{
  "abstract": "We study the recovery of a finite three-dimensional point cloud from its spherical Fourier signal subspace at a fixed wavenumber. Two ESPRIT constructions are analyzed. The first uses finite shifts between paired small circles; the second uses angular derivatives on the whole sphere. Both recover the same commuting coordinate matrices, either through their finite exponentials or directly from a coupled linear system. We prove that the continuous generator system is injective for every distinct point cloud and that one guard harmonic degree preserves the retained equations exactly. For $s$ targets, the cutoff $K\\ge s$ gives generic finite identifiability, but not uniform conditioning. We also derive a finite-cutoff perturbation bound. The accuracy of the coordinate estimates is a separate issue. A one-target perturbation calculation shows that the original generator estimate can retain a nonzero bias as the wavenumber increases. To address this bias, we use the generator eigenbasis to separate approximate atoms and recover their locations from amplitude-normalized phases. Under pointwise atom dominance, the resulting error is $O(κ^{-1})$; for a dominant two-atom mixture at fixed separation, it is $O(κ^{-2})$. Experiments on structured point clouds with smooth perturbations compare the two constructions and their use as initializers for a common MUSIC refinement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33024",
  "author_total": 1,
  "authors": [
    {
      "name": "Albert Fannjiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eswrdbrkpn3b3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33024",
  "fulltext_url": null,
  "id": "eswrdbrkpn3b3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33024",
  "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",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "1711|Direction-of-Arrival Estimation Techniques"
    ]
  ],
  "openalex": "W7214704750",
  "pdf_url": "https://arxiv.org/pdf/2609.33024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eswrdbrkpn3b3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spherical ESPRIT by Paired Small Circles and Infinitesimal Rotations",
  "title_text": "Spherical ESPRIT by Paired Small Circles and Infinitesimal Rotations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/eswrdbrkpn3b3",
  "venue": "arXiv",
  "versions": []
}