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

Abstract

This paper extends the non-unique games framework introduced in Bandeira et al. (2020) to address symmetric structures. Precisely, we consider the problem undersetg₁,…,g_n∈ 𝒢min 1/|S|∑_i,j=1ⁿ ∑_{s∈ S} f_ij(g_i s g_j⁻¹), where 𝒢 is a compact group, S⊂ 𝒢 is a finite subgroup of symmetry elements, and f_ij:𝒢→ 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 SO(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.

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BibTeX RIS

BibTeX

@misc{shi2026orientation,
  title = {{Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming}},
  author = {Yunpeng Shi and Amit Singer and Jinxin Wang and Ruiyi Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18691},
  eprint = {2610.18691},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18691},
}

RIS

TY  - UNPB
TI  - Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming
AU  - Yunpeng Shi
AU  - Amit Singer
AU  - Jinxin Wang
AU  - Ruiyi Yang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18691
UR  - https://arxiv.org/abs/2610.18691
AB  - This paper extends the non-unique games framework introduced in Bandeira et al. (2020) to address symmetric structures. Precisely, we consider the problem undersetg_1,…,g_n∈ 𝒢min 1/|S|∑_i,j=1^n ∑_s∈ S f_ij(g_i s g_j^−1), where 𝒢 is a compact group, S⊂ 𝒢 is a finite subgroup of symmetry elements, and f_ij:𝒢→ 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 SO(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.
ER  -

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