Optimal Transport Structure of CycleGAN for Unsupervised Learning for Inverse Problems

Optimal transport (OT) is a mathematical theory that can provide a tool how to transfer one measure to another measure at minimal cost, thus serve another framework for computer vision tasks of image processing without reference. Cycleconsistent generative adversarial network (cycleGAN) is a recent extension of GAN to learn target distributions with less mode collapsing behavior, and also does not need matched data during training. In this article, we explain the link between these two framework by mathematical formula and experimental results. We prove that cycleGAN architecture can be derived from optimal transport problem, and this implies that cycleGAN is a plausible way to learn target distribution when it comes to handling data far from the training set. Using accelerated MR imaging experiments, we confirmed the flexibility and efficacy of our theoretical framework.