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

arXiv: https://arxiv.org/abs/2610.18691 · HTML: https://mlsanity.com/paper/2610.18691/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [Multireference Alignment using Semidefinite Programming](https://mlsanity.com/paper/1308.5256/) (2013)
- [Semidefinite descriptions of the convex hull of rotation matrices](https://mlsanity.com/paper/1403.4914/) (2014)
- [Non-unique games over compact groups and orientation estimation in cryo-EM](https://mlsanity.com/paper/1505.03840/) (2015)
- [A common lines approach for ab-initio modeling of cyclically-symmetric molecules](https://mlsanity.com/paper/1901.10888/) (2019)
- [A General System for Heuristic Solution of Convex Problems over Nonconvex Sets](https://mlsanity.com/paper/1601.07277/) (2016)
- [Approximating the Little Grothendieck Problem over the Orthogonal and Unitary Groups](https://mlsanity.com/paper/1308.5207/) (2013)
- [Common lines ab-initio reconstruction of D2-symmetric molecules](https://mlsanity.com/paper/1904.00757/) (2019)
- [A common lines approach for ab-initio modeling of molecules with tetrahedral and octahedral symmetry](https://mlsanity.com/paper/2206.08623/) (2022)

## Abstract (arXiv)

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.