On Representer Theorems and Convex Regularization
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 quasiconvex regularizers is also discussed. As a side result, we characterize the minimizers of the total gradient variation, which was still an unresolved problem.
 Publication:

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1806.09810
 Bibcode:
 2018arXiv180609810B
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Information Theory