{
  "id": "1402.4053",
  "version": "v1",
  "published": "2014-02-17T16:49:38.000Z",
  "updated": "2014-02-17T16:49:38.000Z",
  "title": "The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold",
  "authors": [
    "Franz J Király",
    "Martin Ehler"
  ],
  "categories": [
    "math.FA",
    "cs.CV",
    "cs.IT",
    "math.AG",
    "math.IT",
    "stat.ML"
  ],
  "abstract": "We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals. Our results solve a few open problems stated in the recent literature. Furthermore, we show how the algebraic estimation problem can be solved by a closed-form algebraic estimation technique, termed ideal regression, providing non-asymptotic success guarantees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-17T16:49:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase retrieval",
      "algebraic approach",
      "identifiability threshold",
      "explicit inversion",
      "algebraic estimation problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4053K"
    }
  }
}