Stochastic Image Denoising by Sampling from the Posterior Distribution
Open accessAbstract
Image denoising is a well-known and well studied problem, commonly targeting a minimization of the mean squared error (MSE) between the outcome and the original image. Unfortunately, especially for severe noise levels, such Minimum MSE (MMSE) solutions may lead to blurry output images. In this work we propose a novel stochastic denoising approach that produces viable and high perceptual quality results, while maintaining a small MSE. Our method employs Langevin dynamics that relies on a repeated application of any given MMSE denoiser, obtaining the reconstructed image by effectively sampling from the posterior distribution. Due to its stochasticity, the proposed algorithm can produce a variety of high-quality outputs for a given noisy input, all shown to be legitimate denoising results. In addition, we present an extension of our algorithm for handling the inpainting problem, recovering missing pixels while removing noise from partially given data.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Diffusion models have shown potential in computer vision, natural language processing, temporal data modeling, multi-modal modeling, robust machine learning, computational chemistry, and medical image reconstruction.
“and have also shown potential in a variety of domains, ranging from computer vision [2,11,19,23,88,90,113,115,134,150,160,173,198,200,248,270,271,283,290], natural language processing [6,93,139,205,275], temporal data modeling [1,33,124,191,233,262], multi-modal modeling [7,186,196,199,288], robust machine learning [18,28,112,242,273], to interdisciplinary applications in fields such as computa”
From Diffusion Models: A Comprehensive Survey of Methods and Applications (2024) · cites this paper as [113]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Part of this paper’s reference list could not be split into single entries.
Image quality assessment: from error visibility to structural similarity
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.819861 · Cited by 57,892 · see citing works
The Unreasonable Effectiveness of Deep Features as a Perceptual MetricPreprint
Zhang, R., Isola, P., Efros, A. A., Shechtman, E., & Wang, O. (2018) · 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition · doi:10.48550/arxiv.1801.03924 · Cited by 21,362 · see citing works
The Unreasonable Effectiveness of Deep Features as a Perceptual Metric
Zhang, R., Isola, P., Efros, A. A., Shechtman, E., & Wang, O. (2018) · 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2018.00068 · Cited by 14,623 · see citing works
Image denoising by sparse 3-D transform-domain collaborative filtering
Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.901238 · Cited by 9,283 · see citing works
Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising
Zhang, K., Zuo, W., Chen, Y., Meng, D., & Zhang, L. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2017.2662206 · Cited by 8,983 · see citing works
Deep Learning Face Attributes in the Wild
Liu, Z., Luo, P., Wang, X., & Tang, X. (2015) · 2015 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2015.425 · Cited by 7,747 · see citing works
A Non-Local Algorithm for Image Denoising
Buades, A., Coll, B., & Morel, J.-M. (2005) · 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) · doi:10.1109/cvpr.2005.38 · Cited by 7,616 · see citing works
Analyzing and Improving the Image Quality of StyleGAN
Karras, T., Laine, S., Aittala, M., Hellsten, J., Lehtinen, J., & Aila, T. (2020) · 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr42600.2020.00813 · Cited by 6,332 · see citing works
Multiscale structural similarity for image quality assessment
Wang, Z., Simoncelli, E. P., & Bovik, A. C. (2004) · The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003 · doi:10.1109/acssc.2003.1292216 · Cited by 6,253 · cited 1× · see citing works
“Many alternative distance measures to the MSE have been suggested, including SSIM [48], MS-SSIM [49], IFC [38], VIF [37], VSNR [14], and FSIM [55].”
MethodImage Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
Elad, M., & Aharon, M. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2006.881969 · Cited by 5,321 · cited 1× · see citing works
“Various successful algorithms, both classically oriented and deep learning based, were proposed over the years for handling this task, such as NLM [13], KSVD [19], BM3D [17], EPLL [59], WNNM [21], TNRD [16], DnCNN [53], NLRN [29] and others [52, 36, 4, 45, 25, 54, 42, 44, 26, 57].”
