IJBI International Journal of Biomedical Imaging 1687-4196 1687-4188 Hindawi Publishing Corporation 063634 10.1155/2007/63634 Research Article A General Local Reconstruction Approach Based on a Truncated Hilbert Transform Ye Yangbo yangbo-ye@uiowa.edu 1 Yu Hengyong hengyongyu@vt.edu 2 Wei Yuchuan ywei@wfubmc.edu 3 Wang Ge wangg@vt.edu 2, 3 Sun Lizhi 1 Department of Mathematics University of Iowa Iowa City, IA 52242 USA uiowa.edu 2 CT Laboratory Biomedical Imaging Division VT-WFU School of Biomedical Engineering Virginia Tech Blacksburg, VA 24061 USA vt.edu 3 CT Laboratory Biomedical Imaging Division VT-WFU School of Biomedical Engineering Wake Forest University Winston-Salem, NC 27157 USA wfu.edu 2007 17 06 2007 2007 15 05 2007 22 05 2007 2007 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.

 http://dx.doi.org/10.13039/100000070 National Institute of Biomedical Imaging and Bioengineering EB002667 http://dx.doi.org/10.13039/100000070 National Institute of Biomedical Imaging and Bioengineering EB004287