{
  "abstract": "Plug-and-Play (PnP) algorithms are a class of iterative methods for inverse imaging. Within an optimization algorithm, they combine a flexible fidelity term, encoding the forward operator, and a pretrained image denoiser, in order to deal with more severe corruptions such as blurring or downsampling when reconstructing an image. This work studies provably convergent PnP methods for mixed-noise forward processes by using the infimal convolution as a fidelity term, providing a statistical interpretation as a joint maximum a-posteriori estimator over both noises, and preserving the Bayesian MAP interpretation of PnP methods. Independently, we extend the PnP formulation to multiple prior terms using the Davis--Yin three-operator splitting. This extension can be combined with either standard fidelities or the proposed mixed-noise infimal-convolution fidelities. We verify that these generalized PnP methods are convergent under standard Kurdyka--Lojasiewicz conditions. Numerical experiments on Laplace-Gaussian and Poisson--Gaussian noise demonstrate stable convergence of single-prior and multiple-prior PnP methods, and divergence under fidelity mismatch. Furthermore, PnP with infimal convolution fidelities are able to scale to noise up to 38% standard deviation, with multiple priors reaching different stationary points that qualitatively preserve more textural properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33897",
  "author_total": 5,
  "authors": [
    {
      "name": "Ziqi Qin"
    },
    {
      "name": "Hong Ye Tan"
    },
    {
      "name": "Ander Biguri"
    },
    {
      "name": "Jingwei Liang"
    },
    {
      "name": "Carola-Bibiane Schönlieb"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fm1k0ppc0ew6f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33897",
  "fulltext_url": null,
  "id": "fm1k0ppc0ew6f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33897",
  "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"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "openalex",
      "1707|Image and Signal Denoising Methods"
    ]
  ],
  "openalex": "W7214772144",
  "pdf_url": "https://arxiv.org/pdf/2609.33897",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fm1k0ppc0ew6f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33897",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33897"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors",
  "title_text": "Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/fm1k0ppc0ew6f",
  "venue": "arXiv",
  "versions": []
}