Discrete Tomography pp 85-113 | Cite as

# Uniqueness and Complexity in Discrete Tomography

Chapter

## Abstract

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.

## Keywords

Lattice Line Finite Subset Truth Assignment Cross Ratio Discrete Tomography
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© Springer Science+Business Media New York 1999