{
  "id": "2307.03709",
  "version": "v1",
  "published": "2023-07-07T16:45:56.000Z",
  "updated": "2023-07-07T16:45:56.000Z",
  "title": "Exact recovery of the support of piecewise constant images via total variation regularization",
  "authors": [
    "Yohann De Castro",
    "Vincent Duval",
    "Romain Petit"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "eess.SP",
    "math.OC"
  ],
  "abstract": "This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show that, if the unknown image is the superposition of a few simple shapes, and if a non-degenerate source condition holds, then, in the low noise regime, the reconstructed images have the same structure: they are the superposition of the same number of shapes, each a smooth deformation of one of the unknown shapes. Moreover, the reconstructed shapes and the associated intensities converge to the unknown ones as the noise goes to zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-07T16:45:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise constant images",
      "total variation regularization",
      "exact recovery",
      "non-degenerate source condition holds",
      "variational reconstruction method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}