  The optimal mass transport problem gives a geometric framework for optimal
allocation, and has recently gained significant interest in application areas
such as signal processing, image processing, and computer vision. Even though
it can be formulated as a linear programming problem, it is in many cases
intractable for large problems due to the vast number of variables. A recent
development to address this builds on an approximation with an entropic barrier
term and solves the resulting optimization problem using Sinkhorn iterations.
In this work we extend this methodology to a class of inverse problems. In
particular we show that Sinkhorn-type iterations can be used to compute the
proximal operator of the transport problem for large problems. A splitting
framework is then used to solve inverse problems where the optimal mass
transport cost is used for incorporating a priori information. We illustrate
the method on problems in computerized tomography. In particular we consider a
limited-angle computerized tomography problem, where a priori information is
used to compensate for missing measurements.
