Julien Fageot. TV- based methods for sparse reconstruction in continuous-domain

Le Lundi 8 Février à 10h30 nous accueillerons Julien Fageot post-doctorant à McGill University qui nous parlera de reconstruction parcimonieuse dans le domaine continu.

Title: TV- based methods for sparse reconstruction in continuous-domain

Abstract: We consider the problem of reconstructing an unknown function from some finitely many and possibly corrupted linear measurements. This is achieved by considering an optimization task using a sparsity-promoting regularization. More precisely, we consider the total-variation norm on Radon measures – which is the infinite-dimensional counterpart of the classic L1 norm used for sparse reconstruction in sparse statistical learning and compressed sensing – and a regularization operator that controls the smoothness of the reconstruction. The goal of this presentation is to discuss some theoretical and computational aspects of this infinite-dimensional optimization problem (form of the solutions, connection with spline theory, uniqueness issues, algorithmic strategies) and to illustrate the potential of the method for continuous-domain signal reconstruction.