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Uniqueness and Complexity in Discrete Tomography

  • Richard J. Gardner
  • Peter Gritzmann
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We study the discrete inverse problem of reconstructing finite subsets of the n-dimensional integer lattice ℤn that are only accessible via their line sums (discrete X-rays) in a finite set of lattice directions. Special emphasis is placed on the question of when such sets are uniquely determined by the data and on the difficulty of the related algorithmic problems. Such questions are motivated by demands from the material sciences for the reconstruction of crystalline structures from images produced by quantitative high-resolution transmission electron microscopy.

Keywords

Lattice Line Finite Subset Truth Assignment Cross Ratio Discrete Tomography 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Richard J. Gardner
    • 1
  • Peter Gritzmann
    • 2
  1. 1.Department of MathematicsWestern Washington UniversityBellinghamUSA
  2. 2.Zentrum MathematikTechnische Universität MünchenMünchenGermany

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