{
  "abstract": "While infinite-dimensional inverse problems are traditionally analyzed assuming continuous data, practical applications rely on finitely many discrete measurements. Recent deterministic approaches establish that unknowns belonging to a $d$-dimensional model class can be stably recovered from finitely many measurements. However, for severely ill-posed problems, such as the Calderón problem and inverse scattering, the known constructions may require a number of measurements that is exponential in $d$. We show that random sampling reduces this count dramatically if one asks only for exact identifiability. By exploiting the analytic geometry of the forward maps, we prove that, whenever the infinite-data problem is injective on the model class, $2d+1$ random scalar measurements determine the unknown uniquely, almost surely. Applications are given to the Calderón problem, with both infinite- and finite-dimensional boundary sampling, and to inverse medium scattering from randomly sampled far-field values.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.14324",
  "author_total": 4,
  "authors": [
    {
      "name": "Giovanni S. Alberti"
    },
    {
      "name": "Damiano Poletti"
    },
    {
      "name": "Simone Sanna"
    },
    {
      "name": "Matteo Santacesaria"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahj6e5zyekdxf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.14324",
  "fulltext_url": null,
  "id": "ahj6e5zyekdxf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.14324",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7203629754",
  "pdf_url": "https://arxiv.org/pdf/2608.14324",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahj6e5zyekdxf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2608.14324",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.14324"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Analytic inverse problems with finitely many random measurements",
  "title_text": "Analytic inverse problems with finitely many random measurements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/ahj6e5zyekdxf",
  "venue": "arXiv",
  "versions": []
}