mlsanityData to 7 Oct 2026

The Little Engine that Could: Regularization by Denoising (RED)

arXiv 1611.02862 ↗First posted 9 Nov 2016cs.CV cs.NA math.NAcited by 303

Not on the map. Why?

Cited by 70 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Removal of noise from an image is an extensively studied problem in image processing. Indeed, the recent advent of sophisticated and highly effective denoising algorithms lead some to believe that existing methods are touching the ceiling in terms of noise removal performance. Can we leverage this impressive achievement to treat other tasks in image processing? Recent work has answered this question positively, in the form of the Plug-and-Play Prior (P3) method, showing that any inverse problem can be handled by sequentially applying image denoising steps. This relies heavily on the ADMM optimization technique in order to obtain this chained denoising interpretation. Is this the only way in which tasks in image processing can exploit the image denoising engine? In this paper we provide an alternative, more powerful and more flexible framework for achieving the same goal. As opposed to the P3 method, we offer Regularization by Denoising (RED): using the denoising engine in defining the regularization of the inverse problem. We propose an explicit image-adaptive Laplacian-based regularization functional, making the overall objective functional clearer and better defined. With a complete flexibility to choose the iterative optimization procedure for minimizing the above functional, RED is capable of incorporating any image denoising algorithm, treat general inverse problems very effectively, and is guaranteed to converge to the globally optimal result. We test this approach and demonstrate state-of-the-art results in the image deblurring and super-resolution problems.

Key facts. Cited by 303 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Nov 2016.

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Citing papers per year: 2021: 40; 2022: 45; 2023: 69; 2024: 42; 2025: 61; 2026: 46.

303 papers.

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  1. 2022Denoising Diffusion Restoration Modelscited by 951
  2. 2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 335
  3. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 275
  4. 2023WIRE: Wavelet Implicit Neural Representationscited by 220
  5. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 217
  6. 2023Generative Diffusion Prior for Unified Image Restoration and Enhancementcited by 198
  7. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  8. 2023Generalization in diffusion models arises from geometry-adaptive harmonic representationscited by 179
  9. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  10. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  11. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 156
  12. 2021Deep Equilibrium Architectures for Inverse Problems in Imagingcited by 126
38 more
  1. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imagingcited by 126
  2. 2023Diffusion with Forward Models: Solving Stochastic Inverse Problems Without Direct Supervisioncited by 112
  3. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  4. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  5. 2021Equivariant Imaging: Learning Beyond the Range Spacecited by 83
  6. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
  7. 2023White-Box Transformers via Sparse Rate Reductioncited by 77
  8. 2022DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstructioncited by 73
  9. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  10. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  11. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  12. 2023Training-free Linear Image Inverses via Flowscited by 70
  13. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  14. 2021Stochastic Image Denoising by Sampling from the Posterior Distributioncited by 45
  15. 2023Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidancecited by 43
  16. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
  17. 2021DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurringcited by 36
  18. 2021Self-supervised Neural Networks for Spectral Snapshot Compressive Imagingcited by 35
  19. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  20. 2021End-to-end reconstruction meets data-driven regularization for inverse problemscited by 32
  21. 2023On the Posterior Distribution in Denoising: Application to Uncertainty Quantificationcited by 31
  22. 2023Regularization by Texts for Latent Diffusion Inverse Solverscited by 31
  23. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priorscited by 28
  24. 2021Interpretable Unsupervised Diversity Denoising and Artefact Removalcited by 26
  25. 2023Equivariant plug-and-play image reconstructioncited by 26
  26. 2021Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Priorcited by 24
  27. 2021Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmscited by 24
  28. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  29. 2021Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Conditioncited by 22
  30. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  31. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  32. 2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
  33. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  34. 2023On the use of deep learning for phase recoverycited by 20
  35. 2021Universal and Flexible Optical Aberration Correction Using Deep-Prior Based Deconvolutioncited by 19
  36. 2021Fixed-Point and Objective Convergence of Plug-and-Play Algorithmscited by 19
  37. 2021FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removalcited by 19
  38. 2021SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guaranteescited by 18

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