{
  "id": "2403.07466",
  "version": "v1",
  "published": "2024-03-12T10:01:06.000Z",
  "updated": "2024-03-12T10:01:06.000Z",
  "title": "Norms in sinogram space and stability estimates for the Radon transform",
  "authors": [
    "Stefan Kindermann",
    "Simon Hubmer"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider different norms for the Radon transform $Rf$ of a function $f$ and investigate under which conditions they can be estimated from above or below by some standard norms for $f$. We define Fourier-based norms for $Rf$ that can be related to Bessel-potential space norms for $f$. Furthermore, we define a variant of a total-variation norm for $Rf$ and provide conditions under which it is equivalent to the total-variation norm of $f$. As an illustration of potential applications of these results, we propose a novel nonlinear backprojection method for inverting the Radon transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-12T10:01:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "radon transform",
      "sinogram space",
      "stability estimates",
      "novel nonlinear backprojection method",
      "total-variation norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}