On Representer Theorems and Convex Regularization
Optimization and Control
2018-11-27 v3 Information Theory
math.IT
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.
Cite
@article{arxiv.1806.09810,
title = {On Representer Theorems and Convex Regularization},
author = {Claire Boyer and Antonin Chambolle and Yohann De Castro and Vincent Duval and Frédéric De Gournay and Pierre Weiss},
journal= {arXiv preprint arXiv:1806.09810},
year = {2018}
}