{
  "id": "2103.05718",
  "version": "v1",
  "published": "2021-03-09T21:01:27.000Z",
  "updated": "2021-03-09T21:01:27.000Z",
  "title": "Data driven reconstruction using frames and Riesz bases",
  "authors": [
    "Andrea Aspri",
    "Leon Frischauf",
    "Yury Korolev",
    "Otmar Scherzer"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide an application of a projection algorithm, utilized and applied in frames theory, as a data driven reconstruction procedure in inverse problems, generalizing the algorithm proposed by the authors in Inverse Problems 36 (2020), n. 12, 125009, based on an orthonormalization procedure for the training pairs. We show some numerical experiments, comparing the different methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-09T21:01:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A52",
      "65J20",
      "65J22",
      "65F22"
    ],
    "keywords": [
      "riesz bases",
      "inverse problems",
      "data driven reconstruction procedure",
      "purely data driven approach",
      "regularization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}