{
  "id": "2307.03940",
  "version": "v1",
  "published": "2023-07-08T09:17:05.000Z",
  "updated": "2023-07-08T09:17:05.000Z",
  "title": "Uncovering the limits of uniqueness in sampled Gabor phase retrieval: A dense set of counterexamples in $L^2(\\mathbb{R})$",
  "authors": [
    "Rima Alaifari",
    "Francesca Bartolucci",
    "Matthias Wellershoff"
  ],
  "comment": "5 pages, 2 figures",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "Sampled Gabor phase retrieval - the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice - is a fundamental problem in signal processing, with important applications in areas such as imaging and audio processing. Recently, a classification of square-integrable signals which are not phase retrievable from Gabor measurements on parallel lines has been presented. This classification was used to exhibit a family of counterexamples to uniqueness in sampled Gabor phase retrieval. Here, we show that the set of counterexamples to uniqueness in sampled Gabor phase retrieval is dense in $L^2(\\mathbb{R})$, but is not equal to the whole of $L^2(\\mathbb{R})$ in general. Overall, our work contributes to a better understanding of the fundamental limits of sampled Gabor phase retrieval.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-08T09:17:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "94A12"
    ],
    "keywords": [
      "sampled gabor phase retrieval",
      "dense set",
      "uniqueness",
      "counterexamples",
      "square-integrable signal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}