Multilevel fista for image restoration
Guillaume Lauga (DANTE), Elisa Riccietti (DANTE), Nelly Pustelnik, (Phys-ENS), Paulo Gon\c{c}alves (DANTE)

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.
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Taxonomy
TopicsNumerical methods in inverse problems · Medical Image Segmentation Techniques · Image and Signal Denoising Methods
