{
  "abstract": "We develop a factorization framework for magnetic induction tomography in the eddy-current regime. The induced current density is represented by a divergence-free current vector potential, and the external excitation by magnetic dipole densities on an observation sphere. This choice reveals a natural physical factorization of the near-field operator into a data operator, an interior boundary response operator, and an adjoint counterpart. By introducing the Riesz map on the flux space, we recast this factorization in a Hilbert-space setting, which yields a positive-semidefinite operator with a coercive middle factor. Douglas' range theorem then identifies the range of the square root of this dissipative operator with the range of the data operator. For inclusions with a regular boundary, this range identity yields a uniqueness theorem for the support of the conductivity. This characterization leads to a non-iterative spectral indicator based on a regularized Picard quotient computed from the Hermitian imaginary part of the near-field data matrix. The reconstruction stage requires no forward solves. Numerical experiments confirm that the indicator localizes and separates the inclusions accurately, degrades gracefully under increasing noise, and captures non-convex support geometry without any convexity prior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18235",
  "author_total": 2,
  "authors": [
    {
      "name": "Junqing Chen"
    },
    {
      "name": "Chengzhe Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/96n4pthrb8a9r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18235",
  "fulltext_url": null,
  "id": "96n4pthrb8a9r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18235",
  "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",
      "math.NA"
    ],
    [
      "openalex",
      "2208|Electrical and Bioimpedance Tomography"
    ]
  ],
  "openalex": "W7213511473",
  "pdf_url": "https://arxiv.org/pdf/2609.18235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/96n4pthrb8a9r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18235"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Factorization Method for Support Recovery in Magnetic Induction Tomography",
  "title_text": "A Factorization Method for Support Recovery in Magnetic Induction Tomography",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/96n4pthrb8a9r",
  "venue": "arXiv",
  "versions": []
}