Quality bounds for binary tomography with arbitrary projection matrices

Binary tomography deals with the problem of reconstructing a binary image from a set of its projections. The problem of finding binary solutions of underdetermined linear systems is, in general, very difficult and many such solutions may exist. In a previous paper we developed error bounds on differences between solutions of binary tomography problems restricted to projection models where the corresponding matrix has constant column sums. In this paper, we present a series of computable bounds that can be used with any projection model. In fact, the study presented here is not restricted to tomography and works for more general linear systems. We report the results of computational experiments for some phantom images, focused on parallel and fan beam projection models. Our results show that in some cases the computed bounds can be used to prove that the difference between binary solutions must be small, even if the corresponding linear system is severely underdetermined.