{
  "id": "1312.0158",
  "version": "v1",
  "published": "2013-11-30T22:34:13.000Z",
  "updated": "2013-11-30T22:34:13.000Z",
  "title": "An algebraic characterization of injectivity in phase retrieval",
  "authors": [
    "Aldo Conca",
    "Dan Edidin",
    "Milena Hering",
    "Cynthia Vinzant"
  ],
  "comment": "11 pages",
  "categories": [
    "math.FA",
    "cs.IT",
    "math.AG",
    "math.IT"
  ],
  "abstract": "A complex frame is a collection of vectors that span $\\mathbb{C}^M$ and define measurements, called intensity measurements, on vectors in $\\mathbb{C}^M$. In purely mathematical terms, the problem of phase retrieval is to recover a complex vector from its intensity measurements, namely the modulus of its inner product with these frame vectors. We show that any vector is uniquely determined (up to a global phase factor) from $4M-4$ generic measurements. To prove this, we identify the set of frames defining non-injective measurements with the projection of a real variety and bound its dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-30T22:34:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase retrieval",
      "algebraic characterization",
      "injectivity",
      "intensity measurements",
      "global phase factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0158C"
    }
  }
}