Iteratively reweighted penalty alternating minimization methods with continuation for image deblurring

TL;DR

This paper introduces an iteratively reweighted penalty alternating minimization algorithm with continuation for nonconvex image deblurring problems, offering faster convergence and improved efficiency over existing methods.

Contribution

The paper proposes a novel algorithm combining reweighted minimization and continuation strategies, with proven convergence and superior performance in image deblurring tasks.

Findings

The algorithm converges under weaker conditions.

It achieves faster speed compared to nonconvex ADMM.

Numerical results confirm high efficiency and effectiveness.

Abstract

In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating minimization algorithm. To speed up the algorithm, we also apply the continuation strategy to the penalty parameter. A convergence result is proved for the algorithm. Compared with the nonconvex ADMM, the proposed algorithm enjoys both theoretical and computational advantages like weaker convergence requirements and faster speed. Numerical results demonstrate the efficiency of the proposed algorithm.