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arXiv · 1812.04355

Convex Regularization and Representer Theorems

Claire Boyer·Antonin Chambolle·Yohann de Castro·Vincent Duval·Frédéric de Gournay·Pierre Weiss
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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.

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Claire Boyer, Antonin Chambolle, Yohann de Castro, Vincent Duval, Frédéric de Gournay, Pierre Weiss. 2018-12-11. Convex Regularization and Representer Theorems. https://arxiv.org/abs/1812.04355

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