Block-coordinate Plug-And-Play Methods with Armijo-like line-search for Image Restoration

TL;DR

This paper introduces block-coordinate Plug-and-Play methods with line-search for image restoration, reducing memory use and maintaining high reconstruction quality in large-scale inverse problems.

Contribution

It proposes a novel block-coordinate PnP framework with convergence guarantees, enabling efficient large-scale image restoration with lower memory requirements.

Findings

Achieves state-of-the-art image reconstruction quality.

Substantially reduces GPU memory consumption.

Effective for large-scale and resource-constrained applications.

Abstract

In this paper, we develop a class of block-coordinate Plug-and-Play (PnP) methods to address imaging inverse problems. The block-coordinate strategy is designed to reduce the high memory consumption arising in PnP methods that rely on Gradient Step denoisers, whose implementation typically requires storing large computational graphs. The proposed methods are based on a block-coordinate forward-backward framework for solving non-convex and non-separable composite optimization problems. Furthermore, such methods allow for the joint use of inertial acceleration, variable metric strategies, inexact proximal computations, and adaptive steplength selection via an appropriate line-search procedure. Under mild assumptions on the objective function, we establish a sublinear convergence rate and the stationarity of the limit points. Moreover, convergence of the entire sequence of the iterates is guaranteed under a Kurdyka-{\L}ojasiewicz assumption. Numerical experiments on ill-posed imaging problems, including deblurring and super-resolution, demonstrate that the proposed PnP approach achieves state-of-the-art reconstruction quality while substantially reducing GPU memory requirements, making it particularly suitable for large-scale and resource-constrained imaging applications.