{
  "abstract": "We study the recovery of a three-dimensional volume in single-particle cryo-electron microscopy (cryo-EM) from noisy tomographic projections acquired at unknown viewing rotations, drawn independently and uniformly from $\\mathrm{SO}(3)$. We show that, in a spherical-shell representation satisfying an explicit shell-separation condition, the first three moments generically determine the underlying real volume up to its intrinsic global $\\mathrm{O}(3)$ ambiguity. The proof is constructive and yields a frequency-marching procedure that successively recovers the volume. Consequently, consistent recovery in the high-noise regime has sample complexity $n=ω(σ^6)$, where $n$ is the number of observations and $σ^2$ is the noise variance. Numerical experiments validate the constructive recovery scheme under finite sampling and additive noise, and indicate that direct third-moment optimization can succeed beyond the structural assumptions required by the constructive proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17892",
  "author_total": 6,
  "authors": [
    {
      "name": "Amnon Balanov"
    },
    {
      "name": "Tamir Bendory"
    },
    {
      "name": "Dan Edidin"
    },
    {
      "name": "Josh Katz"
    },
    {
      "name": "Shay Kreymer"
    },
    {
      "name": "Nir Sharon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7q8m8pv9edxmy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17892",
  "fulltext_url": null,
  "id": "7q8m8pv9edxmy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17892",
  "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.NA"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1315|Advanced Electron Microscopy Techniques and Applications"
    ]
  ],
  "openalex": "W7221778499",
  "pdf_url": "https://arxiv.org/pdf/2610.17892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7q8m8pv9edxmy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Provable Method of Moments for Cryo-EM",
  "title_text": "Provable Method of Moments for Cryo-EM",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/7q8m8pv9edxmy",
  "venue": "arXiv",
  "versions": []
}