Fast algorithm for determining orientations using angular correlation functions and Bayesian statistics

Cryogenic electron microscopy (cryo-EM) method achieved revolutionary improvement in the past a few years, yet the orientation recovery for each particle remains computational challenging. Orientation determination can be solved using Bayesian approach, through which a model can be constructed to best match a whole set of experimental projections at their correct orientations. Without considering the centering of each particle projection, there are three degrees of freedoms (three Euler angles) that need to be fixed, usually resulting a computational complexity O(n3) where n is the number of discretization for each rotation angle. Here, we propose a method based on Maximum Likelihood approach with angular auto-correlation function of each projection, which is utilized to decouple the determination of three Euler angles to stepwise determination of two Euler angles and the subsequent third angle, the in-plane rotation. This approach reduces computational complexity from O(n3) to O(n2). Using simulation data, the accuracy and speed of the method is compared with the original maximum likelihood approach. We also investigated the impact of noise to the performance of this proposed method.