{
  "id": "0906.0711",
  "version": "v2",
  "published": "2009-06-03T13:32:58.000Z",
  "updated": "2009-07-30T09:24:23.000Z",
  "title": "An Algebraic Framework for Discrete Tomography: Revealing the Structure of Dependencies",
  "authors": [
    "Arjen Stolk",
    "K. Joost Batenburg"
  ],
  "comment": "20 pages, 1 figure, updated to reflect reader input",
  "categories": [
    "math.CO"
  ],
  "abstract": "Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is typically a small discrete set. In this paper we present a framework for studying these problems from an algebraic perspective, based on Ring Theory and Commutative Algebra. A principal advantage of this abstract setting is that a vast body of existing theory becomes accessible for solving Discrete Tomography problems. We provide proofs of several new results on the structure of dependencies between projections, including a discrete analogon of the well-known Helgason-Ludwig consistency conditions from continuous tomography.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-30T09:24:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94A12",
      "94C10",
      "11H71"
    ],
    "keywords": [
      "algebraic framework",
      "dependencies",
      "lattice point",
      "well-known helgason-ludwig consistency conditions",
      "small discrete set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.0711S"
    }
  }
}