Single-molecule localization microscopy as nonlinear inverse problem.

We present a statistical framework to model the spatial distribution of molecules based on a single-molecule localization microscopy (SMLM) dataset. The latter consists of a collection of spatial coordinates and their associated uncertainties. We describe iterative parameter-estimation algorithms based on this framework, as well as a sampling algorithm to numerically evaluate the complete posterior distribution. We demonstrate that the inverse computation can be viewed as a type of image restoration process similar to the classical image deconvolution methods, except that it is performed on SMLM images. We further discuss an application of our statistical framework in the task of particle fusion using SMLM data. We show that the fusion algorithm based on our model outperforms the current state-of-the-art in terms of both accuracy and computational cost.