Multilevel fista for image restoration

TL;DR

This paper introduces a multilevel FISTA algorithm leveraging the Moreau envelope for improved image restoration, providing theoretical guarantees and outperforming classical FISTA on large-scale images.

Contribution

The paper proposes a novel multilevel FISTA method with theoretical convergence guarantees, enhancing image restoration performance over classical FISTA.

Findings

Outperforms classical FISTA on large-scale images

Provides convergence rate and iterate convergence proofs

Effective for ill-posed image restoration problems

Abstract

This paper presents a multilevel FISTA algorithm, based on the use of the Moreau envelope to build the correction brought by the coarse models, which is easy to compute when the explicit form of the proximal operator of the considered functions is known. This approach is supported by strong theoretical guarantees: we prove both the rate of convergence and the convergence of the iterates to a minimum in the convex case, an important result for ill-posed problems. We evaluate our approach on image restoration problems and we show that it outperforms classical FISTA for large-scale images.