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New $L_2$−$L_0$ algorithm for 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 : Among the many super-resolution techniques for microscopy, single-molecule localization microscopy methods are widely used. This technique raises the difficult question of precisely localizing fluorophores from a blurred, under-resolved, and noisy acquisition. In this work, we focus on the grid-based approach in the context of a high density of fluorophores formalized by a 2 least-square term and sparsity term modeled with 0 pseudo-norm. We consider both the constrained formulation and the penalized formulation. Based on recent results, we formulate the 0 pseudo-norm as a convex minimization problem. This is done by introducing an auxiliary variable. An exact biconvex reformulation of the 2 − 0 constrained and penalized problems is proposed with a minimization algorithm. The algorithms, named CoBic (Constrained Biconvex) and PeBic (Penalized Biconvex) are applied to the problem of single-molecule localization microscopy and we compare the results with other recently proposed methods.
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https://hal.inria.fr/hal-02556389
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Submitted on : Monday, December 21, 2020 - 2:36:21 PM
Last modification on : Wednesday, December 1, 2021 - 11:18:54 AM

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Arne Bechensteen, Laure Blanc-Féraud, Gilles Aubert. New $L_2$−$L_0$ algorithm for single-molecule localization microscopy. Biomedical optics express, Optical Society of America - OSA Publishing, 2020, 11 (2), pp.1153. ⟨10.1364/BOE.381666⟩. ⟨hal-02556389⟩

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