{
  "id": "2001.05005",
  "version": "v1",
  "published": "2020-01-14T19:01:50.000Z",
  "updated": "2020-01-14T19:01:50.000Z",
  "title": "Total Deep Variation for Linear Inverse Problems",
  "authors": [
    "Erich Kobler",
    "Alexander Effland",
    "Karl Kunisch",
    "Thomas Pock"
  ],
  "comment": "21 pages, 10 figures",
  "categories": [
    "math.OC",
    "cs.CV",
    "cs.LG"
  ],
  "abstract": "Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We cast the learning problem as a discrete sampled optimal control problem, for which we derive the adjoint state equations and an optimality condition. By exploiting the variational structure of our approach, we perform a sensitivity analysis with respect to the learned parameters obtained from different training datasets. Moreover, we carry out a nonlinear eigenmode analysis, which reveals interesting properties of the learned regularizer. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-14T19:01:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68T45",
      "93A30",
      "34H05",
      "49K15",
      "65L05"
    ],
    "keywords": [
      "linear inverse problems",
      "total deep variation",
      "learnable general-purpose regularizer exploiting",
      "discrete sampled optimal control problem",
      "task-specific data fidelity term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}