From Event: SPIE Optical Engineering + Applications, 2016
X-ray phase contrast imaging is an important mode due to its sensitivity to subtle features of soft biological tissues.
Grating-based differential phase contrast (DPC) imaging is one of the most promising phase imaging techniques because
it works with a normal x-ray tube of a large focal spot at a high flux rate. However, a main obstacle before this paradigm
shift is the fabrication of large-area gratings of a small period and a high aspect ratio. Imaging large objects with a size-limited
grating results in data truncation which is a new type of the interior problem. While the interior problem was
solved for conventional x-ray CT through analytic extension, compressed sensing and iterative reconstruction, the
difficulty for interior reconstruction from DPC data lies in that the implementation of the system matrix requires the
differential operation on the detector array, which is often inaccurate and unstable in the case of noisy data. Here, we
propose an iterative method based on spline functions. The differential data are first back-projected to the image space.
Then, a system matrix is calculated whose components are the Hilbert transforms of the spline bases. The system matrix
takes the whole image as an input and outputs the back-projected interior data. Prior information normally assumed for
compressed sensing is enforced to iteratively solve this inverse problem. Our results demonstrate that the proposed
algorithm can successfully reconstruct an interior region of interest (ROI) from the differential phase data through the
Qingsong Yang, Wenxiang Cong, and Ge Wang, "Interior tomography from differential phase contrast data via Hilbert transform based on spline functions," Proc. SPIE 9967, Developments in X-Ray Tomography X, 996709 (Presented at SPIE Optical Engineering + Applications: August 29, 2016; Published: 4 October 2016); https://doi.org/10.1117/12.2237818.
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