mlsanityData to 7 Oct 2026

Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling

arXiv 2402.12292 ↗First posted 19 Feb 2024stat.ML cs.CV cs.LGcited by 9

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Abstract (arXiv)

This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It additionally implements a Monte Carlo algorithm specifically tailored for sampling from the resulting posterior distribution, based on an asymptotically exact data augmentation (AXDA). The proposed algorithm is an approximate instance of split Gibbs sampling (SGS) which embeds one Langevin Monte Carlo step. The proposed method is applied to common imaging tasks such as deblurring, inpainting and super-resolution, demonstrating its efficacy through extensive numerical experiments. These contributions advance Bayesian inference in imaging by leveraging data-driven regularization strategies within a probabilistic framework.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 19 of its 42 references that are in the map. First posted on arXiv 19 Feb 2024.

Builds on

19 of 42 references.

References · 19

  1. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  2. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  3. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 467
  4. 2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 335
  5. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  6. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  7. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  8. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  9. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
  10. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 102
  11. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  12. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 83
7 more
  1. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
  2. 2020Regularization by Denoising via Fixed-Point Projection (RED-PRO)cited by 55
  3. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  4. 2021Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmscited by 24
  5. 2017Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methodscited by 13
  6. 2021DG-LMC: A Turn-key and Scalable Synchronous Distributed MCMC Algorithm via Langevin Monte Carlo within Gibbscited by 11
  7. 2019Asymptotically exact data augmentation: models, properties and algorithmscited by 8

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 2; 2026: 3.

9 papers.

  1. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  2. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  3. 2024Repulsive Latent Score Distillation for Solving Inverse Problemscited by 15
  4. 2024Plug-and-Play Priors as a Score-Based Methodcited by 5
  5. 2026Stochastic Generative Plug-and-Play Priorscited by 3
  6. 2025Net2Net: When Un-trained Meets Pre-trained Networks for Robust Real-World Denoisingcited by 0
  7. 2025Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problemscited by 0
  8. 2026Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental studycited by 0
  9. 2026FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolantscited by 0