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1404. Multilevel proximal methods for image restoration

Invited abstract in session TA-32: Nonsmooth optimization and applications, Part I, stream Advances in large scale nonlinear optimization.

Tuesday, 8:30-10:00
Room: 41 (building: 303A)

Authors (first author is the speaker)

1. Guillaume Lauga
Informatique, ENS Lyon
2. Elisa Riccietti
LIP, ENS Lyon
3. Nelly Pustelnik
Univ Lyon, Ens de Lyon, Univ Lyon 1, CNRS, Laboratoire de Physique, Lyon

Abstract

Solving high-dimensional optimisation problems is a difficult task, and numerous methods have been proposed to compensate for the high cost in computation time. The approach explored in this work exploits the structure of these optimisation problems, in order to reduce the computational cost of their solution.

Specifically, we focus on the multi-resolution structure at the heart of multi-level optimisation methods. These approaches take advantage of the definition of coarse approximations of the objective function to make its minimisation more efficient. In this talk, we present a proximal multilevel algorithm IML FISTA - Inexact Multilevel FISTA - suitable for the solution of optimisation problems where the non-smooth component of the objective function has no explicit formulation for the proximal operator.

The proposed method is then adapted to solve imaging problem in radio-astronomy. To reconstruct such images, a high number of observations in the Fourier space are combined. Such high number creates a computational bottleneck. We demonstrate that IML FISTA can provide considerable acceleration by using coarse approximation constructed in the observation space.

Keywords

Status: accepted

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