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Mathematical Problems in Engineering
Volume 2017, Article ID 8160354, 9 pages
Research Article

Multivalued Discrete Tomography Using Dynamical System That Describes Competition

1Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan
2Center for Administration of Information Technology, Tokushima University, 2-1 Minami-Josanjima, Tokushima 770-8506, Japan

Correspondence should be addressed to Takeshi Kojima;

Received 2 June 2017; Revised 15 October 2017; Accepted 19 October 2017; Published 12 November 2017

Academic Editor: Guillermo Botella-Juan

Copyright © 2017 Takeshi Kojima et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown.