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We present a novel convex relaxation and a corresponding inference algorithmfor the non-binary discrete tomography problem, that is, reconstructingdiscrete-valued images from few linear measurements. In contrast to state ofthe art approaches that split the problem into a continuous reconstructionproblem for the linear measurement constraints and a discrete labeling problemto enforce discrete-valued reconstructions, we propose a joint formulation thataddresses both problems simultaneously, resulting in a tighter convexrelaxation. For this purpose a constrained graphical model is set up andevaluated using a novel relaxation optimized by dual decomposition. We evaluateour approach experimentally and show superior solutions both mathematically(tighter relaxation) and experimentally in comparison to previously proposedrelaxations.

A Novel Convex Relaxation for Non-Binary Discrete Tomography