# Block Coordinate Regularization by Denoising

## TL;DR

This paper introduces a block coordinate RED algorithm for large-scale estimation problems, combining theoretical convergence analysis with numerical validation using CNN denoisers, advancing plug-and-play prior methods.

## Contribution

Develops a novel block coordinate RED algorithm that decomposes large problems, with theoretical convergence analysis and validation using CNN-based denoisers.

## Key findings

- Algorithm converges under certain conditions
- Effective with CNN denoisers in imaging tasks
- Extends theoretical understanding of RED methods

## Abstract

We consider the problem of estimating a vector from its noisy measurements using a prior specified only through a denoising function. Recent work on plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the state-of-the-art performance of estimators under such priors in a range of imaging tasks. In this work, we develop a new block coordinate RED algorithm that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables. We theoretically analyze the convergence of the algorithm and discuss its relationship to the traditional proximal optimization. Our analysis complements and extends recent theoretical results for RED-based estimation methods. We numerically validate our method using several denoiser priors, including those based on convolutional neural network (CNN) denoisers.