Discrete Tomography by Continuous Multilabeling Subject to Projection Constraints

We present a non-convex variational approach to non-binary discrete tomography which combines non-local projection constraints with a continuous convex relaxation of the multilabeling problem. Minimizing this non-convex energy is achieved by a fixed point iteration which amounts to solving a sequence of convex problems, with guaranteed convergence to a critical point. A competitive numerical evaluation using standard test-datasets demonstrates a significantly improved reconstruction quality for noisy measurements from a small number of projections.