Exact biconvex reformulation of the $L2 − L0$ minimization problem

Arne Bechensteen 1, 2 Laure Blanc-Féraud 2 Gilles Aubert 3
2 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : We focus on the minimization of the least square loss function under a k-sparse constraint. Based on recent results, we reformulate the $L0$ pseudo-norm as a convex minimization problem by introducing an auxiliary variable. We then propose an exact biconvex reformulation of the $L2 −L 0$ constrained problem. We give correspondence results between minimizers of the initial function and the reformulated one. The reformulation is biconvex which allows efficient alternating minimization methods to be used. The reformulation is tested numerically on Single Molecule Localization Microscopy and compared to IHT.
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Arne Bechensteen, Laure Blanc-Féraud, Gilles Aubert. Exact biconvex reformulation of the $L2 − L0$ minimization problem. GRETSI 2019, Aug 2019, Lille, France. ⟨hal-02382369⟩

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