# Monotonically Convergent Regularization by Denoising

arXiv: https://arxiv.org/abs/2202.04961 · HTML: https://mlsanity.com/paper/2202.04961/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [An Online Plug-and-Play Algorithm for Regularized Image Reconstruction](https://mlsanity.com/paper/1809.04693/) (2018)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Regularization by Denoising via Fixed-Point Projection (RED-PRO)](https://mlsanity.com/paper/2008.00226/) (2020)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Block Coordinate Regularization by Denoising](https://mlsanity.com/paper/1905.05113/) (2019)
- [Deep Unfolding of a Proximal Interior Point Method for Image Restoration](https://mlsanity.com/paper/1812.04276/) (2018)
- [Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition](https://mlsanity.com/paper/2106.03668/) (2021)

## Built on by (most cited first, 3 of 3)

- [Provable Probabilistic Imaging using Score-Based Generative Priors](https://mlsanity.com/paper/2310.10835/) (2023)
- [Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems](https://mlsanity.com/paper/2406.02462/) (2024)
- [Patch-Based Diffusion Models Beat Whole-Image Models for Mismatched Distribution Inverse Problems](https://mlsanity.com/paper/2410.11730/) (2024)

## Abstract (arXiv)

Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications using pre-trained deep neural nets as denoisers. Despite the recent progress, the stable convergence of RED algorithms remains an open problem. The existing RED theory only guarantees stability for convex data-fidelity terms and nonexpansive denoisers. This work addresses this issue by developing a new monotone RED (MRED) algorithm, whose convergence does not require nonexpansiveness of the deep denoising prior. Simulations on image deblurring and compressive sensing recovery from random matrices show the stability of MRED even when the traditional RED algorithm diverges.