{
  "id": "1812.08540",
  "version": "v1",
  "published": "2018-12-20T13:03:54.000Z",
  "updated": "2018-12-20T13:03:54.000Z",
  "title": "Recent Advances in Denoising of Manifold-Valued Images",
  "authors": [
    "Ronny Bergmann",
    "Friederike Laus",
    "Johannes Persch",
    "Gabriele Steidl"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny inaccuracies, which result in noisy data. In this chapter, we review recent advances in denoising of manifold-valued signals and images, where we restrict our attention to variational models and appropriate minimization algorithms. The algorithms are either classical as the subgradient algorithm or generalizations of the half-quadratic minimization method, the cyclic proximal point algorithm, and the Douglas-Rachford algorithm to manifolds. An important aspect when dealing with real-world data is the practical implementation. Here several groups provide software and toolboxes as the Manifold Optimization (Manopt) package and the manifold-valued image restoration toolbox (MVIRT).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-20T13:03:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic proximal point algorithm",
      "half-quadratic minimization method",
      "manifold-valued image restoration toolbox",
      "occur tiny inaccuracies",
      "image acquisition systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}