An alternative derivation and description of Smith's data sufficiency condition for exact cone-beam reconstruction

Article type: Research Article

Authors: Li, Liang | Kang, Kejun | Chen, Zhiqiang | Zhang, Li | Xing, Yuxiang | Yu, Hengyong | Wang, Ge

Affiliations: Department of Engineering Physics, Tsinghua University, Beijing, 100084, China | Biomedical Imaging Division, School of Biomedical Engineering and Science, Virginia Tech, Blacksburg, VA 24061, USA

Note: [] Corresponding author. E-mail: liliang02@mails.tsinghua.edu.cn

Abstract: In this paper, we present an alternative derivation and description of Smith's data sufficiency condition for exact cone-beam reconstruction. Different from Smith's condition, our condition with new description can be considered as a bridge between the approximate and exact cone-beam reconstruction. When the data sufficiency condition is satisfied, a set of parallel-beam projections can be obtained for exact 3-D reconstruction. When it is not satisfied, some directional parallel-beam projections will be missed, and only approximate reconstruction is achieved. Although our data sufficiency condition is theoretically proved to be equivalent to Smith's condition, its derivation is totally different.

Keywords: CT, reconstruction, data sufficiency condition, projection transform

Journal: Journal of X-Ray Science and Technology, vol. 16, no. 1, pp. 43-49, 2008