Bounds on the Difference between Reconstructions in Binary Tomography

Kees Joost Batenburg, Wagner Fortes, Lajos Hajdu, Robert Tijdeman

Abstract: Tomography is concerned with the reconstruction of images from their projections. In this paper, we consider the reconstruction problem for a class of tomography problems, where the images are restricted to binary grey levels. For any given set of projections, we derive an upper bound on the difference between any two binary images having these projections, and a bound on the difference between a particular binary image and any binary image having the given projections. Both bounds are evaluated experimentally for different geometrical settings, based on simulated projection data for a range of images.