  Optimal transport has gained much attention in image processing field, such
as computer vision, image interpolation and medical image registration.
Recently, Bredies et al. (ESAIM:M2AN 54:2351-2382, 2020) and Schmitzer et al.
(IEEE T MED IMAGING 39:1626-1635, 2019) established the framework of optimal
transport regularization for dynamic inverse problems. In this paper, we
incorporate Wasserstein distance, together with total variation, into static
inverse problems as a prior regularization. The Wasserstein distance formulated
by Benamou-Brenier energy measures the similarity between the given template
and the reconstructed image. Also, we analyze the existence of solutions of
such variational problem in Radon measure space. Moreover, the first-order
primal-dual algorithm is constructed for solving this general imaging problem
in a specific grid strategy. Finally, numerical experiments for undersampled
MRI reconstruction are presented which show that our proposed model can recover
images well with high quality and structure preservation.
