New methods for $\ell_2-\ell_0$ minimization and their applications to 2D Single-Molecule Localization Microscopy

Arne Bechensteen 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 : We present in this paper a biconvex reformulation of an $\ell_2-\ell_0$ problem composed of a least-square data term plus a sparsity term introduced as a constraint or a penalization. Minimization algorithms are derived and compared with the state of the art in $\ell_2-\ell_0$ minimization by relaxation or deep learning. Application results are shown on Single-Molecule Localization Microscopy.
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Arne Bechensteen, Laure Blanc-Féraud, Gilles Aubert. New methods for $\ell_2-\ell_0$ minimization and their applications to 2D Single-Molecule Localization Microscopy. ISBI 2019 - IEEE International Symposium on Biomedical Imaging, Apr 2019, Venice, Italy. ⟨hal-02107577v2⟩

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