{
  "id": "2204.01225",
  "version": "v1",
  "published": "2022-04-04T03:59:15.000Z",
  "updated": "2022-04-04T03:59:15.000Z",
  "title": "The X-ray transform on a generic family of smooth curves",
  "authors": [
    "Yang Zhang"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the X-ray transform over a generic family of smooth curves in $\\mathbb{R}^2$ with a Riemannian metric $g$. We show that the singularities cannot be recovered from local data in the presence of conjugate points, and therefore artifacts may arise in the reconstruction. We perform numerical experiments to illustrate the results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-04T03:59:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth curves",
      "x-ray transform",
      "generic family",
      "perform numerical experiments",
      "conjugate points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}