The optimal transport problem gives a geometric framework for optimal mappings, but is computationally expensive and often intractable for large imaging problems. A recent development to address this is to use Sinkhorn iterations, and we extend this idea for fast computation of the proximal operator of the optimal transport cost. This opens up for using optimal transport in variational formulations for solving inverse problems in imaging, e.g., spatio-temporal reconstruction and problems with prior information.

This presentation is part of Minisymposium “MS73 - Mathematical Methods for Spatiotemporal Imaging (2 parts)”
organized by: Chong Chen (LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences) , Barbara Gris (Laboratoire Jacques-Louis Lions) , Ozan Öktem (KTH - Royal Institute of Technology) .

Authors:

Axel Ringh (KTH - Royal Institute of Technology)

Johan Karlsson (KTH - Royal Institute of Technology)

Keywords:

computed tomography, image reconstruction, inverse problems, optimal mass transport, proximal methods, variable splitting