Self-citationFSIM: A Feature Similarity Index for Image Quality Assessment
Zhang, L., Lei Zhang, A., Mou, X., & Zhang, D. D. (2011) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2109730 · Cited by 5,220 · see citing works
Image information and visual quality
Sheikh, H. R., & Bovik, A. C. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.859378 · Cited by 4,104 · see citing works
Large Scale GAN Training for High Fidelity Natural Image Synthesis
Brock, A., Donahue, J., & Simonyan, K. (2018) · arXiv · doi:10.48550/arxiv.1809.11096 · Cited by 3,717 · see citing works
Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures
Wang, Z., & Bovik, A. C. (2009) · IEEE Signal Processing Magazine · doi:10.1109/msp.2008.930649 · Cited by 3,175 · see citing works
FFDNet: Toward a Fast and Flexible Solution for CNN-Based Image Denoising
Zhang, K., Zuo, W., & Lei Zhang, A. (2018) · IEEE Transactions on Image Processing · doi:10.1109/tip.2018.2839891 · Cited by 2,921 · see citing works
Weighted Nuclear Norm Minimization with Application to Image Denoising
Gu, S., Zhang, L., Zuo, W., & Feng, X. (2014) · 2014 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2014.366 · Cited by 2,316 · see citing works
Lempitsky, V., Vedaldi, A., & Ulyanov, D. (2018) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2018.00984 · Cited by 2,023 · see citing works
Score-Based Generative Modeling through Stochastic Differential Equations
Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., & Poole, B. (2020) · arXiv · doi:10.48550/arxiv.2011.13456 · Cited by 1,953 · see citing works
MemNet: A Persistent Memory Network for Image Restoration
Tai, Y. Y., Yang, J. J., Liu, X., & Xu, C. (2017) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.486 · Cited by 1,940 · see citing works
From learning models of natural image patches to whole image restoration
Zoran, D., & Weiss, Y. (2011) · 2011 International Conference on Computer Vision · doi:10.1109/iccv.2011.6126278 · Cited by 1,522 · see citing works
Generative Modeling by Estimating Gradients of the Data Distribution
Song, Y., & Ermon, S. (2019) · arXiv · doi:10.48550/arxiv.1907.05600 · Cited by 1,453 · see citing works
An information fidelity criterion for image quality assessment using natural scene statistics
Sheikh, H. R., Bovik, A. C., & de Veciana, G. (2005) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.859389 · Cited by 1,399 · see citing works
Chen, Y., & Pock, T. (2017) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2016.2596743 · Cited by 1,344 · see citing works
LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the LoopPreprint
Yu, F., Seff, A., Zhang, Y., Song, S., Funkhouser, T., & Xiao, J. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1506.03365 · Cited by 1,339 · see citing works
Plug-and-Play priors for model based reconstruction
Venkatakrishnan, S. V., Bouman, C. A., & Wohlberg, B. (2013) · 2013 IEEE Global Conference on Signal and Information Processing · doi:10.1109/globalsip.2013.6737048 · Cited by 1,178 · see citing works
VSNR: A Wavelet-Based Visual Signal-to-Noise Ratio for Natural Images
Chandler, D. M., & Hemami, S. S. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.901820 · Cited by 1,147 · see citing works
Fields of Experts: A Framework for Learning Image Priors
Roth, S., & Black, M. J. (2005) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2005.160 · Cited by 1,087 · see citing works
The Perception-Distortion Tradeoff
Blau, Y., & Michaeli, T. (2018) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2018.00652 · Cited by 1,001 · see citing works
Exponential Convergence of Langevin Distributions and Their Discrete Approximations
Roberts, G. O., & Tweedie, R. L. (1996) · Bernoulli · doi:10.2307/3318418 · Cited by 1,000 · see citing works
