Work

On Representer Theorems and Convex Regularization

Year: 2018

Type: preprint

Abstract: We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and elements of the extreme rays of the regularizer level sets. An extension to a broader class of quasi-convex regularizers is also discussed. As a side result, we characterize the minimizers of the total gradient variation, which was still an unresolved problem.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1806.09810

Authors: Boyer, Claire, Chambolle, Antonin, De Castro, Yohann, Duval, Vincent, De Gournay, Frédéric, Weiss, Pierre