# Solving RED with Weighted Proximal Methods

## TL;DR

This paper introduces weighted proximal methods (WPMs) to improve the computational efficiency of the RED framework by reducing the number of denoiser calls needed for inverse problem solving.

## Contribution

It demonstrates that existing RED solvers are special cases of WPMs and proposes variants that significantly decrease computation time.

## Key findings

- WPMs encompass existing RED solvers as special cases.
- Variants of WPM reduce denoiser calls and computation time.
- Numerical experiments confirm improved efficiency of WPM-based RED solutions.

## Abstract

REgularization by Denoising (RED) is an attractive framework for solving inverse problems by incorporating state-of-the-art denoising algorithms as the priors. A drawback of this approach is the high computational complexity of denoisers, which dominate the computation time. In this paper, we apply a general framework called weighted proximal methods (WPMs) to solve RED efficiently. We first show that two recently introduced RED solvers (using the fixed point and accelerated proximal gradient methods) are particular cases of WPMs. Then we show by numerical experiments that slightly more sophisticated variants of WPM can lead to reduced run times for RED by requiring a significantly smaller number of calls to the denoiser.