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Analysis and Synthesis Denoisers for Forward-Backward Plug-and-Play Algorithms

arXiv 2411.13276 ↗First posted 20 Nov 2024math.OC cs.CV eess.IVcited by 0

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Abstract (arXiv)

In this work we study the behavior of the forward-backward (FB) algorithm when the proximity operator is replaced by a sub-iterative procedure to approximate a Gaussian denoiser, in a Plug-and-Play (PnP) fashion. In particular, we consider both analysis and synthesis Gaussian denoisers within a dictionary framework, obtained by unrolling dual-FB iterations or FB iterations, respectively. We analyze the associated minimization problems as well as the asymptotic behavior of the resulting FB-PnP iterations. In particular, we show that the synthesis Gaussian denoising problem can be viewed as a proximity operator. For each case, analysis and synthesis, we show that the FB-PnP algorithms solve the same problem whether we use only one or an infinite number of sub-iteration to solve the denoising problem at each iteration. To this aim, we show that each "one sub-iteration" strategy within the FB-PnP can be interpreted as a primal-dual algorithm when a warm-restart strategy is used. We further present similar results when using a Moreau-Yosida smoothing of the global problem, for an arbitrary number of sub-iterations. Finally, we provide numerical simulations to illustrate our theoretical results. In particular we first consider a toy compressive sensing example, as well as an image restoration problem in a deep dictionary framework.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 20 of its 65 references that are in the map. First posted on arXiv 20 Nov 2024.

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20 of 65 references.

References · 20

  1. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  2. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 467
  3. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  4. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  5. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  6. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  7. 2022A framework for bilevel optimization that enables stochastic and global variance reduction algorithmscited by 99
  8. 2022Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imagingcited by 94
  9. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  10. 2018Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholdscited by 83
  11. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
  12. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
8 more
  1. 2020Learning Maximally Monotone Operators for Image Recoverycited by 62
  2. 2019Learning step sizes for unfolded sparse codingcited by 29
  3. 2019Deep K-SVD Denoisingcited by 26
  4. 2014Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problemscited by 25
  5. 2020A deep primal-dual proximal network for image restorationcited by 9
  6. 2020Learning to solve TV regularized problems with unrolled algorithmscited by 8
  7. 2023Unfolded proximal neural networks for robust image Gaussian denoisingcited by 7
  8. 2024Learning Firmly Nonexpansive Operatorscited by 3

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