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.
Highlights
Single-Molecule localization microscopy (SMLM) is an acquisition method that makes it possible to obtain images with a higher resolution than the diffraction limit
The Jaccard index evaluates the localization of the reconstructed fluorophores, and is defined as the ratio between the correctly reconstructed (CR) fluorophores and the sum of CR, false negatives (FN)- and false positives (FP) fluorophores
Results of the real dataset We compare the algorithms on a high-density dataset of tubulins provided from the 2013 ISBI SMLM challenge
Summary
Single-Molecule localization microscopy (SMLM) is an acquisition method that makes it possible to obtain images with a higher resolution than the diffraction limit. Ernst Abbe first developed the equation of the diffraction in 1873, which gives the resolution limit of a microscope in the lateral plane. Where λ is the wavelength of the light and N A is the numerical aperture of the optical system [1]. This limit is around 200 nm in the lateral plane of the microscope. This is not sufficient when observing small biological structures, such as proteins and viruses. Among the many super-resolution techniques for microscopy (STED, SIM etc, see [2]), SMLM is widely used. 20 nm resolution is reported on SMLM when it was first introduced in [3,4,5], and can be used to observe fine structures
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