A method for the analysis of superresolution microscopy images is presented. This method is based on the analysis of stochastic trajectories of particles moving on the membrane of a cell with the assumption that this motion is determined by the properties of this membrane. Thus, the purpose of this method is to recover the structural properties of the membrane by solving an inverse problem governed by the Fokker-Planck equation related to the stochastic trajectories. Results of numerical experiments demonstrate the ability of the proposed method to reconstruct the potential of a cell membrane by using synthetic data similar those captured by superresolution microscopy of luminescent activated proteins.

翻译：本文提出了一种分析超分辨显微图像的方法。该方法基于细胞膜上粒子随机运动轨迹的分析，假设该运动由细胞膜的特性决定。因此，本方法旨在通过求解与随机轨迹相关的福克-普朗克方程所支配的反问题，来恢复细胞膜的结构特性。数值实验结果表明，该方法能够利用与发光激活蛋白超分辨显微成像捕获数据相似的合成数据，重建细胞膜的势能分布。