Monotonically Convergent Regularization by Denoising

TL;DR

This paper introduces a new monotone RED (MRED) algorithm that guarantees stable convergence in inverse imaging problems, even with deep neural network denoisers that are not nonexpansive, improving reliability over traditional RED methods.

Contribution

The paper develops a monotone RED algorithm that ensures convergence without requiring denoisers to be nonexpansive, addressing a key stability limitation of existing RED frameworks.

Findings

MRED converges stably in image deblurring tasks.

MRED remains stable where traditional RED diverges.

Simulations confirm improved convergence in compressive sensing.

Abstract

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.