{
  "abstract": "We consider single-time wave inversion, that is, recovering the initial pressure $f$ from the wave field $\\mathcal{W}_T f = u(\\cdot,T)$ at a single time $T$, where $u$ solves the wave equation with sound speed $c$ and initial data $(f,0)$. In two dimensions this is the main reconstruction step of full-field photoacoustic projection imaging, where each camera image is a two-dimensional wave field at a single time instant. An efficient direct method is back-propagation by the Fourier multiplier $2\\cos(cT|ξ|)$. It yields exact inversion in odd dimensions but not in two. We give its error in closed form, with bounds, and derive an exact explicit filtered back-propagation $f = 2\\mathcal{W}_T \\mathcal{M}_K \\mathcal{W}_T f$ in analogy to filtered backprojection for the Radon transform.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35302",
  "author_total": 1,
  "authors": [
    {
      "name": "Markus Haltmeier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47er7b3xngqec.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35302",
  "fulltext_url": null,
  "id": "47er7b3xngqec",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35302",
  "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.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7223841917",
  "pdf_url": "https://arxiv.org/pdf/2610.35302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47er7b3xngqec.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35302"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A theoretically exact filtered back-propagationformula for single-time wave inversion",
  "title_text": "A theoretically exact filtered back-propagationformula for single-time wave inversion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/47er7b3xngqec",
  "venue": "arXiv",
  "versions": []
}