A discrete tomography algorithm for improving the quality of three-dimensional X-ray diffraction grain maps

A discrete tomography algorithm is presented for the reconstruction of grain maps based on X-ray diffraction data. This is the first algorithm for this task, inherently exploiting the discrete structure of grain maps. Gibbs potentials serve to characterize the statistics of the local morphology of the grain boundaries. A Monte Carlo based algorithm is applied as a restoration method for improving the quality of grain maps produced by a classical (non-discrete) tomography algorithm (ART). The quality of the restored maps is demonstrated and quantified by simulation studies. The robustness of the algorithm with respect to the choice of Gibbs potentials is investigated.