mlsanityData to 7 Oct 2026

Regularization by Denoising via Fixed-Point Projection (RED-PRO)

arXiv 2008.00226 ↗First posted 1 Aug 2020eess.IV cs.CVcited by 55

Not on the map. Why?

Abstract (arXiv)

Inverse problems in image processing are typically cast as optimization tasks, consisting of data-fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED). While both have shown state-of-the-art results in various recovery tasks, their theoretical justification is incomplete. In this paper, we aim to bridge between RED and PnP, enriching the understanding of both frameworks. Towards that end, we reformulate RED as a convex optimization problem utilizing a projection (RED-PRO) onto the fixed-point set of demicontractive denoisers. We offer a simple iterative solution to this problem, by which we show that PnP proximal gradient method is a special case of RED-PRO, while providing guarantees for the convergence of both frameworks to globally optimal solutions. In addition, we present relaxations of RED-PRO that allow for handling denoisers with limited fixed-point sets. Finally, we demonstrate RED-PRO for the tasks of image deblurring and super-resolution, showing improved results with respect to the original RED framework.

Key facts. Cited by 55 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Aug 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 12; 2022: 7; 2023: 14; 2024: 11; 2025: 6; 2026: 5.

55 papers.

Sort:

By area:

  1. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 217
  2. 2021Learning to Optimize: A Primer and A Benchmarkcited by 206
  3. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  4. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  5. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  6. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  7. 2023Training-free Linear Image Inverses via Flowscited by 70
  8. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  9. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  10. 2023Equivariant plug-and-play image reconstructioncited by 26
  11. 2021Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Priorcited by 24
  12. 2021Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmscited by 24
38 more
  1. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  2. 2021Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Conditioncited by 22
  3. 2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
  4. 2023Self-Supervised Learning for Endoscopic Video Analysiscited by 22
  5. 2022WaveFit: An Iterative and Non-autoregressive Neural Vocoder based on Fixed-Point Iterationcited by 20
  6. 2021Fixed-Point and Objective Convergence of Plug-and-Play Algorithmscited by 19
  7. 2021Feasibility-based Fixed Point Networkscited by 17
  8. 2023Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restorationcited by 17
  9. 2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
  10. 2023Provably Convergent Plug-and-Play Quasi-Newton Methodscited by 15
  11. 2022On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descentcited by 14
  12. 2021Non-uniform Blur Kernel Estimation via Adaptive Basis Decompositioncited by 10
  13. 2024Regularization by denoising: Bayesian model and Langevin-within-split Gibbs samplingcited by 9
  14. 2022Deep Model-Based Architectures for Inverse Problems under Mismatched Priorscited by 8
  15. 2023Block Coordinate Plug-and-Play Methods for Blind Inverse Problemscited by 8
  16. 2024Learning pseudo-contractive denoisers for inverse problemscited by 6
  17. 2024FiRe: Fixed-points of Restoration Priors for Solving Inverse Problemscited by 6
  18. 2021Deep Gaussian Denoiser Epistemic Uncertainty and Decoupled Dual-Attention Fusioncited by 4
  19. 2022PAC-Bayesian Learning of Optimization Algorithmscited by 4
  20. 2025Continuous Representation Methods, Theories, and Applications: An Overview and Perspectivescited by 4
  21. 2022Monotonically Convergent Regularization by Denoisingcited by 3
  22. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithmcited by 3
  23. 2025Plug-and-Play Image Restoration with Flow Matching: A Continuous Viewpointcited by 3
  24. 2022Accelerating Plug-and-Play Image Reconstruction via Multi-Stage Sketched Gradientscited by 2
  25. 2023RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imagingcited by 2
  26. 2024Learning truly monotone operators with applications to nonlinear inverse problemscited by 2
  27. 2021OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regressioncited by 1
  28. 2023On the Contractivity of Plug-and-Play Operatorscited by 1
  29. 2023Compressive Recovery of Sparse Precision Matricescited by 1
  30. 2024A Generalization Result for Convergence in Learning-to-Optimizecited by 1
  31. 2026Efficient Unrolled Networks for Large-Scale 3D Inverse Problemscited by 1
  32. 2026GSNR: Graph Smooth Null-Space Representation for Inverse Problemscited by 1
  33. 2021An Interpretation of Regularization by Denoising and its Application with the Back-Projected Fidelity Termcited by 0
  34. 2023Untrained neural network embedded Fourier phase retrieval from few measurementscited by 0
  35. 2024Plug-and-Play Algorithm Convergence Analysis From The Standpoint of Stochastic Differential Equationcited by 0
  36. 2024HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restorationcited by 0
  37. 2024A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problemscited by 0
  38. 2025RELD: Regularization by Latent Diffusion Models for Image Restorationcited by 0

50 most cited of 55 All 55 (JSON)