mlsanityData to 7 Oct 2026

Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition

arXiv 2106.03668 ↗First posted 7 Jun 2021cs.CV cs.LG eess.IVcited by 22

Not on the map. Why?

Abstract (arXiv)

The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixed-points of a deep neural network. We also present numerical results comparing the recovery performance of PnP/RED in compressive sensing against that of recent compressive sensing algorithms based on generative models. Our numerical results suggest that PnP with a pre-trained artifact removal network provides significantly better results compared to the existing state-of-the-art methods.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 46 of its 85 references that are in the map. First posted on arXiv 7 Jun 2021.

Builds on

46 of 85 references.

References · 46

  1. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  2. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,580
  3. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  4. 2021Convex optimizationcited by 2,479
  5. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  6. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  7. 2017Deep Image Priorcited by 1,097
  8. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 407
  9. 2017MoDL: Model Based Deep Learning Architecture for Inverse Problemscited by 384
  10. 2020PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Modelscited by 358
  11. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  12. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
34 more
  1. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  2. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  3. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  4. 2017Non-convex Optimization for Machine Learningcited by 132
  5. 2021Deep Equilibrium Architectures for Inverse Problems in Imagingcited by 126
  6. 2018Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networkscited by 120
  7. 2019Deep Plug-and-Play Super-Resolution for Arbitrary Blur Kernelscited by 112
  8. 2017Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problemscited by 107
  9. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 102
  10. 2019DeepRED: Deep Image Prior Powered by REDcited by 84
  11. 2017A Review of Convolutional Neural Networks for Inverse Problems in Imagingcited by 81
  12. 2019Deep Learning Methods for Parallel Magnetic Resonance Image Reconstructioncited by 81
  13. 2018Denoising Prior Driven Deep Neural Network for Image Restorationcited by 80
  14. 2015Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolationcited by 78
  15. 2019Plug and play methods for magnetic resonance imaging (long version)cited by 75
  16. 2018An Online Plug-and-Play Algorithm for Regularized Image Reconstructioncited by 70
  17. 2014From Denoising to Compressed Sensingcited by 67
  18. 2019RARE: Image Reconstruction using Deep Priors Learned without Ground Truthcited by 64
  19. 2017Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibriumcited by 58
  20. 2018Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guaranteescited by 58
  21. 2020Regularization by Denoising via Fixed-Point Projection (RED-PRO)cited by 55
  22. 2020Scalable Plug-and-Play ADMM with Convergence Guaranteescited by 49
  23. 2018prDeep: Robust Phase Retrieval with a Flexible Deep Networkcited by 46
  24. 2015A Deep Learning Approach to Structured Signal Recoverycited by 43
  25. 2020Provable Convergence of Plug-and-Play Priors with MMSE denoiserscited by 39
  26. 2020Tuning-free Plug-and-Play Proximal Algorithm for Inverse Imaging Problemscited by 38
  27. 2019Block Coordinate Regularization by Denoisingcited by 33
  28. 2015On learning optimized reaction diffusion processes for effective image restorationcited by 25
  29. 2019Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrievalcited by 18
  30. 2019Fast and Provable ADMM for Learning with Generative Priorscited by 18
  31. 2021SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guaranteescited by 18
  32. 2020Boosting the Performance of Plug-and-Play Priors via Denoiser Scalingcited by 12
  33. 2018Algorithmic Aspects of Inverse Problems Using Generative Modelscited by 8
  34. 2020Joint Reconstruction and Calibration using Regularization by Denoisingcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 6; 2023: 4; 2024: 1; 2025: 7; 2026: 3.

22 papers.

Sort:

By area:

  1. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  2. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
  3. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  4. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
  5. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  6. 2023Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysiscited by 10
  7. 2022Deep Model-Based Architectures for Inverse Problems under Mismatched Priorscited by 8
  8. 2023Block Coordinate Plug-and-Play Methods for Blind Inverse Problemscited by 8
  9. 2024Learning pseudo-contractive denoisers for inverse problemscited by 6
  10. 2022Learning Sparsity-Promoting Regularizers using Bilevel Optimizationcited by 4
  11. 2022Monotonically Convergent Regularization by Denoisingcited by 3
  12. 2023Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problemscited by 3
10 more
  1. 2025Radio Map Estimation via Latent Domain Plug-and-Play Denoisingcited by 3
  2. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithmcited by 3
  3. 2025NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problemscited by 3
  4. 2025Plug-and-Play Posterior Sampling for Blind Inverse Problemscited by 2
  5. 2025Neural Inverse Scattering with Score-based Regularizationcited by 1
  6. 2025Moir'eXNet: Adaptive Multi-Scale Demoir'eing with Linear Attention Test-Time Training and Truncated Flow Matching Priorcited by 1
  7. 2026Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstructioncited by 1
  8. 2025From the Gradient-Step Denoiser to the Proximal Denoiser and their associated convergent Plug-and-Play algorithmscited by 0
  9. 2026ScoreField: Neural Inverse Scattering with Score-Based Generative Priorscited by 0
  10. 2026Plug-and-Play Methods Provably Converge Even with Improperly Trained Denoisers: Convergence by Architectural Designcited by 0