Differential phase-contrast interior tomography

Differential phase-contrast interior tomography allows reconstruction of a refractive index distribution over a region of interest (ROI) for visualization and analysis of structures inside a large biological specimen. In the imaging mode, x-ray scanning only targets an ROI in an object and a narrow beam passes through the object, allowing a significant reduction of both radiation dose and system cost. Inspired by recently developed compressive sensing theory, in a numerical analysis framework we show that accurate interior reconstruction can be achieved on an ROI from truncated differential projection data through the ROI via the total variation minimization, assuming a piecewise constant distribution of the refractive indices in the ROI. Then, we develop a practical iterative algorithm for such an interior reconstruction and perform numerical experiments to demonstrate the feasibility of the proposed approach.