Affiliations: School of Automation, Xi'an University of Posts and
Telecommunications, Xi'an, Shanxi, China | Institute of Image Processing & Pattern
Recognition, Xi'an Jiaotong University, Xi'an, Shanxi, China | Department of Radiology, Division of Radiologic
Sciences, Wake Forest University Health Sciences, Winston-Salem, NC, USA | Biomedical Imaging Division, VT-WFU School of
Biomedical Engineering and Sciences, Wake Forest University Health Sciences,
Winston-Salem, NC, USA
Abstract: An algorithm is proposed to directly reconstruct a CT gradient image
in a region of interest(ROI). First, the central slice theorem is generalized
and a differential constraint condition (DCC) is introduced in parallel-beam
geometry. Then, an algorithm is developed to reconstruct the gradient images in
both Cartesian and polar coordinate systems based on a two-step Hilbert
transform method. Finally, the reconstruction algorithm is extended into the
equi-distant fan-beam geometry. Meanwhile, a conditional truncation for
projection data acquisition is permitted by using a one-dimensional(1-D) finite
Hilbert transform in image domain. Because the reconstructed gradient image is
in terms of local operator, it have a better performance in CT image analysis
and other CT applications compared to the global Calderon operator in Lambda Tomography.
Keywords: Computed tomography, region of interest, hilbert transform, lambda tomography
