A Linear Programming Relaxation for Binary Tomography with Smoothness Priors

We focus on the reconstruction of binary functions from a small number of X-ray projections. The linear–programming (LP) relaxation to this combinatorial optimization problem due to Fishburn et al. is extended to objective functionals with quadratic smoothness priors. We show that the regularized LP–relaxation provides a good approximation and thus allows to bias the reconstruction towards solutions with spatially coherent regions. These solutions can be computed with any interior– point solver and a related rounding technique. Our approach provides an alternative to computationally expensive MCMC–sampling (Markov Chain Monte Carlo) techniques and other heuristic rounding schemes.