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On the Local Minimizers of the CEL0 Relaxation

Emmanuel Soubies 1, 2, 3 Laure Blanc-Féraud 4 Gilles Aubert 5 
1 IRIT-SC - Signal et Communications
IRIT - Institut de recherche en informatique de Toulouse
4 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : We study the strict local minimizers of the CEL0 func-tional, an exact continuous relaxation of the`0-regularized least-squarescriterion. More precisely, we derive a necessary and sufficient conditionfor strict local optimality, recalling that global minimizers are strict.Moreover, we quantify the number of strict local (not global) minimizersof the initial functional that are eliminated by the relax.
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Submitted on : Monday, August 5, 2019 - 4:23:12 PM
Last modification on : Thursday, August 4, 2022 - 4:58:12 PM
Long-term archiving on: : Wednesday, January 8, 2020 - 10:47:59 PM


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  • HAL Id : hal-02263782, version 1


Emmanuel Soubies, Laure Blanc-Féraud, Gilles Aubert. On the Local Minimizers of the CEL0 Relaxation. SPARS 2019 - Signal Processing with Adaptive Sparse Structured Representations - Workshop, Jul 2019, Toulouse, France. ⟨hal-02263782⟩



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