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International Journal of Biomedical Imaging
Volume 2007, Article ID 63634, 8 pages
Research Article

A General Local Reconstruction Approach Based on a Truncated Hilbert Transform

1Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
2CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Virginia Tech, Blacksburg, VA 24061, USA
3CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Wake Forest University, Winston-Salem, NC 27157, USA

Received 15 May 2007; Accepted 22 May 2007

Academic Editor: Lizhi Sun

Copyright © 2007 Yangbo Ye et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Exact image reconstruction from limited projection data has been a central topic in the computed tomography (CT) field. In this paper, we present a general region-of-interest/volume-of-interest (ROI/VOI) reconstruction approach using a truly truncated Hilbert transform on a line-segment inside a compactly supported object aided by partial knowledge on one or both neighboring intervals of that segment. Our approach and associated new data sufficient condition allows the most flexible ROI/VOI image reconstruction from the minimum account of data in both the fan-beam and cone-beam geometry. We also report primary numerical simulation results to demonstrate the correctness and merits of our finding. Our work has major theoretical potentials and innovative practical applications.