{
  "id": "0911.5521",
  "version": "v2",
  "published": "2009-11-29T22:34:15.000Z",
  "updated": "2009-12-15T19:37:48.000Z",
  "title": "On singularities and instability of reconstruction in thermoacoustic tomography",
  "authors": [
    "Linh V. Nguyen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the problem of thermoacoustic tomography (TAT), in which one needs to reconstruct the initial value of a solution of the wave equation from its value on an observation surface. We show that if some geometric rays for the equation do not intersect the observation surface, the reconstruction in TAT is not H\\\"{o}lder stable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-15T19:37:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "92C55"
    ],
    "keywords": [
      "thermoacoustic tomography",
      "reconstruction",
      "singularities",
      "observation surface",
      "instability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.5521N"
    }
  }
}