A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems

TL;DR

This paper introduces an adaptive Plug-and-Play algorithm with a Projected Landweber Operator for split convex feasibility problems, demonstrating superior performance in inverse imaging tasks with theoretical convergence guarantees.

Contribution

It proposes a novel PnP algorithm with theoretical guarantees based on the Projected Landweber Operator, addressing practical step size issues and noise limitations.

Findings

Outperforms RED and RED-PRO in image deblurring.

Effective in super-resolution and compressed sensing MRI.

Provides convergence guarantees for practical PnP applications.

Abstract

In recent years Plug-and-Play (PnP) methods have achieved state-of-the-art performance in inverse imaging problems by replacing proximal operators with denoisers. Based on the proximal gradient method, some theoretical results of PnP have appeared, where appropriate step size is crucial for convergence analysis. However, in practical applications, applying PnP methods with theoretically guaranteed step sizes is difficult, and these algorithms are limited to Gaussian noise. In this paper,from a perspective of split convex feasibility problems (SCFP), an adaptive PnP algorithm with Projected Landweber Operator (PnP-PLO) is proposed to address these issues. Numerical experiments on image deblurring, super-resolution, and compressed sensing MRI experiments illustrate that PnP-PLO with theoretical guarantees outperforms state-of-the-art methods such as RED and RED-PRO.