Abstract:
The talk deals with various theoretical and algorithmic aspects of inverse problems in discrete tomography that are primarily motivated by demands from material sciences for the reconstruction of crystalline structures from images produced by quantitative high resolution transmission electron microscopy. Special emphasis is placed on the question of when finite lattice sets are uniquely determined by their discrete X-rays in a given number of directions, on the problem of determining the computational complexity of the basic underlying tasks and on the description of successful algorithmic approaches in the presence of NP-completeness.