X-ray differential phase-contrast tomographic reconstruction with a phase line integral retrieval filter

We report an alternative reconstruction technique for x-ray differential phase-contrast computed tomography (DPC-CT). This approach is based on a new phase line integral projection retrieval filter, which is rooted in the derivative property of the Fourier transform and counteracts the differential nature of the DPC-CT projections. It first retrieves the phase line integral from the DPC-CT projections. Then the standard filtered back-projection (FBP) algorithms popular in x-ray absorption-contrast CT are directly applied to the retrieved phase line integrals to reconstruct the DPC-CT images. Compared with the conventional DPC-CT reconstruction algorithms, the proposed method removes the Hilbert imaginary filter and allows for the direct use of absorption-contrast FBP algorithms. Consequently, FBP-oriented image processing techniques and reconstruction acceleration softwares that have already been successfully used in absorption-contrast CT can be directly adopted to improve the DPC-CT image quality and speed up the reconstruction.