Fast Maximum Likelihood Algorithm for Localization of Fluorescent Molecules

Abstract

In super-resolution fluorescence microscopy, one key objective is to localize fluorescent molecules as quickly and precisely as possible. The most common approaches involve fitting an image of a molecule to a point spread function, often a Gaussian for simplicity. The separable property of the 2D Gaussian function allows us to separate the tasks of estimating the x and y coordinates. We did this by summing the columns of an image, then we used a maximum likelihood algorithm to estimate the position of the molecule along the x axis. Because we were able to separate the Gaussian, our computational time went from O(L2) to O(L) where L is the width (in pixels) of the pixel array. This algorithm gives us precision close to the Cramer-Rao Lower Bound, and is robust against variations of pixel size, window size, or displacements of the molecule relative to the center of the computational window.