{
  "abstract": "We develop regularisation theory for dynamic inverse problems, solved using online methods with an infinite time horizon. Using concepts of subregularity to treat nonsmooth regularisers, we prove that time-averaged reconstruction errors converge to zero as noise, algorithmic errors, and regularisation vanish as the horizon grows. We illustrate the theory numerically with a dynamic electrical impedance tomography example.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.26022",
  "author_total": 3,
  "authors": [
    {
      "name": "Jyrki Jauhiainen"
    },
    {
      "name": "Yassine Nabou"
    },
    {
      "name": "Tuomo Valkonen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ckt29vwz2n8rh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.26022",
  "fulltext_url": null,
  "id": "ckt29vwz2n8rh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.26022",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7162400615",
  "pdf_url": "https://arxiv.org/pdf/2605.26022",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ckt29vwz2n8rh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2605.26022",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.26022"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Dynamic inverse problems: Online regularisation theory",
  "title_text": "Dynamic inverse problems: Online regularisation theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/ckt29vwz2n8rh",
  "venue": "arXiv",
  "versions": []
}