{
  "abstract": "A novel Data-driven STochastic Asymptotic Regularization (\\texttt{D-STAR}) method is proposed for solving linear and nonlinear ill-posed inverse problems, which incorporates a data-driven drift and a stochastic diffusion mechanism. Both known and unknown noise level cases are accommodated by the method, thereby making the framework applicable to a broader range of practical inverse problems. For known noise level, a modified discrepancy principle is employed, whereas for unknown noise level, a heuristic stopping rule based solely on noisy data is developed. For each stopping rule, an appropriate diffusion term is defined and the well-posedness of the associated stochastic differential equation is demonstrated. The finite termination of \\texttt{D-STAR} method under both stopping rules is established and its convergence to the exact solution in the noise-free setting is proved. For the noisy data, stability and the regularization property in the mean-square sense are further established. In addition, the uncertainty quantification of the proposed method and its comparison with the Stochastic Asymptotic Regularization (\\texttt{SAR}) method under both rules are provided. Furthermore, it is shown that local minima arising in the Data-Driven Iteratively Regularized Landweber (\\texttt{DDIRLI}) method may be escaped. Finally, detailed numerical experiments, including comparisons with existing \\texttt{DDIRLI} and \\texttt{SAR} methods, are presented on X-ray computed tomography and nonlinear schlieren tomography for both stopping rules, thereby demonstrating the performance of \\texttt{D-STAR}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38279",
  "author_total": 3,
  "authors": [
    {
      "name": "Simran Soni"
    },
    {
      "name": "Harshit Bajpai"
    },
    {
      "name": "Ankik Kumar Giri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58qzse3cx6pky.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38279",
  "fulltext_url": null,
  "id": "58qzse3cx6pky",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38279",
  "language": null,
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  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38279",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58qzse3cx6pky.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38279",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38279"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Data-driven stochastic asymptotic regularization for ill-posed inverse problems with a posteriori and heuristic stopping",
  "title_text": "Data-driven stochastic asymptotic regularization for ill-posed inverse problems with a posteriori and heuristic stopping",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/58qzse3cx6pky",
  "venue": "arXiv",
  "versions": []
}