{
  "abstract": "We consider the problem of phase retrieval for continuous and discrete Fourier transforms in multidimensions. Using finite difference operators, we give a large class of unexpected examples of non-uniqueness for this problem, including examples with the sparsity condition. A prototype of this construction in the continuous case is given in the work Novikov, Xu (JFAA,2026), using linear differential operators. The construction of the present work also yields a large class of non-trivial Pauli partners, i.e., different functions with the same intensities in both configuration and Fourier domains. We also consider the problem of phase retrieval with background information. We show that this problem is not uniquely solvable if the known and unknown function parts are not sufficiently disjoint.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Roman Novikov"
    },
    {
      "name": "Tianli Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fj2wxkehfvck9.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "fj2wxkehfvck9",
  "issns": [],
  "landing_url": "https://hal.science/hal-05604553v2",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-mp"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05604553/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fj2wxkehfvck9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05604553",
      "source": "hal",
      "url": "https://hal.science/hal-05604553v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On non-uniqueness of phase retrieval for continuous and discrete Fourier transforms",
  "title_text": "On non-uniqueness of phase retrieval for continuous and discrete Fourier transforms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:40Z",
  "url": "https://research.draconitic.com/paper/fj2wxkehfvck9",
  "venue": "HAL",
  "versions": []
}