Maximal Solutions of Sparse Analysis Regularization

Abstract : This paper deals with the non-uniqueness of the solutions of an analysis-Lasso regularization. Most of previous works in this area is concerned with the case where the solution set is a singleton, or to derive guarantees to enforce uniqueness. Our main contribution consists in providing a geometrical interpretation of a solution with a maximal D-support, namely the fact that such a solution lives in the relative interior of the solution set. With this result in hand, we also provide a way to exhibit a maximal solution using a primal-dual interior point algorithm.
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https://hal.archives-ouvertes.fr/hal-01467965
Contributeur : Samuel Vaiter <>
Soumis le : mardi 14 février 2017 - 22:25:42
Dernière modification le : mercredi 1 mars 2017 - 10:30:47
Document(s) archivé(s) le : lundi 15 mai 2017 - 18:05:06

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  • HAL Id : hal-01467965, version 1
  • ARXIV : 1703.00192

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Abdessamad Barbara, Abderrahim Jourani, Samuel Vaiter. Maximal Solutions of Sparse Analysis Regularization. 2017. <hal-01467965>

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