1. Convex Regularization and Representer Theorems
- Author
-
Boyer, Claire, Chambolle, Antonin, de Castro, Yohann, Duval, Vincent, de Gournay, Frédéric, and Weiss, Pierre
- Subjects
Mathematics - Optimization and Control ,Computer Science - Information Theory ,15A29 - Abstract
We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be understood as the \textit{atoms} of the regularizer. We then explicit that general principle by using a few popular applications. In particular, we relate it to the common wisdom that total gradient variation minimization favors the reconstruction of piecewise constant images., Comment: in Proceedings of iTWIST'18, Paper-ID: 30, Marseille, France, November, 21-23, 2018
- Published
- 2018