{
  "abstract": "Motivated by blind denoising in diffusion models, we study estimation of an unknown Gaussian noise level from a single high-dimensional observation, assuming the signal law P is known. We characterize the minimax mean-squared error under two structural assumptions on P. For signals with covering complexity k, the minimax rate is $\\widetildeΘ_Λ(\\min\\{Δ_Λ^2,d^{-1}+k^2d^{-2}\\})$, and the constrained MLE attains it up to logarithmic factors. For $α$-strongly log-concave signals, the rate is $Θ_Λ(\\min\\{Δ_Λ^2,(1+α^{-1})^2d^{-1}\\})$, attained up to constants by a $P$-centered norm estimator. These results show that the structure of the signal law determines both the difficulty of blind noise estimation and the appropriate estimator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33008",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhuoer Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xdp0ypx2xgm8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33008",
  "fulltext_url": null,
  "id": "5xdp0ypx2xgm8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33008",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1707|Image and Signal Denoising Methods"
    ]
  ],
  "openalex": "W7214776897",
  "pdf_url": "https://arxiv.org/pdf/2609.33008",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xdp0ypx2xgm8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33008",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33008"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A statistical theory for blind denoising: minimax estimation of the noise level from a single sample",
  "title_text": "A statistical theory for blind denoising: minimax estimation of the noise level from a single sample",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/5xdp0ypx2xgm8",
  "venue": "arXiv",
  "versions": []
}