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# Equivariant Self-supervised Deep Pose Estimation for Cryo EM

*Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML)*, PMLR 221:21-36, 2023.

#### Abstract

Reconstructing the 3D volume of a molecule from its differently oriented 2D projections is the central problem of cryo-EM, one of the main techniques for macro-molecule imaging. Because the orientations are unknown, the estimation of the images’ poses is essential to solve this inverse problem. Typical methods either rely on *synchronization*, which leverages the estimated relative poses of the images to constrain their absolute ones, or *jointly estimate* the poses and the 3D density of the molecule in an iterative fashion. Unfortunately, synchronization methods don’t account for the complete images’ generative process and, therefore, achieve lower noise robustness. In the second case, the iterative joint optimization suffers from convergence issues and a higher computational cost, due to the 3D reconstruction steps. In this work, we directly estimate individual poses with equivariant deep graph networks trained using a self-supervised loss, which enforces agreement in Fourier domain of images pairs along the *common lines* defined by their poses. In particular, the *equivariant* design turns out essential for the proper convergence. As a result, our method can leverage the synchronization constraints - encoded by the synchronization graph structure - to improve convergence as well as the images generative process - via the common lines loss -, with no need to perform intermediate reconstructions.