{
  "abstract": "In this paper, we develop and analyze techniques for recovering a linear image $Bx$ of an unknown signal $x$ from indirect noisy observation $ω=Ax+ξ$. It is {\\em a priori} known that $x\\in \\cX$, a given convex compact set, and that $x$ is $s$-sparse---has at most $s$ nonvanishing entries. The proposed estimates belong to a large family of recovery routines by $\\ell_1$-minimization. However, unlike the classical result describing performance of such estimates, we do not make any special (and hard to check) assumptions about the sensing matrix $A$ such as nullspace or Restricted Isometry condition and the like. As a consequence, parameters of the estimates and the upper bounds on their risks are not available in a closed analytic form, but are delivered instead by efficient computation as solutions to explicit convex optimization problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06182",
  "author_total": 2,
  "authors": [
    {
      "name": "Anatoli Juditsky"
    },
    {
      "name": "Arkadi Nemirovski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9r320w43qtk2j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06182",
  "fulltext_url": null,
  "id": "9r320w43qtk2j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06182",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2206|Sparse and Compressive Sensing Techniques"
    ]
  ],
  "openalex": "W7212086379",
  "pdf_url": "https://arxiv.org/pdf/2609.06182",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9r320w43qtk2j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06182",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06182"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Recovering linear images of sparse signals from indirect observations",
  "title_text": "Recovering linear images of sparse signals from indirect observations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/9r320w43qtk2j",
  "venue": "arXiv",
  "versions": []
}