mlsanityData to 7 Oct 2026

Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications

arXiv 1605.01710 ↗First posted 5 May 2016cs.CVcited by 244

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Cited by 59 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name "Plug-and-Play ADMM". Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since Plug-and-Play ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for common Gaussian and Poissonian image restoration problems. In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixed point convergence. We show that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on super-resolution and single-photon imaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in each problem type, and demonstrate promising experimental results of the algorithm.

Key facts. Cited by 244 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 May 2016.

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Citing papers per year: 2021: 31; 2022: 42; 2023: 44; 2024: 52; 2025: 47; 2026: 28.

244 papers.

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  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  2. 2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 335
  3. 2021Learning to Optimize: A Primer and A Benchmarkcited by 206
  4. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  5. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  6. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 156
  7. 2021Deep Equilibrium Architectures for Inverse Problems in Imagingcited by 126
  8. 2022Deep Generalized Unfolding Networks for Image Restorationcited by 119
  9. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  10. 2022ShadowDiffusion: When Degradation Prior Meets Diffusion Model for Shadow Removalcited by 102
  11. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  12. 2021Blind Image Super-Resolution: A Survey and Beyondcited by 93
38 more
  1. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  2. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  3. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
  4. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  5. 2023Training-free Linear Image Inverses via Flowscited by 70
  6. 2024Guidance with Spherical Gaussian Constraint for Conditional Diffusioncited by 69
  7. 2022Coarse-to-Fine Sparse Transformer for Hyperspectral Image Reconstructioncited by 67
  8. 2022Degradation-Aware Unfolding Half-Shuffle Transformer for Spectral Compressive Imagingcited by 66
  9. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problemscited by 65
  10. 2024DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Modelscited by 60
  11. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 58
  12. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  13. 2022Model-Based Deep Learning: On the Intersection of Deep Learning and Optimizationcited by 50
  14. 2024Tutorial on Diffusion Models for Imaging and Visioncited by 49
  15. 2021Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fieldscited by 48
  16. 2022Learned reconstruction methods with convergence guaranteescited by 46
  17. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 45
  18. 2023Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidancecited by 43
  19. 2021Plug-and-Play Algorithms for Video Snapshot Compressive Imagingcited by 42
  20. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 41
  21. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
  22. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  23. 2021End-to-end reconstruction meets data-driven regularization for inverse problemscited by 32
  24. 2021Dense Deep Unfolding Network with 3D-CNN Prior for Snapshot Compressive Imagingcited by 31
  25. 2021Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Priorcited by 24
  26. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problemscited by 23
  27. 2021Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Conditioncited by 22
  28. 2021NTIRE 2021 Challenge on Burst Super-Resolution: Methods and Resultscited by 22
  29. 2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
  30. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  31. 2022Deep Plug-and-Play Prior for Hyperspectral Image Restorationcited by 22
  32. 2022Residual Degradation Learning Unfolding Framework with Mixing Priors across Spectral and Spatial for Compressive Spectral Imagingcited by 22
  33. 2021Lucas-Kanade Reloaded: End-to-End Super-Resolution from Raw Image Burstscited by 21
  34. 2021Fixed-Point and Objective Convergence of Plug-and-Play Algorithmscited by 19
  35. 2021FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removalcited by 19
  36. 2023Interpreting and Improving Diffusion Models from an Optimization Perspectivecited by 19
  37. 2021SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guaranteescited by 18
  38. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18

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