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1 IMB - Institut de Mathématiques de Bourgogne Dijon 2 CNRS - Centre National de la Recherche Scientifique

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.

Keywords : inverse problem analysis sparsity Lasso support identification barrier penalization





Author: Abdessamad Barbara - Abderrahim Jourani - Samuel Vaiter -

Source: https://hal.archives-ouvertes.fr/



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