{
  "id": "1812.10319",
  "version": "v1",
  "published": "2018-12-26T14:06:15.000Z",
  "updated": "2018-12-26T14:06:15.000Z",
  "title": "Inverse optical tomography through PDE constrained optimisation in $L^\\infty$",
  "authors": [
    "Nikos Katzourakis"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Fluorescent Optical Tomography (FOT) is a new bio-medical imaging method with wider industrial applications. It is currently intensely researched since it is very precise and with no side effects for humans, as it uses non-ionising red and infrared light. Mathematically, FOT can be modelled as an inverse parameter identification problem, associated with a coupled elliptic system with Robin boundary conditions. Herein we utilise novel methods of Calculus of Variations in $L^\\infty$ to lay the mathematical foundations of FOT which we pose as a PDE-constrained minimisation problem in $L^p$ and $L^\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-26T14:06:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse optical tomography",
      "pde constrained optimisation",
      "inverse parameter identification problem",
      "utilise novel methods",
      "wider industrial applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}