       | 37.87     |\n| MASH                           | 75.3             | 1.0        | 11.44     |\n| **Ours**                       | 65.4        | 0.5    | 32.97 |\n\n---\n\nPlease let us know if you have any further questions. Thank you again for the helpful feedback."}, {"review_id": "oIzhsU1ZJ5", "reviewer": "Reviewer_A71X", "summary": "The paper highlights the limitations of blind-spot networks (BSNs) for zero-shot image denoising in the presence of locally correlated noise, which is the case with real-world camera or microscope noise. It introduces a theoretical trade-off between noise correlation and structural similarity when replacing masked pixels. Based on this, the authors propose a method that substitutes masked pixels with non-local, but visually similar ones to reduce noise correlation while preserving structure. Experiments show improved denoising performance compared to existing methods.", "questions": "N/A", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n- Clear motivation, good results, several recent baselines used for comparisons\n\nWeaknesses:\n- The proposed method seems similar to Pixel2Pixel, which also replaces masked pixels with the most similar pixels from non-local regions. A dedicated section in the paper with clear explanation of how the proposed method differs from Pixel2Pixel would help make the contribution and novelty more appreciated. \n- As Pixel2Pixel is also made for solving the problem of correlated noise, it should be used as a baseline in Table 1 for the real-world noise, having it as a baseline in Table 2 is not sufficient.\n- More on missing comparisons: Since ZS-N2N works well for pixel wise independent noise, it should be used as a baseline in Table 2, as the noise added there is AWGN.\n- A concern for zero shot methods is the denoising time, since a network is trained for each image. Therefore a comparison of the denoising speed/compute with competing zero-shot methods is essential.\n- Table 1 would benefit from having the DND as a benchmark dataset, since the paper's main contribution is denoising correlated noise, which is prevalent in real-world camera noise, and DND is a standard benchmark for that. \n- It is common to have an intermediate noise level for AWGN denoising with $\\sigma=$ 25 or 30, which is missing in Table 2. \n- Missing description of the architecture/model size of the NN used in the paper.  \n- Many typos and grammatical mistakes such as \"(BSD) method offer\" line 1, \"an noisy\" line 240, \"we also uses\" line 252, \"Our method consistently outperforming existing\" line 322, and several others.\n- No code provided", "was_revised": true, "final_justification": "The rebuttal clarified a lot of my concerns, specially the similarity to Pixel2Pixel, and the complexity of the proposed method. Overall, based on the extra experiments provided in the rebuttal, the method seems to achieve good performance compared to existing work while having moderate computational complexity. After reading other reviews, I recommend acceptance considering the authors will add the extra experiments from the rebuttal in the final paper.", "rebuttal": "Thank you for the constructive feedback. Our method builds on the Blind-Spot Denoising (BSD) framework, a fundamental approach in recent truth-free denoising methods, and introduces a novel pixel refilling strategy. We also provide, to the best of our knowledge, the first theoretical analysis of BSD, offering insights into its assumptions and implications for practical implementation. See below for our clarifications and requested additional experiments. All these clarifications and experimental results will be included in the revision.\n\n---\n\n**[W1]** *Key Differences from Pixel2Pixel and Our Contributions* \n\nThank you to the reviewer for pointing out the relevance of Pixel2Pixel. We will include it in the revised manuscript and provide a detailed discussion.