Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:4-2-2
Session:
Number:4-2-2-3
Bifurcations of a Dynamical System Defined by PMART
Yoshihiro Imakura, Tetsushi Ueta, Tetsuya Yoshinaga,
pp.38-41
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
In this paper, We investigate dynamical behavior of an iterative image reconstruction technique called PMART(Power Multiplicative Algebraic Reconstruction Technique) used for the X-ray computed tomography(CT). This technique can obtain an accurate image by iterating an updating scheme for simultaneous equations even though the iteration consumes much time at first. In addition, the updating schemes fails sometimes when the parameters of PMART are provided inappropriately. Recently this method is revised since the scheme can be solved within a reasonable processing time with high-speed computers. In this paper, we analyze the PMART updating scheme as a bifurcation problem of the dynamical system. We would like to insist that above failure is caused by bifurcations of the system. We develop a method for solving this bifurcation problem, and as a result, we obtain bifurcations diagrams of the fixed or periodic points. This result suggests us parameter regions and an initial value set in which the PMART can operate normally