Binary Tomography by Iterating Linear Programs

Abstract

A novel approach to the reconstruction problem of binary tomography from a small number of X-ray projections is presented. Based on our previous work, we adopt a linear programming relaxation of this combinatorial problem which includes an objective function for the reconstruction, the approximation of a smoothness prior enforcing spatially homogeneous solutions, and the projection constraints. We supplement this problem with an unbiased concave functional in order to gradually enforce binary minimizers. Application of a primal-dual subgradient iteration for optimizing this enlarged problem amounts to solve a sequence of linear programs, where the objective function changes in each step, yielding a sequence of solutions which provably converges.