The Little Engine That Could: Regularization by Denoising (RED)
Romano, Y., Elad, M., & Milanfar, P. (2017) · SIAM Journal on Imaging Sciences · doi:10.1137/16m1102884 · Cited by 934 · see citing works
Self-citationFFDNet: Toward a fast and flexible solution for CNN-Based image denoising
Zhang, K., Zuo, W., & Zhang, L. (2018) · TUScholarShare (Temple University) · Cited by 916 · see citing works
Residual Dense Network for Image Restoration
Zhang, Y., Tian, Y., Kong, Y., Zhong, B., & Fu, Y. (2020) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2020.2968521 · Cited by 904 · see citing works
Tests for departure from normality. Empirical results for the distributions of b2 and √b1
D’Agostino, R. B., & Pearson, E. S. (1973) · Biometrika · doi:10.1093/biomet/60.3.613 · Cited by 607 · see citing works
Yu, G., Sapiro, G., & Mallat, S. (2011) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2176743 · Cited by 564 · see citing works
Non-Local Recurrent Network for Image RestorationPreprint
Liu, D., Wen, B., Fan, Y., Loy, C. C., & Huang, T. S. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1806.02919 · Cited by 557 · see citing works
PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models
Menon, S., Damian, A., Hu, S., Ravi, N., & Rudin, C. D. (2020) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr42600.2020.00251 · Cited by 552 · see citing works
Improved Techniques for Training Score-Based Generative Models
Song, Y., & Ermon, S. (2020) · arXiv · doi:10.48550/arxiv.2006.09011 · Cited by 482 · see citing works
A Review Paper : Noise Models in Digital Image Processing
Boyat, A. K., & Joshi, B. K. (2015) · Signal & Image Processing : An International Journal · doi:10.5121/sipij.2015.6206 · Cited by 418 · see citing works
Chatterjee, P., & Milanfar, P. (2009) · IEEE Transactions on Image Processing · doi:10.1109/tip.2009.2037087 · Cited by 414 · see citing works
A Nonlocal Bayesian Image Denoising Algorithm
Lebrun, M., Buades, A., & Morel, J. (2013) · SIAM Journal on Imaging Sciences · doi:10.1137/120874989 · Cited by 318 · see citing works
Universal Denoising Networks : A Novel CNN Architecture for Image Denoising
Lefkimmiatis, S. (2018) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2018.00338 · Cited by 310 · see citing works
Sparse and Redundant Modeling of Image Content Using an Image-Signature-Dictionary
Aharon, M., & Elad, M. (2008) · SIAM Journal on Imaging Sciences · doi:10.1137/07070156x · Cited by 166 · see citing works
Self-citationPatch Complexity, Finite Pixel Correlations and Optimal Denoising
Levin, A., Nadler, B., Durand, F., & Freeman, W. T. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-33715-4_6 · Cited by 124 · see citing works
Class-Aware Fully Convolutional Gaussian and Poisson Denoising
Remez, T., Litany, O., Giryes, R., & Bronstein, A. M. (2018) · IEEE Transactions on Image Processing · doi:10.1109/tip.2018.2859044 · Cited by 92 · see citing works
Markov Chain Monte Carlo for Statistical Inference
Besag, J. E. (2002) · Cited by 79 · see citing works
Adler, J., & Öktem, O. (2024) · De Gruyter eBooks · doi:10.1515/9783111251233-011 · Cited by 77 · see citing works
Bahat, Y., & Michaeli, T. (2020) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr42600.2020.00279 · Cited by 59 · see citing works
Denoising diffusion probabilistic models
Ho, J. (2024) · TIB Data Manager · doi:10.57702/q2z1tfp2 · Cited by 45 · see citing works
Stochastic image denoising based on Markov-chain Monte Carlo sampling
Wong, A. K. C., Mishra, A. K., Zhang, W., Fieguth, P., & Clausi, D. A. (2011) · Signal Processing · doi:10.1016/j.sigpro.2011.03.021 · Cited by 43 · see citing works
Solving Linear Inverse Problems Using the Prior Implicit in a DenoiserPreprint
