Affiliations: CT Laboratory, Biomedical Imaging Division, VT-WFU
School of Biomedical Engineering and Science, Virginia Polytechnic Institute
and State University, Blacksburg, VA, USA | Department of Mathematics, University of Iowa, Iowa
City, IA, USA
Abstract: The state-of-the-art technology for theoretically exact local
computed tomography (CT) is to reconstruct an object function using the
truncated Hilbert transform (THT) via the projection onto convex sets (POCS)
method, which is iterative and computationally expensive. Here we propose to
reconstruct the object function using the THT via singular value decomposition
(SVD). First, we review the major steps of our algorithm. Then, we implement
the proposed SVD method and perform numerical simulations. Our numerical
results indicate that our approach runs two orders of magnitude faster than the
iterative approach and produces an excellent region-of-interest (ROI)
reconstruction that was previously impossible, demonstrating the feasibility of
localized pre-clinical and clinical CT as a new direction for research on exact
local image reconstruction. Finally, relevant issues are discussed.
Keywords: Computed tomography (CT), truncated Hilbert transform (THT), singular value decomposition (SVD), regularization, local image reconstruction
