mlsanityData to 14 Oct 2026

PnP-ReG: Learned Regularizing Gradient for Plug-and-Play Gradient Descent

arXiv 2204.13940 ↗First posted 29 Apr 2022eess.IV cs.CV cs.LGcited by 7

Not on the map. Why?

Abstract (arXiv)

The Plug-and-Play (PnP) framework makes it possible to integrate advanced image denoising priors into optimization algorithms, to efficiently solve a variety of image restoration tasks generally formulated as Maximum A Posteriori (MAP) estimation problems. The Plug-and-Play alternating direction method of multipliers (ADMM) and the Regularization by Denoising (RED) algorithms are two examples of such methods that made a breakthrough in image restoration. However, while the former method only applies to proximal algorithms, it has recently been shown that there exists no regularization that explains the RED algorithm when the denoisers lack Jacobian symmetry, which happen to be the case of most practical denoisers. To the best of our knowledge, there exists no method for training a network that directly represents the gradient of a regularizer, which can be directly used in Plug-and-Play gradient-based algorithms. We show that it is possible to train a network directly modeling the gradient of a MAP regularizer while jointly training the corresponding MAP denoiser. We use this network in gradient-based optimization methods and obtain better results comparing to other generic Plug-and-Play approaches. We also show that the regularizer can be used as a pre-trained network for unrolled gradient descent. Lastly, we show that the resulting denoiser allows for a better convergence of the Plug-and-Play ADMM.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 37 of its 67 references that are in the map. First posted on arXiv 29 Apr 2022.

Builds on

37 of 67 references.

References · 37

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25 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 2; 2024: 2; 2025: 1; 2026: 1.

7 papers.

  1. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 41
  2. 2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
  3. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 15
  4. 2023RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imagingcited by 2
  5. 2023Convergence analysis of equilibrium methods for inverse problemscited by 2
  6. 2024Gradient Networkscited by 0
  7. 2026Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstructioncited by 0