Estimating Moments from Crowded Images

Abstract: Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of reconstructing high-resolution three-dimensional (3D) structure of biological macromolecules from a set of noisy projection images taken at random viewing directions. The mathematical model for cryo-EM images assumes that each image contains exactly one centered particle, whereas in practice datasets may contain many images with multiple particles. Since the model and the data disagree, this leads to inaccuracies when estimating low-order image statistics, which can lead to further inaccuracies down the reconstruction pipeline. In this talk, I present a model of image moments while accounting for the crowdedness from the datasets and a method to correct the estimated moments for the effect of extra particles, which is tested via several numerical experiments on synthetic data. While the theory derived holds for general moments of order n, the experiments presented will focus on correction of the first and second moments due to computational constraints (e.g. storage).