{
  "abstract": "In this paper we propose a novel regularisation strategy for structured linear inverse problems of the form $Ax=F \\circ G x = z$. Instead of using the operator $A$ or a complex scheme involving both $F$ and $G$ simultaneously, combining already existing and simpler regularisations for $F$ and $G$ allows the use of established and optimised programs for high-speed computations. As classical parameter choice rules fail in the scenario when no source conditions are known because intermediate error bounds may be unavailable, we provide both a-priori and a-posteriori rules with a convergence speed analysis given source conditions. We test the proposed method on the pre-clinical medical imaging technique of magnetic particle imaging with different choices of regularisation and on a convolution problem for an analysis of the convergence speed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13483",
  "author_total": 2,
  "authors": [
    {
      "name": "Christina Brandt"
    },
    {
      "name": "Patrick Horn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ncfffpyfd0v0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13483",
  "fulltext_url": null,
  "id": "9ncfffpyfd0v0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13483",
  "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",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7221572337",
  "pdf_url": "https://arxiv.org/pdf/2610.13483",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ncfffpyfd0v0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13483",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13483"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Regularisation and Parameter Choice Rules for Composite Linear Inverse Problems",
  "title_text": "Regularisation and Parameter Choice Rules for Composite Linear Inverse Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9ncfffpyfd0v0",
  "venue": "arXiv",
  "versions": []
}