{
  "id": "1502.06933",
  "version": "v1",
  "published": "2015-02-24T20:14:05.000Z",
  "updated": "2015-02-24T20:14:05.000Z",
  "title": "Asymptotic behaviour of total generalised variation",
  "authors": [
    "Konstantinos Papafitsoros",
    "Tuomo Valkonen"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "The recently introduced second order total generalised variation functional $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ has been a successful regulariser for image processing purposes. Its definition involves two positive parameters $\\alpha$ and $\\beta$ whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ in the cases where the parameters $\\alpha, \\beta$ as well as their ratio $\\beta/\\alpha$ becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and large ratio $\\beta/\\alpha$, $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ regularisation coincides with total variation ($\\mathrm{TV}$) regularisation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-24T20:14:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic behaviour",
      "second order total generalised variation",
      "order total generalised variation functional",
      "regularisation",
      "total variation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}