Online Regularization by Denoising with Applications to Phase Retrieval

TL;DR

This paper introduces an online version of the RED algorithm, enabling efficient processing of large datasets in imaging inverse problems, with proven convergence in convex cases and promising results in phase retrieval applications.

Contribution

The paper presents a novel online RED algorithm that processes data incrementally, extending RED's applicability to large-scale problems and demonstrating its effectiveness in phase retrieval.

Findings

On-RED converges in convex settings.

On-RED performs well in phase retrieval tasks.

It is a scalable alternative to batch RED algorithms.

Abstract

Regularization by denoising (RED) is a powerful framework for solving imaging inverse problems. Most RED algorithms are iterative batch procedures, which limits their applicability to very large datasets. In this paper, we address this limitation by introducing a novel online RED (On-RED) algorithm, which processes a small subset of the data at a time. We establish the theoretical convergence of On-RED in convex settings and empirically discuss its effectiveness in non-convex ones by illustrating its applicability to phase retrieval. Our results suggest that On-RED is an effective alternative to the traditional RED algorithms when dealing with large datasets.