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Journal of Applied Mathematics
Volume 2013, Article ID 454706, 11 pages
http://dx.doi.org/10.1155/2013/454706
Research Article

Image Reconstruction Based on Homotopy Perturbation Inversion Method for Electrical Impedance Tomography

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 9 May 2013; Revised 26 November 2013; Accepted 27 November 2013

Academic Editor: Md. Sazzad Chowdhury

Copyright © 2013 Jing Wang and Bo Han. 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.

Linked References

  1. M. Cheney, D. Isaacson, and J. C. Newell, “Electrical impedance tomography,” SIAM Review, vol. 41, no. 1, pp. 85–101, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. L. Borcea, “Electrical impedance tomography,” Inverse Problems, vol. 18, no. 6, pp. R99–R136, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. Lionheart, N. Polydorides, and A. Borsic, “The reconstruction problem in electrical impedance tomography,” in Methods, History and Applications, chapter 1, IOP, Philadelphia, Pa, USA, 2005. View at Google Scholar
  4. T. Yorkey, J. Webster, and W. Tompkins, “Comparing reconstruction algorithms for electrical impedance tomography,” IEEE Transactions on Biomedical Engineering, vol. 34, no. 11, pp. 843–852, 1987. View at Google Scholar · View at Scopus
  5. W. L. Weng and F. J. Dickin, “Improved modified Newton-Raphson algorithm for electrical impedance tomography,” Electronics Letters, vol. 32, no. 3, pp. 206–207, 1996. View at Google Scholar · View at Scopus
  6. M. Wang, “Inverse solutions for electrical impedance tomography based on conjugate gradients methods,” Measurement Science and Technology, vol. 13, no. 1, pp. 101–117, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Vauhkonen, D. Vadasz, P. Karjalainen, E. Somersalo, and J. Kaipio, “Tikhonov regularization and prior information in electrical impedance tomography,” IEEE Transactions on Medical Imaging, vol. 17, no. 2, pp. 285–293, 2002. View at Google Scholar · View at Scopus
  8. E. Chung, T. Chan, and X. Tai, “Electrical impedance tomography using level set representation and total variational regularization,” Journal of Computational Physics, vol. 205, no. 1, pp. 357–372, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Borsic, B. Graham, A. Adler, and W. Lionheart, “In vivo impedance imaging with total variation regularization,” IEEE Transactions on Medical Imaging, vol. 29, no. 1, pp. 44–54, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. B. T. Jin, T. Khan, and P. Maass, “A reconstruction algorithm for electrical impedance tomography based on sparsity regularization,” International Journal for Numerical Methods in Engineering, vol. 89, no. 3, pp. 337–353, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. W. Q. Yang, D. M. Spink, T. A. York, and H. Mccann, “An image-reconstruction algorithm based on Landweber's iteration method for electrical-capacitance tomography,” Measurement Science and Technology, vol. 10, no. 11, pp. 1065–1069, 1999. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. Li and W. Q. Yang, “Image reconstruction by nonlinear Landweber iteration for complicated distributions,” Measurement Science and Technology, vol. 19, no. 9, Article ID 094014, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. Z. H. Guo, F. Shao, and D. C. Lv, “Sensitivity matrix construction for electrical capacitance tomography based on the difference model,” Flow Measurement and Instrumentation, vol. 20, no. 3, pp. 95–102, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Liu, G. Y. Yang, N. He, and X. Y. Tan, “Landweber iterative algorithm based on regularization in electromagnetic tomography for multiphase flow measurement,” Flow Measurement and Instrumentation, vol. 27, pp. 53–56, 2012. View at Publisher · View at Google Scholar
  15. H. X. Wang, C. Wang, and W. L. Yin, “A pre-iteration method for the inverse problem in electrical impedance tomography,” IEEE Transactions on Instrumentation and Measurement, vol. 53, no. 4, pp. 1093–1096, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. G. Lu, L. H. Peng, B. F. Zhang, and Y. B. Liao, “Preconditioned Landweber iteration algorithm for electrical capacitance tomography,” Flow Measurement and Instrumentation, vol. 16, no. 2-3, pp. 163–167, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. J. D. Jang, S. H. Lee, K. Y. Kim, and B. Y. Choi, “Modified iterative Landweber method in electrical capacitance tomography,” Measurement Science and Technology, vol. 17, no. 7, pp. 1909–1917, 2006. View at Publisher · View at Google Scholar · View at Scopus
  18. J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  19. J.-H. He, “Homotopy perturbation method for bifurcation of nonlinear problems,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, no. 2, pp. 207–209, 2005. View at Google Scholar · View at Scopus
  20. H. Jafari and S. Momani, “Solving fractional diffusion and wave equations by modified homotopy perturbation method,” Physics Letters A, vol. 370, no. 5-6, pp. 388–396, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. F. Shakeri and M. Dehghan, “Inverse problem of diffusion equation by He's homotopy perturbation method,” Physica Scripta, vol. 75, no. 4, pp. 551–556, 2007. View at Publisher · View at Google Scholar
  22. L. Cao, B. Han, and W. Wang, “Homotopy perturbation method for nonlinear ill-posed operator equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 10, pp. 1319–1322, 2009. View at Google Scholar · View at Scopus
  23. K.-S. Cheng, D. Isaacson, J. Newell, and D. Gisser, “Electrode models for electric current computed tomography,” IEEE Transactions on Biomedical Engineering, vol. 36, no. 9, pp. 918–924, 1989. View at Publisher · View at Google Scholar · View at Scopus
  24. E. Somersalo, M. Cheney, and D. Isaacson, “Existence and uniqueness for electrode models for electric current computed tomography,” SIAM Journal on Applied Mathematics, vol. 52, no. 4, pp. 1023–1040, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. E. J. Woo, P. Hua, J. G. Webster, and W. J. Tompkins, “Finite-element method in electrical impedance tomography,” Medical and Biological Engineering and Computing, vol. 32, no. 5, pp. 530–536, 1994. View at Publisher · View at Google Scholar · View at Scopus
  26. N. Polydorides and W. R. B. Lionheart, “A matlab toolkit for three-dimensional electrical impedance tomography: a contribution to the electrical impedance and diffuse optical reconstruction software project,” Measurement Science and Technology, vol. 13, no. 12, pp. 1871–1883, 2002. View at Publisher · View at Google Scholar · View at Scopus
  27. M. Hanke, A. Neubauer, and O. Scherzer, “A convergence analysis of the Landweber iteration for nonlinear ill-posed problems,” Numerische Mathematik, vol. 72, no. 1, pp. 21–37, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. L. Cao and B. Han, “Convergence analysis of the homotopy perturbation method for solving nonlinear ill-posed operator equations,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 2058–2061, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. M. Vauhkonen, W. R. B. Lionheart, L. M. Heikkinen, P. J. Vauhkonen, and J. P. Kaipio, “A matlab package for the EIDORS project to reconstruct two-dimensional EIT images,” Physiological Measurement, vol. 22, no. 1, pp. 107–111, 2001. View at Publisher · View at Google Scholar · View at Scopus