Kadkhodaie, Z., & Simoncelli, E. P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.13640 · Cited by 39 · see citing works
Deep class-aware image denoising
Remez, T., Litany, O., Giryes, R., et al. (2017) · International Conference on Sampling Theory and Applications · doi:10.1109/sampta.2017.8024474 · Cited by 38 · see citing works
LIDIA: Lightweight Learned Image Denoising with Instance Adaptation
Vaksman, G., Elad, M., & Milanfar, P. (2020) · IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) · doi:10.1109/cvprw50498.2020.00270 · Cited by 36 · see citing works
Self-citationPatch Ordering as a Regularization for Inverse Problems in Image Processing
Vaksman, G., Zibulevsky, M., & Elad, M. (2016) · SIAM Journal on Imaging Sciences · doi:10.1137/15m1038074 · Cited by 17 · see citing works
Self-citationFast Mixing of Multi-Scale Langevin Dynamics under the Manifold HypothesisPreprint
Block, A., Mroueh, Y., Rakhlin, A., & Ross, J. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.11166 · Cited by 9 · see citing works
When and How Can Deep Generative Models be Inverted?Preprint
Aberdam, A., Simon, D., & Elad, M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.15555 · Cited by 7 · see citing works
Self-citationDeep Energy: Using Energy Functions for Unsupervised Training of DNNsPreprint
Golts, A., Freedman, D. Z., & Elad, M. (2018) · arXiv (Cornell University) · Cited by 6 · see citing works
Self-citationDeep posterior sampling: Uncertainty quantification for large scale inverse problems
Adler, J., & Öktem, O. (2019) · Cited by 6 · see citing works
Towards theoretically-founded learning-based denoising
Zhou, W., & Jalali, S. (2019) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2019.8849348 · Cited by 3 · see citing works
Image Denoising by Wavelet Bayesian Network based on MAP Estimation
Bhanumathi, V., & Lavanya, S. R. (2017) · International Journal of Mathematical and Computational Methods · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- [5][5] Yuval Bahat and Tomer Michaeli. Explorable super resolu- tion. In Proceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition, pages 2716–2725, 2020.
- [8][8] Yochai Blau and Tomer Michaeli. The perception-distortion tradeoff. arXiv preprint arXiv:1711.06077, 2017. · arXiv
- [22][22] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffu- sion probabilistic models. Advances in Neural Information Processing Systems, 33, 2020.
- [27][27] Qi Lei, Ajil Jalal, Inderjit S Dhillon, and Alexandros G Di- makis. Inverting deep generative models, one layer at a time. In Advances in Neural Information Processing Sys- tems, pages 13910–13919, 2019.
Cited by
Sorted by citations
Diffusion Models: A Comprehensive Survey of Methods and Applications
Yang, L., Zhang, Z., Song, Y., Hong, S., Xu, R., Zhao, Y., Zhang, W., Cui, B., & Yang, M.-H. (2024) · ACM Computing Surveys · doi:10.1145/3626235 · Cited by 1,704 · see citing works
- Authors
- Kawar, B., Vaksman, G., & Elad, M.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- ORCID
- Elad, Michael
- Venue
- 2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW)
- Publisher
- IEEE
- Published
- 2021-10
- Pages
- 1866-1875
- ISSN
- 2473-9936 (ISSN-L)
- OpenAlex
- W3124183862
- Cited by
- 42
- References
- 59
- Citations by year
- 2026: 2 · 2025: 7 · 2024: 13 · 2023: 10 · 2022: 6 · 2021: 4
- FWCI
- 2.70
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE International Conference on Computer Vision Workshops (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image Enhancement Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Image Processing Techniques
- Keywords
- image denoising, Langevin dynamics, posterior sampling, image inpainting, perceptual image quality, noise reduction
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
