Stability and Instability in Discrete Tomography

The paper gives strong instability results for a basic reconstruction problem of discrete tomography, an area that is particularly 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 show that even extremely small changes in the data may lead to entirely different solutions. We will also give some indication of how one can possibly handle the ill-posedness of the reconstruction problem in practice.     «

The paper gives strong instability results for a basic reconstruction problem of discrete tomography, an area that is particularly 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 show that even extremely small changes in the data may lead to entirely different solutions. We will also give some indication of how one can possibly handle the ill-pose...     »