Convergence Analysis of a Proximal Stochastic Denoising Regularization Algorithm

TL;DR

This paper proves the convergence of SNORE Prox, a stochastic proximal gradient algorithm for image restoration, under non-convex assumptions, advancing theoretical understanding of Plug-and-Play methods.

Contribution

It provides the first convergence analysis of SNORE Prox, a stochastic proximal gradient algorithm, under non-convex conditions, enhancing theoretical foundations of PnP methods.

Findings

Proves convergence of SNORE Prox under non-convex assumptions.

Establishes theoretical guarantees for stochastic PnP algorithms.

Supports the effectiveness of SNORE Prox in image restoration tasks.

Abstract

Plug-and-Play methods for image restoration are iterative algorithms that solve a variational problem to recover a clean image from a degraded observation. These algorithms are known to be flexible to changes of degradation and to perform state-of-the-art restoration. Recently, significant efforts have been made to explore new stochastic algorithms based on the Plug-and-Play or REgularization by Denoising (RED) frameworks, such as SNORE, which is a convergent stochastic gradient descent algorithm. A variant of this algorithm, named SNORE Prox, reaches state-of-the-art performances, especially for inpainting tasks. However, the convergence of SNORE Prox, that can be seen as a stochastic proximal gradient descent, has not been analyzed so far. In this paper, we prove the convergence of SNORE Prox under non convex assumptions.