Takeshi Kojima, Tetsushi Ueta, Tetsuya Yoshinaga, Multivalued discrete tomography using dynamical system that describes competition, Hindawi Publishing Corporation, Mathematical Problems in Engineering, Vol.2017, No.Article ID 8160354, 9-pages, Oct. 2017.
Abstract: 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.