  Biological soft tissues encountered in clinical and pre-clinical imaging
mainly consist of light element atoms, and their composition is nearly uniform
with little density variation. Thus, x-ray attenuation imaging suffers from low
image contrast resolution. By contrast, x-ray phase shift of soft tissues is
about a thousand times greater than x-ray absorption over the diagnostic energy
range, thereby a significantly higher sensitivity can be achieved in terms of
phase shift. In this paper, we propose a novel Fourier transform based
iterative method to perform x-ray tomographic imaging of the refractive index
directly from differential phase shift data. This approach offers distinct
advantages in cases of incomplete and noisy data than analytic reconstruction,
and especially suitable for phase-contrast interior tomography by incorporating
prior knowledge in a region of interest (ROI). Biological experiments
demonstrate the merits of the proposed approach.
