A Majorize-Minimize subspace approach for l2-l0 image regularization

TL;DR

This paper introduces a Majorize-Minimize subspace algorithm for nonconvex l2-l0 regularized image processing, demonstrating fast convergence and effectiveness in data recovery tasks.

Contribution

It proposes a novel efficient algorithm for l2-l0 regularization in image processing, with convergence analysis and practical effectiveness shown through experiments.

Findings

Algorithm converges rapidly in image recovery tasks.

Effective in sparse image regularization with nonconvex penalties.

Demonstrated superior performance over existing methods.

Abstract

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes edge-preserving measures or frame-analysis potentials commonly used in image processing. As shown by our asymptotic results, the l2-l0 penalties we consider may be employed to provide approximate solutions to l0-penalized optimization problems. One of the advantages of the proposed approach is that it allows us to derive an efficient Majorize-Minimize subspace algorithm. The convergence of the algorithm is investigated by using recent results in nonconvex optimization. The fast convergence properties of the proposed optimization method are illustrated through image processing examples. In particular, its effectiveness is demonstrated on several data recovery problems.