{
  "id": "1302.4396",
  "version": "v6",
  "published": "2013-02-18T19:34:20.000Z",
  "updated": "2013-10-04T08:45:36.000Z",
  "title": "On the Determination of a Function from an Elliptical Radon Transform",
  "authors": [
    "Sunghwan Moon"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that integrates a given function in $\\RR^n$ over a set of solid ellipsoids of rotation with a fixed eccentricity and foci restricted to a hyperplane. Inversion formulas are obtained for appropriate classes of functions that are even with respect to the hyperplane. Stability estimates, range description, and local uniqueness results are also provided.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2013-10-04T08:45:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A12",
      "92C55"
    ],
    "keywords": [
      "elliptical radon transform",
      "determination",
      "radon type transforms",
      "ultrasound reflection tomography",
      "local uniqueness results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.4396M"
    }
  }
}