Far East Journal of Dynamical Systems

The Far East Journal of Dynamical Systems publishes original research papers and survey articles in all aspects of dynamical systems, including chaos, fractals, and ergodic theory. It encourages application-oriented research in physics, life sciences, and social sciences.

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CONTINUOUS-TIME IMAGE RECONSTRUCTION SYSTEM WITH PRECONDITIONING MATRIX

Authors

  • Yuichi Tanji
  • Ken’ichi Fujimoto

Keywords:

computed tomography (CT), filter back projection (FBP) method, preconditioning matrix

DOI:

https://doi.org/10.17654/0972111825012

Abstract

This paper presents a continuous-time image reconstruction system that incorporates a preconditioning matrix. We demonstrate that the system’s equilibria correspond to an optimal solution of a quadratic programming problem with box constraints. Additionally, we provide numerical evidence demonstrating that the proposed system generates a higher-quality reconstruction image compared to a sparse modeling technique.

Received: June 20, 2025
Accepted: July 21, 2025

References

[1] T. M. Buzug, Computed Tomography, Springer, 2008.

[2] K. Zeng, Z. Chen, L. Zhang and G. Wang, An error-reduction-based algorithm for cone-beam computed tomography, Med. Phys. 31 (2004), 3206-3212.

[3] J. Sunnegardh and P.-E. Danielssonet, Regularized iterative weighted filtered backprojection for helical cone-beam CT, Med. Phys. 35 (2008), 4173-4185.

[4] K. Fujimoto, O. A. Al-Ola and T. Yoshinaga, Continuous-time image reconstruction using differential equations for computed tomography, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), 1648-1654.

[5] Y. Yamaguchi, K. Fujimoto, O. M. A. Al-Ola and T. Yoshinaga, Continuous-time image reconstruction for binary tomography, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), 2081-2087.

[6] Y. Tanji, T. Suehiro and K. Fujimoto, Learning-based nonlinear model order reduction for image reconstruction, Nonlinear Theory and Its Applications, IEICE 15 (2024), 538-552.

[7] D. H. Jacobson, Extensions of Linear-Quadratic Control, Optimization and Matrix Theory, Academic Press, New York, 1977.

[8] D. P. Bertsekas, Nonlinear Programming, Athena Scientific, 2016.

[9] A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sciences 2 (2009), 183-2002.

[10] M. Zibulevsky and M. Elad, L1-L2 optimization in signal and image processing, IEEE Signal Processing Mag. (2010), 76-88.

[11] H. Kubo, F. Yamazaki, T. Nemoto and K. Takaki, A very fast iterative algorithm for TV-regularized image reconstruction with applications to low-dose and few-view CT, SPIE Proceedings, Vol. 9967, 2016.

Published

2025-09-05

Issue

Section

Articles

How to Cite

CONTINUOUS-TIME IMAGE RECONSTRUCTION SYSTEM WITH PRECONDITIONING MATRIX. (2025). Far East Journal of Dynamical Systems, 38(2), 271-285. https://doi.org/10.17654/0972111825012

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