\n\n\n\nWhile both methods aim to address noise correlation in self-supervised denoising, they are grounded in two different frameworks. Pixel2Pixel is built upon the Noise2Noise (N2N) paradigm [1], \n\n$$\n\\min_\\phi \\left\\\\| \\mathcal{D}_\\phi(\\mathbf{y}_1) - \\mathbf{y}_2 \\right\\\\|_2^2  \\quad (\\text{Noise2Noise}),\n$$\n\nwhere its aim is to generate image pairs with uncorrelated noise that approximate noise-clean pairs for defining the loss function. \n\nIn contrast, our method builds on the Blind-Spot Denoising (BSD) framework:\n\n$$\n\\min_\\phi\\\\|(1-M)\\odot[\\mathcal{D}_\\phi(M\\odot \\mathbf{y})-\\mathbf{y}]\\\\|_2^2 \\quad (\\text{Blind-spot}).\n$$\n\n where $M$ is the zero mask and the NN $\\mathcal{D}_\\phi(\\cdot)$ is trained to predict masked-out pixels from un-masked-out pixels. \n\n\nWhile both approaches leverage patch similarity to mitigate noise correlation between input-output pairs, Pixel2Pixel uses matched patches to construct pseudo image pairs for Noise2Noise-style training, and is more closely related to methods like ZS-N2N[2], R2R[3], and NBR2NBR[4]. In contrast, our method employs matched patches to refill masked pixels within the BSD  framework. Importantly, our approach is supported by a mathematical analysis that provides theoretical justification for the design, offering a deeper understanding of BSD and paving the way for future advancements in this framework.\n\n\n[1] *Lehtinen et al. (2018). Noise2Noise: Learning image restoration without clean data. (ICML).*\n\n[2] *Mansour et al. (2023). Zero-shot Noise2Noise: Efficient image denoising without any data. (CVPR).*\n\n[3] *Pang et al. (2021). Recorrupted-to-Recorrupted: Unsupervised deep learning for image denoising. (CVPR).*\n\n[4] *Huang et al. (2021). Neighbor2Neighbor: Self-supervised denoising from single noisy images. (CVPR).*\n\n---\n\n**[W2]** *Comparison to pixel2pixel in Table 1*\n\nSee the table below for the comparison to pixel2pixel, where the results of pixel2pixels on SIDD validation and PolyU are cited from the paper and others are generated using the authors' code. Our method outperformed pixel2pixel by a large margin on all datasets.\n\n*Table D.2.1. Comparison of zero-shot denoising methods on different real denoising datasets.*\n\n|Method|DND|PolyU|NIND ISO3200|NIND ISO5000|SIDD Val|SIDD Ben|\n|-|-|-|-|-|-|-|\n|ZS-N2N| 30.67/0.737| 35.17/--|29.40/0.642|26.58/0.546|25.59/0.565|30.19/0.428|\n|Pixel2Pixel|34.16/0.836|*36.11*/--|32.30/0.783|30.18/0.745|30.29/--|31.87/0.631|\n|ScoreDVI|*36.19/0.929*|34.00/--|34.12/0.845|31.64/0.803|34.75/0.857|*35.39/0.859*|\n|MASH|34.75/0.910|31.97/--|*33.32/0.834*|*31.34/0.802*|*35.06/0.851*|34.80/0.814|\n|Ours|**36.79/0.924**|**36.29/0.942**|**34.40/0.860**|**32.58/0.835**|**36.32/0.874**|**36.81/0.874**|\n\n\nwhere we also include DND[5], PolyU[6] and NIND[7] subsets results for comprehensiveness. DND[5] consists of 50 noisy-clean pairs, formed by shooting the same scene twice with different ISO values. PolyU[6] contains 40 pairs of noisy-clean images captured at various ISO levels, and NIND[7] is a real-world dataset consisting of clean-noisy image pairs captured at ISO levels of 3200, 4000, 5000, and 6400, with 22, 14, 13, and 79 pairs, respectively, where we selected ISO 3200 and ISO 5000 subsets for comparison.\n\n\n[5] *Plotz et al. (2017). Benchmarking denoising algorithms with real photographs. (CVPR).*\n\n[6] *Xu et al. (2018). Real-world noisy image denoising: A new benchmark. (arXiv).*\n\n[7] *Brummer et al. (2019). Natural image noise dataset. (CVPRW).*\n\n---\n\n**[W3]** *Comparison to ZS-N2N in Table 2*\n\nSee the table below for the comparison. The results of ZS-N2N are directly quoted from the paper of pixel2pixel. Our method outperformed ZS-N2N by a large margin, as shown in the table below.