Kimura, Masashi Tokushima University
Yamaguchi, Yusaku Shikoku Medical Center for Children and Adults
Abou Al-Ola, Omar M. Tanta University
Nonlinear Dynamical System
Metal Artifact Reduction
Thesis or Dissertation
Image reconstruction in computed tomography can be treated as an inverse problem, namely, obtaining pixel values of a tomographic image from measured projections. However, a seriously degraded image with artifacts is produced when a certain part of the projections is inaccurate or missing. A novel method for simultaneously obtaining a reconstructed image and an estimated projection by solving an initial-value problem of differential equations is proposed. A system of differential equations is constructed on the basis of optimizing a cost function of unknown variables for an image and a projection. Three systems described by nonlinear differential equations are constructed, and the stability of a set of equilibria corresponding to an optimized solution for each system is proved by using the Lyapunov stability theorem. To validate the theoretical result given by the proposed method, metal artifact reduction was numerically performed.
Mathematical Problems in Engineering
Copyright © 2019 Masashi Kimura et al. This is an open access article distributed under the Creative Commons Attribution License ( https://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Doctor of Health Science