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International Journal of Biomedical Imaging
Volume 2008, Article ID 427989, 6 pages
http://dx.doi.org/10.1155/2008/427989
Research Article

Exact Interior Reconstruction from Truncated Limited-Angle Projection Data

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

Received 6 December 2007; Accepted 24 January 2008

Academic Editor: Lizhi Sun

Copyright © 2008 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.

Abstract

Using filtered backprojection (FBP) and an analytic continuation approach, we prove that exact interior reconstruction is possible and unique from truncated limited-angle projection data, if we assume a prior knowledge on a subregion or subvolume within an object to be reconstructed. Our results show that (i) the interior region-of-interest (ROI) problem and interior volume-of-interest (VOI) problem can be exactly reconstructed from a limited-angle scan of the ROI/VOI and a 180 degree PI-scan of the subregion or subvolume and (ii) the whole object function can be exactly reconstructed from nontruncated projections from a limited-angle scan. These results improve the classical theory of Hamaker et al. (1980).