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Pré-Publication, Document De Travail Année : 2023

IML FISTA: Inexact MuLtilevel FISTA for Image Restoration

Résumé

This paper presents IML FISTA, a multilevel inertial and inexact forward-backward algorithm, based on the use of the Moreau envelope to build efficient and useful coarse corrections. Such construction is provided for a broad class of composite optimization problems with proximable functions. 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 several image reconstruction problems and we show that it considerably accelerates the convergence of classical methods such as FISTA, for large-scale images.
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Dates et versions

hal-04075814 , version 1 (25-04-2023)
hal-04075814 , version 2 (03-07-2023)
hal-04075814 , version 3 (28-03-2024)

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Guillaume Lauga, Elisa Riccietti, Nelly Pustelnik, Paulo Gonçalves. IML FISTA: Inexact MuLtilevel FISTA for Image Restoration. 2023. ⟨hal-04075814v1⟩
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