Semi-Unbalanced Regularized Optimal Transport for Image Restoration

We consider in this paper the use of a penalty based on the theory of optimal transport (OT) in order to regularize inverse problems in imaging. The proposed approach is formulated in a variational setting and aims at promoting images whose patch distribution is close either to the one learned by a generative model, or to available uncorrupted reference patches. With the aid of numerical illustrations, we argue in favor of adopting an asymmetric form of unbalanced OT. We then provide details concerning the computation and the differentiation of the proposed penalty. Finally, we detail the application of our approach to a particular super-resolution setting.