{
  "id": "2407.12984",
  "version": "v1",
  "published": "2024-07-17T20:03:54.000Z",
  "updated": "2024-07-17T20:03:54.000Z",
  "title": "Nonlinear tomographic reconstruction via nonsmooth optimization",
  "authors": [
    "Vasileios Charisopoulos",
    "Rebecca Willett"
  ],
  "comment": "45 pages, 8 figures",
  "categories": [
    "math.OC",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data with a log transform and then solving the resulting linear inverse problem are tempting since they are amenable to convex optimization methods; however, such methods perform poorly when the underlying image has high dynamic range, as in X-ray imaging of tissue with embedded metal. We show that a suitably initialized subgradient method applied to a natural nonsmooth, nonconvex loss function produces iterates that converge to the unknown signal of interest at a geometric rate under the statistical model proposed by Fridovich-Keil et al. (arXiv:2310.03956). Our recovery program enjoys improved conditioning compared to the formulation proposed by the latter work, enabling faster iterative reconstruction from substantially fewer samples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-17T20:03:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65K10",
      "90C06"
    ],
    "keywords": [
      "nonlinear tomographic reconstruction",
      "nonsmooth optimization",
      "initialized subgradient method",
      "nonconvex loss function produces iterates",
      "unknown signal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}