Fourier transform-based iterative method for differential phase-contrast computed tomography

In this Letter, a novel Fourier transform-based iterative method is proposed to reconstruct a refractive index distribution in an object directly from measured differential phase shifts. This reconstruction method offers distinct advantages over the analytic method in cases of noisy and/or few-view data, since the iterative scheme can easily incorporate compressive sensing and maximum likelihood techniques to achieve high image quality. Numerical simulation and biological sample experiments demonstrate the merits of the proposed approach.