{
  "abstract": "Coded diffraction patterns (CDPs) provide a structured and physically relevant model for phase retrieval, but the dependence among Fourier measurements generated by a common mask makes sharp stability analysis challenging. For a fixed unit-norm signal $\\boldsymbol{x}_\\star \\in \\mathbb{C}^n$, let $\\boldsymbol{X}_\\star=\\boldsymbol{x}_\\star\\boldsymbol{x}_\\star^*$, and let $\\mathcal A$ be the lifted CDP measurement operator. We prove that, with $L=O(\\log n)$ random masks, the following uniform lower isometry holds with high probability: $\\|\\boldsymbol{X}-\\boldsymbol{X}_\\star\\|_F \\lesssim \\log^2(2n) \\frac{\\|\\mathcal A(\\boldsymbol{X}-\\boldsymbol{X}_\\star)\\|_2}{\\sqrt{nL}}, \\boldsymbol{X}\\succeq\\boldsymbol{0},$ from which we derive two consequences. First, for $\\boldsymbol{y}=\\mathcal A(\\boldsymbol{X}_\\star)+\\boldsymbol{e}$, PhaseLift-type convex programs achieve the Gaussian-type stable recovery bound $\\|\\widehat{\\boldsymbol{X}}-\\boldsymbol{X}_\\star\\|_F \\lesssim \\frac{\\log^2(2n)}{\\sqrt{nL}}\\|\\boldsymbol{e}\\|_2.$ Second, in the noiseless case, the nonconvex factorized loss has a benign landscape when the factor width satisfies $r = O(\\log^5(2n))$: every second-order critical point $\\boldsymbol{V}\\in\\mathbb C^{n\\times r}$ satisfies $\\boldsymbol{V}\\boldsymbol{V}^*=\\boldsymbol{X}_\\star$. The key ingredient is a uniform operator-norm bound over row subsets of the dependent CDP measurement matrix, which permits the removal of a controlled set of adaptively selected rows while preserving tangent injectivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30825",
  "author_total": 4,
  "authors": [
    {
      "name": "Jian-Feng Cai"
    },
    {
      "name": "Zhibo Jin"
    },
    {
      "name": "Tong Wu"
    },
    {
      "name": "Ruizhe Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6wv8xt952r2d6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30825",
  "fulltext_url": null,
  "id": "6wv8xt952r2d6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30825",
  "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.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "2206|Sparse and Compressive Sensing Techniques"
    ]
  ],
  "openalex": "W7214681854",
  "pdf_url": "https://arxiv.org/pdf/2609.30825",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6wv8xt952r2d6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30825",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30825"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Stable Recovery and Benign Overparameterized Landscapes for Phase Retrieval from Coded Diffraction Patterns",
  "title_text": "Stable Recovery and Benign Overparameterized Landscapes for Phase Retrieval from Coded Diffraction Patterns",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/6wv8xt952r2d6",
  "venue": "arXiv",
  "versions": []
}