The Moments of Orientation Estimations Considering Molecular Symmetry in Cryo-EM

arXiv2301.05426MaRDI QIDQ6423290

Hai Lin, Mingxu Hu, Qi Zhang, Chenglong Bao

Publication date: 13 January 2023

Abstract: Cryogenic electron microscopy (cryo-EM) is a powerful imaging tool for determining the high-resolution three-dimensional structure of biological macromolecules using numerous transmission particle images. Since the orientation information of each particle is unknown, the orientation estimation and its statistics are challenging in cryo-EM image processing. Existing approaches establish the orientation statistics in $mathrmSO(3)$ or $mathrm{S}^2$, while the molecular symmetry, common in structural biology study, has yet to be explored. In this paper, we propose a novel method for estimating the mean and variance of orientations, including spatial rotations and projection directions, by considering molecular symmetry in cryo-EM. Using the tools from non-unique games, the proposed non-convex formulation can be relaxed as a semi-definite programming problem. Furthermore, we propose a rounding procedure for determining the representatives. Experimental results show that our method can obtain the global minima and the proper representatives with high probability. The code is released as an open-source Python package pySymStat (url{https://github.com/mxhulab/pySymStat}).

Has companion code repository: https://github.com/mxhulab/pysymstat

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