We study various theoretical and algorithmic aspects of inverse problems in discrete tomography that are motivated by demands from material sciences for the reconstruction of crystalline structures from images produced by quantitative high resolution transmission electron microscopy. In particular, we discuss questions related to the ill-posedness of the problem, determine the computational complexity of the basic underlying tasks and indicate algorithmic approaches in the presence of XXX-hardness. Supported in part by a Max Planck Research Award and by the German Federal Ministry of Education, Science, Research and Technology Grant 03-GR7TM1.     «

We study various theoretical and algorithmic aspects of inverse problems in discrete tomography that are motivated by demands from material sciences for the reconstruction of crystalline structures from images produced by quantitative high resolution transmission electron microscopy. In particular, we discuss questions related to the ill-posedness of the problem, determine the computational complexity of the basic underlying tasks and indicate algorithmic approaches in the presence of XXX-hardn...     »