Template-based CT reconstruction with optimal transport and total generalized variation

Abstract

x-ray computed tomography (CT) has been widely used in clinical diagnosis as a modality of medical imaging. To decrease the radiation dose patients suffering from, sparse-view CT has gained much attention in medical imaging field. In this paper, we propose to design a variational model based on dynamic optimal transportation and total generalized variation for CT reconstruction. This is a joint task involving inverse problem and template registration. The final state image of the optimal transport problem is unknown and needs to be reconstructed through CT inversion, while the given initial state can be regarded as a template to provide some structural information for the final one. Moreover, the existence and stability of minimizers to our proposed model are shown in continuous space. In discretization with the continuity equation, we utilize the well-known staggered grid in fluid mechanics and develop a first-order algorithm based on primal-dual method for numerically solving the proposed model. Finally, numerical experiments for sparse-view CT reconstruction are exhibited to show the performance of our proposed model in recovering images with high quality and structure preservation.