The paper IML FISTA: A Multilevel Framework for Inexact and Inertial Forward-Backward. Application to Image Restoration, by Guillaume Lauga, Elisa Riccietti, Nelly Pustelnik and Paulo Gonçalves, was accepted for publication at SIAM Journal on Imaging Sciences!
This work presents a multilevel framework for inertial and inexact proximal algorithms, that encompasses multilevel versions of classical algorithms such as forward-backward and FISTA.
The methods are 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.
Several image restoration problems (image deblurring, hyperspectral images reconstruction, etc …) are considered where the proposed multilevel algorithm greatly accelerates the convergence of the one level (i.e. standard) version of the method.
Paper: https://inria.hal.science/hal-04075814
