Limited view reconstruction for differential phase-contrast computed tomography

This paper describes an algebraic reconstruction algorithm that uses total variation (TV) regularization for differential phase contrast computed tomography (DPC-CT) using a limited number of views. In order to overcome over-flattening inherent in TV regularization, a two-step reconstruction process is used: we first reconstruct tomographic images of gradient refractive index from differential projections with TV regularization; these images are then used to compute tomographic images of refractive index by solving the Poisson equation. We incorporate TV regularization in the reconstruction process because the distribution of gradient refractive index is much more flattened than the refractive index. Simulations of the proposed method demonstrate that it can achieve satisfactory image quality from a much smaller number of projections than is required by the Nyquist sampling theorem. We experimentally prove the feasibility of the proposed method using dark field imaging optics at PF-14C beamline at the Photon Factory, KEK. The differential phase contrast projection data was experimentally acquired from a biological sample and DPC-CT images were reconstructed. We show that far fewer projections are needed when the proposed algorithm is used.