Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming

This paper extends the non-unique games framework introduced in Bandeira et al. (2020) to address symmetric structures. Precisely, we consider the problem [ beginaligned undersetg1,ldots,gn∈ Goperatornamemin,, frac1|S|sumi,j=1n sums∈ S fij(gi s gj-1), endaligned ] where G is a compact group, Ssubset G is a finite subgroup of symmetry elements, and fij:Grightarrow ℝ is a loss function. A notable example is common lines based orientation estimation of cryo-EM images for molecules with point group symmetry S, where G is the rotation group operatornameSO(3). With a semidefinite programming relaxation, we turn the problem into a convex program that is solved with the alternating direction method of multipliers. Unlike existing approaches which are tailored to specific symmetry groups, ours provides a unified computational framework for addressing all point group symmetries. We demonstrate the applicability of the proposed algorithm on the cryo-EM orientation estimation problem on both simulated and experimental datasets. In particular, our algorithm is effective in generating high-quality ab initio models from only a few class averages computed from experimental images.