\n\n\n*Table D.3.1. Comparison of PSNR results (dB) under Gaussian noise*\n\n| Method       | fastMRI σ=18 | McMaster18 σ=25 | McMaster18 σ=50 | Kodak24 σ=25 | Kodak24 σ=50 |\n|--------------|---------------|------------------|------------------|----------------|----------------|\n| DIP          | 31.32         | 27.61           | 23.03           | 27.38         | 23.95         |\n| S2S          | 31.99         | 28.71           | 25.03           | 28.39         | 26.22         |\n| ZS-N2N       | 32.19         | 28.80           | 24.02           | 29.07         | 24.81         |\n| Pixel2Pixel  | 32.25       | 29.50         | 25.28         | *29.31*    | 26.26       |\n| **Ours**     | *32.61*    | *30.12*       | *27.41*       | 29.12       | *26.58*     |\n\n---\n\n\n**[W4]**  *Comparison in terms of speed*\n\nPlease see the table below for the detailed comparison of inference time, parameter count, and FLOPs of competing zero-shot methods.\n\n*Table D.4.1. Complexity comparison of zero-shot methods.*\n\n| Method                          | Infer. time (s) | Params (M) | FLOPs (G) |\n|--------------------------------|------------------|------------|-----------|\n| DIP                            | 146.2            | 13.4       | 31.06     |\n| PD-denoising                   | 0.1              | 0.7        | 46.94     |\n| ZS-N2N                         | 9.8              | 0.02        | 1.45    |\n| Pixel2Pixel                    | 24.3               | 0.2        | 2.72     |\n| Self2Self                      | 3546.5           | 1.0        | 9.55      |\n| ScoreDVI                       | 81.2             | 13.5       | 37.87     |\n| MASH                           | 75.3             | 1.0        | 11.44     |\n| **Ours**                       | 65.4        | 0.5    | 32.97 |\n\n\nWe have detailed a comparison of inference time, parameter count, and FLOPs in Table D.4.1. Our method achieves a favorable balance between performance and computational efficiency among zero-shot denoising methods. While ZS-N2N and Pixel2Pixel are faster, they suffer from a significant drop in performance. On the other hand, ScoreDVI and MASH have performance closer to ours but with comparable computational complexity.\n\n---\n\n**[W5]** *Table 1 would benefit from having the DND as a benchmark dataset*\n\nTo date, no existing zero-shot methods have reported performance on DND. Due to time constraints, we only compared competing zero-shot methods exclusively on DND. As shown in the table below, our method remains the top performer among them.\n\n\n*Table D.5.1. Comparison of zero-shot denoising methods on different real denoising datasets.*\n\n|Method|DND|PolyU|NIND ISO3200|NIND ISO5000|SIDD Val|SIDD Ben|\n|-|-|-|-|-|-|-|\n|ZS-N2N| 30.67/0.74| 35.17/--|29.40/0.642|26.58/0.546|25.59/0.565|30.19/0.428|\n|Pixel2Pixel|34.16/0.84|*36.11*/--|32.30/0.783|30.18/0.745|30.29/--|31.87/0.631|\n|ScoreDVI|*36.19/0.929*|34.00/--|34.12/0.845|31.64/0.803|34.75/0.857|*35.39/0.859*|\n|MASH|34.75/0.910|31.97/--|*33.32/0.834*|*31.34/0.802*|*35.06/0.851*|34.80/0.814|\n|Ours|**36.79/0.924**|**36.29/0.942**|**34.40/0.860**|**32.58/0.835**|**36.32/0.874**|**36.81/0.874**|\n\n\n---\n\n**[W6]** *intermediate noise level for AWGN denoising with 25 or 30 in Table 2*\n\nPlease refer to Table D.3.1 in our response to Q3.\n\n---\n**[W7]** *Missing description of the architecture/model size of the NN used in the paper*\n\nPlease refer to Appendix A of the supplemental material for the details of the architecture. The NN we use is a small DBSN with 64 channels and 4 blocks, which only has 0.5M parameters.\n\n---\n**[W8]** *Many typos and grammatical mistakes*\n\nThank you for pointing out the grammatical errors and typos. We will thoroughly proofread the manuscript and correct all identified typos and grammatical mistakes.\n\n---\n**[W9]** *No code provided*\n\nWe will release the full code upon acceptance of the paper.\n\n---\n\nPlease let us know if you have any further questions. Thank you again for the helpful feedback."}]

Author rebuttal:

Meta-review: Another contribution to the blind-spot denoising literature.  In this case, correlated noise is considered and an interesting trick of refilling pixels is presented.  The paper is well written and the results are good.  However, some additional ablation could clarify the method further.    Some aspects might remain unclear, such as the influence of the size of the used architecture.  Overall the reviewers are leaning to accept to I suggest a poster-accept with somewhat low confidence.
Decision: Accept (poster)