期刊
SIAM JOURNAL ON OPTIMIZATION
卷 29, 期 2, 页码 1260-1281出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1200750
关键词
inverse problems; convex regularization; representer theorem; vector space; total variation
资金
- EPSRC [EP/K032208/1]
- Simons Foundation
- EPSRC [EP/K032208/1] Funding Source: UKRI
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions that 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 previously an unresolved problem.
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