Variable splitting techniques for discrete tomography

Discrete tomography problems require the generation of an underlying attenuation field over a combinatorial set that renders the direct application of conventional tomographic reconstruction techniques obsolete. In this work, we propose a solution approach based on a new variable splitting coupled with the alternating direction method of multipliers (ADMM). The new approach creates subproblems that can be solved using existing and fast techniques, such as graph-cut methods, and results in overall solutions of excellent quality. In particular, compared to state-of-the art techniques, we obtain reliable representations of the underlying fields with substantially lower angular coverage. We develop the method under both Gaussian and Poisson noise models and show results with both binary and multilabel phantoms.