{
  "id": "1308.5028",
  "version": "v1",
  "published": "2013-08-23T02:04:19.000Z",
  "updated": "2013-08-23T02:04:19.000Z",
  "title": "Tight frames, partial isometries, and signal reconstruction",
  "authors": [
    "Enrico Au-Yeung",
    "Somantika Datta"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination of the elements in the original frame. Several examples are considered, such as a Fourier frame on a spiral. The procedure can be applied to the construction of Parseval frames for L^2(B(0,R)), the space of square integrable functions whose domain is the ball of radius R. When a finite number of measurements are used to reconstruct a signal in L^2(B(0,R)), error estimates arising from such approximation are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-23T02:04:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15"
    ],
    "keywords": [
      "tight frame",
      "partial isometries",
      "signal reconstruction",
      "linear combination",
      "resulting parseval frame"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.5028A"
    }
  }
}