Bechensteen Arne, Blanc-Féraud Laure, Aubert Gilles
Université Côte d'Azur, CNRS, INRIA, Laboratoire I3S,UMR 7271,06903 Sophia Antipolis, France.
Université Côte d'Azur, UNS, Laboratoire J. A. Dieudonné UMR 7351, 06100 Nice, France.
Biomed Opt Express. 2020 Jan 28;11(2):1153-1174. doi: 10.1364/BOE.381666. eCollection 2020 Feb 1.
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 ℓ least-square term and sparsity term modeled with ℓ pseudo-norm. We consider both the constrained formulation and the penalized formulation. Based on recent results, we formulate the ℓ pseudo-norm as a convex minimization problem. This is done by introducing an auxiliary variable. An exact biconvex reformulation of the ℓ - ℓ 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.
在众多用于显微镜的超分辨率技术中，单分子定位显微镜方法被广泛使用。该技术引发了一个难题，即如何从模糊、分辨率不足且有噪声的图像采集中精确地定位荧光团。在这项工作中，我们关注在由ℓ最小二乘项形式化的高密度荧光团以及用ℓ拟范数建模的稀疏性项的背景下基于网格的方法。我们考虑了约束形式和惩罚形式。基于最近的研究结果，我们将ℓ拟范数表述为一个凸最小化问题。这是通过引入一个辅助变量来实现的。利用一种最小化算法，对ℓ - ℓ约束问题和惩罚问题提出了一种精确的双凸重写形式。名为CoBic（约束双凸）和PeBic（惩罚双凸）的算法被应用于单分子定位显微镜问题，并且我们将结果与其他最近提出的方法进行了比较。
