{
  "id": "2306.13111",
  "version": "v1",
  "published": "2023-06-21T18:39:34.000Z",
  "updated": "2023-06-21T18:39:34.000Z",
  "title": "Relationships between the Phase Retrieval Problem and Permutation Invariant Embeddings",
  "authors": [
    "Radu Balan",
    "Efstratos Tsoukanis"
  ],
  "comment": "Presented at the SampTA 2023 conference, July 2023, Yale University, New Haven, CT",
  "categories": [
    "math.FA",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "This paper discusses the connection between the phase retrieval problem and permutation invariant embeddings. We show that the real phase retrieval problem for $\\mathbb{R}^d/O(1)$ is equivalent to Euclidean embeddings of the quotient space $\\mathbb{R}^{2\\times d}/S_2$ performed by the sorting encoder introduced in an earlier work. In addition, this relationship provides us with inversion algorithms of the orbits induced by the group of permutation matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-21T18:39:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation invariant embeddings",
      "relationship",
      "real phase retrieval problem",
      "permutation matrices",
      "euclidean embeddings"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}