mlsanityData to 7 Oct 2026

Provable Convergence of Plug-and-Play Priors with MMSE denoisers

arXiv 2005.07685 ↗First posted 15 May 2020eess.SP eess.IVcited by 39

Not on the map. Why?

Abstract (arXiv)

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 May 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 8; 2023: 9; 2024: 4; 2025: 3; 2026: 6.

39 papers.

Sort:

By area:

  1. 2021Learning to Optimize: A Primer and A Benchmarkcited by 206
  2. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  3. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  4. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  5. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  6. 2021Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fieldscited by 48
  7. 2021Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Priorcited by 24
  8. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  9. 2021Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Conditioncited by 22
  10. 2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
  11. 2021Fixed-Point and Objective Convergence of Plug-and-Play Algorithmscited by 19
  12. 2021SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guaranteescited by 18
27 more
  1. 2024Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problemscited by 18
  2. 2022On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descentcited by 14
  3. 2024DiffusionBlend: Learning 3D Image Prior through Position-aware Diffusion Score Blending for 3D Computed Tomography Reconstructioncited by 13
  4. 2023Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysiscited by 10
  5. 2022Deep Model-Based Architectures for Inverse Problems under Mismatched Priorscited by 8
  6. 2023Block Coordinate Plug-and-Play Methods for Blind Inverse Problemscited by 8
  7. 2023Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Modelscited by 8
  8. 2024FiRe: Fixed-points of Restoration Priors for Solving Inverse Problemscited by 6
  9. 2022CoRRECT: A Deep Unfolding Framework for Motion-Corrected Quantitative R2* Mappingcited by 5
  10. 2024Plug-and-Play Priors as a Score-Based Methodcited by 5
  11. 2025MAP Estimation with Denoisers: Convergence Rates and Guaranteescited by 5
  12. 2022A hybrid approach to seismic deblending: when physics meets self-supervisioncited by 4
  13. 2022Bregman Plug-and-Play Priorscited by 3
  14. 2023Convergence of Nonconvex PnP-ADMM with MMSE Denoiserscited by 3
  15. 2022Provably Convergent Plug & Play Linearized ADMM, applied to Deblurring Spatially Varying Kernelscited by 2
  16. 2023RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imagingcited by 2
  17. 2025Plug-and-Play Posterior Sampling for Blind Inverse Problemscited by 2
  18. 2025Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoiserscited by 2
  19. 2026Beyond MMSE: Enhancing PnP Restoration with ProxiMAPcited by 2
  20. 2026NullFlow: One-Step Generative Reconstructioncited by 2
  21. 2022Video Restoration with a Deep Plug-and-Play Priorcited by 1
  22. 2023On the Contractivity of Plug-and-Play Operatorscited by 1
  23. 2021DAEs for Linear Inverse Problems: Improved Recovery with Provable Guaranteescited by 0
  24. 2026A New Convergence Analysis of Plug-and-Play Proximal Gradient Descent Under Prior Mismatchcited by 0
  25. 2026Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstructioncited by 0
  26. 2026Convergent Plug-and-Play Image Restoration with Annealed Noise Levelscited by 0
  27. 2026Plug-and-Play Methods Provably Converge Even with Improperly Trained Denoisers: Convergence by Architectural Designcited by 0