International Journal of Biomedical Imaging 
Volume 2007 (2007), Article ID 10693, 5 pages
doi:10.1155/2007/10693
Research Article

Exact Interior Reconstruction with Cone-Beam CT

Yangbo Ye,1 Hengyong Yu,2 and Ge Wang2

1Department of Mathematics, University of Iowa, Iowa City 52242, IA, USA
2CT Laboratory, Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Virginia Tech, Blacksburg 24061, VA, USA

Received 20 November 2007; Accepted 10 December 2007

Recommended by Lizhi Sun

Abstract

Using the backprojection filtration (BPF) and filtered backprojection (FBP) approaches, respectively, we prove that with cone-beam CT the interior problem can be exactly solved by analytic continuation. The prior knowledge we assume is that a volume of interest (VOI) in an object to be reconstructed is known in a subregion of the VOI. Our derivations are based on the so-called generalized PI-segment (chord). The available projection onto convex set (POCS) algorithm and singular value decomposition (SVD) method can be applied to perform the exact interior reconstruction. These results have many implications in the CT field and can be extended to other tomographic modalities, such as SPECT/PET, MRI.