New $L_2$−$L_0$ algorithm for single-molecule localization microscopy - Archive ouverte HAL Access content directly
Journal Articles Biomedical optics express Year : 2020

## New $L_2$−$L_0$ algorithm for single-molecule localization microscopy

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Arne Bechensteen
• Function : Author
Laure Blanc-Féraud
Gilles Aubert
• Function : Author
• PersonId : 947054

#### 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.

### Dates and versions

hal-02556389 , version 1 (21-12-2020)

### Identifiers

• HAL Id : hal-02556389 , version 1
• DOI :

### Cite

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

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