{
  "abstract": "We study direct recovery of visible phase centers and concentric radial interfaces from full-aperture acoustic far-field data under the Born approximation. Two complementary moment structures are extracted from the two-angle Fourier matrix. At fixed positive total Fourier order, the nonnegative-order channels share the same leading phase-center moment, and a generalized least-squares combination yields an exact variance gain over a single Fourier row. The corresponding Hankel rank and shifted pencil recover distinct phase centers. Signed moments reveal off-center cavities but become degenerate when material and cavity centers coincide. Zero-total-order coefficients retain complementary radial Bessel moments. For a piecewise-constant radial average, low-frequency extrapolation produces a second finite exponential sequence whose nodes are the squared interface radii. We establish rank and perturbation results for both reductions. Numerical experiments verify multichannel stabilization, concentric-cavity resolution, and recovery of multiple radial interfaces. A final full-wave Helmholtz experiment, generated without the Born substitution, assesses the Born-derived reconstruction under model mismatch and shows how nonlinear scattering eventually appears as an additional Hankel tail.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29678",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhiliang Deng"
    },
    {
      "name": "Xiaofei Guan"
    },
    {
      "name": "Xiaomei Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8c4kte5fe4fyv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29678",
  "fulltext_url": null,
  "id": "8c4kte5fe4fyv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29678",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7166654684",
  "pdf_url": "https://arxiv.org/pdf/2606.29678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8c4kte5fe4fyv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2606.29678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29678"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Fourier--Hankel Moment Recovery in Acoustic Scattering: Multichannel Stabilization and Radial Interface Resolution",
  "title_text": "Fourier--Hankel Moment Recovery in Acoustic Scattering: Multichannel Stabilization and Radial Interface Resolution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/8c4kte5fe4fyv",
  "venue": "arXiv",
  "versions": []
}