{
  "id": "2308.01055",
  "version": "v1",
  "published": "2023-08-02T10:05:46.000Z",
  "updated": "2023-08-02T10:05:46.000Z",
  "title": "Towards optimal sensor placement for inverse problems in spaces of measures",
  "authors": [
    "Phuoc-Truong Huynh",
    "Konstantin Pieper",
    "Daniel Walter"
  ],
  "comment": "31 pages, 8 figures",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.OC"
  ],
  "abstract": "This paper studies the identification of a linear combination of point sources from a finite number of measurements. Since the data are typically contaminated by Gaussian noise, a statistical framework for its recovery is considered. It relies on two main ingredients, first, a convex but non-smooth Tikhonov point estimator over the space of Radon measures and, second, a suitable mean-squared error based on its Hellinger-Kantorovich distance to the ground truth. Assuming standard non-degenerate source conditions as well as applying careful linearization arguments, a computable upper bound on the latter is derived. On the one hand, this allows to derive asymptotic convergence results for the mean-squared error of the estimator in the small small variance case. On the other, it paves the way for applying optimal sensor placement approaches to sparse inverse problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-02T10:05:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q62",
      "35R30",
      "62K05",
      "65J22"
    ],
    "keywords": [
      "inverse problems",
      "non-smooth tikhonov point estimator",
      "small small variance case",
      "assuming standard non-degenerate source conditions",
      "applying optimal sensor placement approaches"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}