{
  "id": "2009.05029",
  "version": "v2",
  "published": "2020-09-10T17:50:43.000Z",
  "updated": "2020-09-11T14:04:05.000Z",
  "title": "Phase retrieval of bandlimited functions for the wavelet transform",
  "authors": [
    "Rima Alaifari",
    "Francesca Bartolucci",
    "Matthias Wellershoff"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the problem of phase retrieval in which one aims to recover a function $f$ from the magnitude of its wavelet transform $|\\mathcal{W}_\\psi f|$. We consider bandlimited functions and derive new uniqueness results for phase retrieval, where the wavelet itself can be complex-valued. In particular, we prove the first uniqueness result for the case that the wavelet $\\psi$ has a finite number of vanishing moments. In addition, we establish the first result on unique reconstruction from samples of the wavelet transform magnitude when the wavelet coefficients are complex-valued",
  "revisions": [
    {
      "version": "v2",
      "updated": "2020-09-11T14:04:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase retrieval",
      "bandlimited functions",
      "wavelet transform magnitude",
      "first uniqueness result",
      "finite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}