Some results on sparse L2-L0 reconstruction: Continuous Exact L0 penalties

Laure Blanc-Féraud 1 Emmanuel Soubies 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 : A smooth exact approximation of functional L2-L0 (least squares functional with sparse penalizing term using a L0 norm) is presented. This functional, named CEL0 for Continuous Exact L0 approximation is said exact as it preserves global minimizers and remove some of the local minimizers of the L2-L0 functional. More general results on smooth approximation of the L2-L0 functional are also given, describing a class of continuous functions with the properties of preservation of minimizers as described above. Simulation results are presented.
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Laure Blanc-Féraud, Emmanuel Soubies, Gilles Aubert. Some results on sparse L2-L0 reconstruction: Continuous Exact L0 penalties. NCMIP 2016 - New Computational Methods for Inverse Problem , ENS Cachan, Apr 2016, Cachan, France. ⟨hal-01349670⟩

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