{
  "abstract": "This paper extends the non-unique games framework introduced in Bandeira et al. (2020) to address symmetric structures. Precisely, we consider the problem \\[ \\begin{aligned} \\underset{g_1,\\ldots,g_n\\in \\mathcal{G}}{\\operatorname{min}}\\,\\, \\frac{1}{|S|}\\sum_{i,j=1}^n \\sum_{s\\in S} f_{ij}(g_i s g_j^{-1}), \\end{aligned} \\] where $\\mathcal{G}$ is a compact group, $S\\subset \\mathcal{G}$ is a finite subgroup of symmetry elements, and $f_{ij}:\\mathcal{G}\\rightarrow \\mathbb{R}$ 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 $\\mathcal{G}$ is the rotation group $\\operatorname{SO}(3)$. 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18691",
  "author_total": 4,
  "authors": [
    {
      "name": "Yunpeng Shi"
    },
    {
      "name": "Amit Singer"
    },
    {
      "name": "Jinxin Wang"
    },
    {
      "name": "Ruiyi Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/adpgnapzpbzvz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18691",
  "fulltext_url": null,
  "id": "adpgnapzpbzvz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18691",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CV"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1315|Advanced Electron Microscopy Techniques and Applications"
    ]
  ],
  "openalex": "W7221783561",
  "pdf_url": "https://arxiv.org/pdf/2610.18691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/adpgnapzpbzvz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming",
  "title_text": "Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/adpgnapzpbzvz",
  "venue": "arXiv",
  "versions": []
}