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The optimal mass transport problem gives a geometric framework for optimalallocation, and has recently gained significant interest in application areassuch as signal processing, image processing, and computer vision. Even thoughit can be formulated as a linear programming problem, it is in many casesintractable for large problems due to the vast number of variables. A recentdevelopment to address this builds on an approximation with an entropic barrierterm and solves the resulting optimization problem using Sinkhorn iterations.In this work we extend this methodology to a class of inverse problems. Inparticular we show that Sinkhorn-type iterations can be used to compute theproximal operator of the transport problem for large problems. A splittingframework is then used to solve inverse problems where the optimal masstransport cost is used for incorporating a priori information. We illustratethe method on problems in computerized tomography. In particular we consider alimited-angle computerized tomography problem, where a priori information isused to compensate for missing measurements.

Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transport