A note on the convergence of RED algorithms under minimal hypotheses and open questions

TL;DR

This paper establishes convergence results for a modified RED algorithm under specific measurement and prior conditions, highlighting open questions about its broader convergence properties.

Contribution

It provides the first convergence analysis of RED algorithms under minimal assumptions, connecting restricted isometry and Lipschitz conditions.

Findings

Convergence proven under restricted isometry and Lipschitz conditions.

Highlights open questions about RED algorithm convergence.

Provides theoretical foundation for future research.

Abstract

In this note, we give a convergence result for a modified ''regularization-by-denoising''(RED) algorithm under a restricted isometry condition on measurements and a restricted Lipschitz condition on the considered deep projective prior. This study leads to open questions about the convergence of RED algorithms.