The stability problem and noisy projections in discrete tomography

Abstract

The new field of research of discrete tomography will be described in this paper. It differs from standard computerized tomography in the reduced number of projections. It needs ad hoc algorithms which usually are based on the definition of the model of the object to reconstruct. The main problems will be introduced and an experimental simulation will prove the robustness of a slightly modified version of a well known method for the reconstruction of binary planar convex sets, even in case of projections affected by error. To the best of our knowledge this is one of the first experimental study of the stability problem with a statistical approach. Prospective applications include crystallography, quality control and reverse engineering while biomedical tests, due to their important role, still require further research.