Seuillage CEL0 pour la minimisation l2- l0 : comparaisons avec IHT

Emmanuel Soubies 1 Laure Blanc-Féraud 1 Gilles Aubert 2
1 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : The l2-l0 optimization problem has been widely studied because of its importance in many applications in signal and image processing. In this paper, we focus on the Iterative Hard Thresholding (IHT) algorithm which minimizes directly the l2-l0 criterion, without approximating the l0 pseudo-norm, and converges to a (local) minimizer. Within this framework, we propose to replace the hard thresholding step in the IHT algorithm by the continious CEL0 thresholding associated to the relaxed functional l2-CEL0 recently introduced. This continuous functional preserves minimizers of the initial one as well as some local minimizers. These properties make it a good alternative to the l2-l0 criterion. Numerical experiments show the benefits of the proposed thresholding regarding to the hard thresholding such as its aibility to «avoid» local minimizers of l2-l0 .
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Emmanuel Soubies, Laure Blanc-Féraud, Gilles Aubert. Seuillage CEL0 pour la minimisation l2- l0 : comparaisons avec IHT. Colloque Gretsi, Sep 2015, Lyon, France. pp.4. ⟨hal-01169557⟩

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