An optimal transport regularized model to image reconstruction problems

Optimal transport problem has gained much attention in image processing field, such as computer vision, image interpolation and medical image registration. In this paper, we incorporate optimal transport into linear inverse problems as a regularization technique. We establish a new variational model based on Benamou-Brenier energy to regularize the evolution path from a template to latent image dynamically. The initial state of the continuity equation can be regarded as a template, which can provide priors for the reconstructed images. 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 special 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.