{
  "id": "0704.3822",
  "version": "v1",
  "published": "2007-04-28T23:37:58.000Z",
  "updated": "2007-04-28T23:37:58.000Z",
  "title": "Recovery of edges from spectral data with noise -- a new perspective",
  "authors": [
    "Shlomo Engelberg",
    "Eitan Tadmor"
  ],
  "categories": [
    "math.NA",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We consider the problem of detecting edges in piecewise smooth functions from their N-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the \"smoothness\" scale of order 1/N, the noise scale of order $\\eta$ and the O(1) scale of the jump discontinuities. We use concentration factors which are adjusted to the noise variance, $\\eta$ >> 1/N, in order to detect the underlying O(1)-edges, which are separated from the noise scale, $\\eta$ << 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-28T23:37:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A10",
      "42A50",
      "65T10"
    ],
    "keywords": [
      "spectral data",
      "noise scale",
      "n-degree spectral content",
      "piecewise smooth functions",
      "noise variance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3822E"
    }
  }
}