Uniqueness and Complexity in Discrete Tomography
Richard J. Gardner, Peter Gritzmann · Applied and numerical harmonic analysis · 1999
We study the discrete inverse problem of reconstructing finite subsets of the n-dimensional integer lattice ℤ n 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. 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.