New ℓ2  - ℓ0 algorithm for single-molecule localization microscopy

Biomedical Optics Express
Arne BechensteenGilles Aubert

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 ℓ2 least-square term and sparsity term modeled with ℓ0 pseudo-norm. We consider both the constrained formulation and the penalized formulation. Based on recent results, we formulate the ℓ0 pseudo-norm as a convex minimization problem. This is done by introducing an auxiliary variable. An exact biconvex reformulation of the ℓ2 - ℓ0 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.

References

Aug 10, 2006·Nature Methods·Michael J RustXiaowei Zhuang
Aug 12, 2006·Science·Eric BetzigHarald F Hess
Sep 19, 2006·Biophysical Journal·Samuel T HessMichael D Mason
May 1, 2010·Nature Methods·Ricardo HenriquesMusa M Mhlanga
Jun 20, 2019·Biochemistry. Biokhimii︠a︡·A S Mishin, K A Lukyanov

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Citations

Mar 25, 2020·Biomedical Optics Express·Peter KnerSjoerd Stallinga

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