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.