Differential phase-contrast computed tomography reconstruction based on the projection theorem for Laplacian image

We propose an efficient reconstruction algorithm from limited-view projections for differential phase-contrast computed tomography, based on the projection theorem for Laplacian image, proved in the research. First, the algorithm first reconstructs the Laplacian image of the target phase-shift-term distribution from the second-derivative projections obtained experimentally with the total variation regularization, which is ensured by the theorem. Then, it obtains the phase-shift-term distribution by solving a Poisson equation with a source being the Laplacian image reconstructed in the previous stage under the Dirichlet condition. We demonstrate the efficacy of the algorithm using synthetic data generated by computer codes based a differential phase-contrast imaging. The method can efficiently and satisfactorily reconstruct from the limited number of projections.