Affiliations: LMAM, School of Mathematical Sciences, Peking
University, Beijing 100871, China
Note: [] Corresponding author: Jiansheng Yang, Ph.D., Department of
Information Science, School of Mathematical sciences, Peking University,
Beijing 100871, P.R. China. Tel.: +86 010 62756797; Fax: +86 010 62751801;
E-mail: yjs@math.pku.edu.cn
Abstract: The conventional implementation of Katsevich's inversion formula
involves the computation of PI segment. This is done by solving a nonlinear
equation with a numerical algorithm such as Newton's method. In this study, we
develop an implementation of Katsevich's inversion formula without computing PI
segment. Our implementation involves a new concept, cone beam cover, which is
closely related to PI segment and Tam-Danielsson window. Unlike the
implementation based on PI segment, the algorithm complexity of our
implementation can be estimated with several important imaging parameters. This
result may be instructive for practical applications to choose scanning
parameters and reduce the algorithm complexity. The proposed implementation is
validated with satisfactory numerical experiments.
