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
2 CNRS - Centre National de la Recherche Scientifique
3 UT - Université de Toulouse
4 MORPHEME - Morphologie et Images
5 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Traitement des images [eess.IV]; Optimisation et contrôle [math.OC]; Traitement du signal et de l'image [eess.SP]

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⟩