# Regularization by Denoising via Fixed-Point Projection (RED-PRO)

@article{Cohen2021RegularizationBD, title={Regularization by Denoising via Fixed-Point Projection (RED-PRO)}, author={Regev Cohen and Michael Elad and Peyman Milanfar}, journal={SIAM J. Imaging Sci.}, year={2021}, volume={14}, pages={1374-1406} }

Inverse problems in image processing are typically cast as optimization tasks, consisting of data fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED). While both have shown state-of-the-art results in various recovery tasks, their theoretical justification is incomplete. In this paper, we aim to enrich the understanding…

## Figures and Tables from this paper

## 27 Citations

An Interpretation Of Regularization By Denoising And Its Application With The Back-Projected Fidelity Term

- Computer Science2021 IEEE International Conference on Image Processing (ICIP)
- 2021

This paper shows that the RED gradient can be seen as a (sub)gradient of a prior function--but taken at a denoised version of the point, and proposes to combine RED with the Back-Projection (BP) fidelity term rather than the common Least Squares (LS) term that is used in previous works.

Fixed-Point and Objective Convergence of Plug-and-Play Algorithms

- Mathematics, Computer ScienceIEEE Transactions on Computational Imaging
- 2021

A novelty in this regard is that the analysis covers non-symmetric denoisers such as nonlocal means and almost any convex data-fidelity, and makes use of the convergence theory of averaged operators and a special inner product derived from the linear denoiser.

Learning Maximally Monotone Operators for Image Recovery

- Mathematics, Computer ScienceSIAM J. Imaging Sci.
- 2021

An operator regularization is performed, where a maximally monotone operator (MMO) is learned in a supervised manner, and a universal approximation theorem proving that nonexpansive NNs provide suitable models for the resolvent of a wide class of MMOs is provided.

Async-RED: A Provably Convergent Asynchronous Block Parallel Stochastic Method using Deep Denoising Priors

- Computer ScienceICLR
- 2021

This work proposes a new asynchronous RED (ASYNC-RED) algorithm that enables asynchronous parallel processing of data, making it significantly faster than its serial counterparts for large-scale inverse problems.

Single Image Non-uniform Blur Kernel Estimation via Adaptive Basis Decomposition

- MathematicsArXiv
- 2021

This paper proposes a general, non-parametric model for dense non-uniform motion blur estimation and shows that it contributes to bridging the gap between model-based and data-driven approaches for deblurring real photographs.

Feasibility-based fixed point networks

- MathematicsFixed Point Theory and Algorithms for Sciences and Engineering
- 2021

This work fuses data-driven regularization and convex feasibility in a theoretically sound manner using feasibility-based fixed point networks (F-FPNs), which demonstrate performance increases when compared to standard TV-based recovery methods for CT reconstruction and a comparable neural network based on algorithm unrolling.

CoIL: Coordinate-based Internal Learning for Imaging Inverse Problems

- Computer Science
- 2021

We propose Coordinate-based Internal Learning (CoIL) as a new deep-learning (DL) methodology for continuous representation of measurements. Unlike traditional DL methods that learn a mapping from the…

Gradient Step Denoiser for convergent Plug-and-Play

- Computer Science, MathematicsArXiv
- 2021

This work proposes a new type of PnP method, based on half-quadratic splitting, for which the denoiser is realized as a gradient descent step on a functional parameterized by a deep neural network.

ASYNC-RED: A PROVABLY CONVERGENT ASYN-

- Computer Science, Mathematics
- 2021

This work proposes a new asynchronous RED (ASYNC-RED) algorithm that enables asynchronous parallel processing of data, making it significantly faster than its serial counterparts for large-scale inverse problems.

Accelerating Plug-and-Play Image Reconstruction via Multi-Stage Sketched Gradients

- Computer ScienceArXiv
- 2022

A novel multi-stage sketched gradient iterations which first perform downsampling dimensionality reduction in the image space, and then efficiently approximate the true gradient using the sketches gradient in the low-dimensional space is proposed.

## References

SHOWING 1-10 OF 117 REFERENCES

Image Restoration by Iterative Denoising and Backward Projections

- Computer Science, MathematicsIEEE Transactions on Image Processing
- 2019

An alternative method for solving inverse problems using off-the-shelf denoisers, which requires less parameter tuning and is competitiveness with task-specific techniques and the P&P approach for image inpainting and deblurring is proposed.

Regularization by Denoising: Clarifications and New Interpretations

- Computer ScienceIEEE Transactions on Computational Imaging
- 2019

This work proposes a new framework called Score-Matching by Denoising (SMD), which aims to match a “score” (i.e., the gradient of a log-prior) and shows tight connections between SMD, kernel density estimation, and constrained minimum mean-squared error denoising.

Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems

- Computer Science2017 IEEE International Conference on Computer Vision (ICCV)
- 2017

This paper studies the possibility of replacing the proximal operator of the regularization used in many convex energy minimization algorithms by a denoising neural network, and obtains state-of-the-art reconstruction results.

Block Coordinate Regularization by Denoising

- Computer Science, MathematicsIEEE Transactions on Computational Imaging
- 2020

A new block coordinate RED algorithm is developed that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables and theoretically analyzes the convergence of the algorithm and discusses its relationship to the traditional proximal optimization.

The Little Engine That Could: Regularization by Denoising (RED)

- Computer ScienceSIAM J. Imaging Sci.
- 2017

This paper provides an alternative, more powerful, and more flexible framework for achieving Regularization by Denoising (RED): using the denoising engine in defining the regulariza...

Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective

- Computer ScienceIEEE Transactions on Computational Imaging
- 2019

This paper restricts the denoisers to the class of graph filters under a linearity assumption, or more specifically the symmetric smoothing filters, and introduces a new analysis technique via the concept of consensus equilibrium to provide interpretations to problems involving multiple priors.

Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications

- Computer ScienceIEEE Transactions on Computational Imaging
- 2017

It is shown that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme.

A Convergent Image Fusion Algorithm Using Scene-Adapted Gaussian-Mixture-Based Denoising

- Computer ScienceIEEE Transactions on Image Processing
- 2019

This work proposes using a scene-adapted denoiser plugged into the iterations of the alternating direction method of multipliers, which yields state-of-the-art results but also allows proving convergence of the resulting algorithm.

DeepRED: Deep Image Prior Powered by RED

- Computer ScienceICCV 2019
- 2019

This work proposes to bring-in the concept of Regularization by Denoising (RED), which leverages existing denoisers for regularizing inverse problems, and shows how the two can be merged into a highly effective unsupervised recovery process while avoiding the need to differentiate the chosen denoiser, and leading to very effective results.

Boosting the Performance of Plug-and-Play Priors via Denoiser Scaling

- Computer Science2020 54th Asilomar Conference on Signals, Systems, and Computers
- 2020

A scaling parameter is introduced that adjusts the magnitude of the denoiser input and output so that the performance of plug-and-play prirs for denoising CNN priors that do not have explicitly tunable parameters is improved.