Journal of the Institute of Electronics Engineers of Korea SC (전자공학회논문지SC)

The Institute of Electronics and Information Engineers (대한전자공학회)
권호 표지

Dynamical Electrical Impedance Tomography Based on the Regularized Extended Kalman Filter

조정 확장 칼만 필터를 이용한 동적 전기 임피던스 단층촬영법

  • 김경연 (제주대학교 전기전자공학부) ;
  • 김봉석 (제주대학교 전기전자공학부) ;
  • 강숙인 (제주대학교 전기전자공학부) ;
  • 김민찬 (제주대학교 화학공학과) ;
  • 이정훈 (제주대학교 전산통계학과) ;
  • 이윤준 (제주대학교 에너지공학과)
  • Published : 2001.10.30
Download PDF
⟨ Previous Next ⟩

Abstract

Electrical impedance tomography (EIT) is a relatively new imaging modality in which the resistivity (conductivity) distribution of the unknown object is estimated based on the known sets of injected currents and measured voltages on the surface of the object. In this paper, we propose a dynamical EIT reconstruction algorithm based on the regularized extended Kalman filter(EKF). The EIT inverse problem is formulated as dynamic equation which consists of the slate equation and the observation equation, and the unknown state(resistivity) is estimated recursively with the aid of the EKF. In doing so, the generalized Tikhonov regularization technique is employed in the cost functional to mitigate the ill-posedness characteristics of the inverse problem. Computer simulations for the 16-channel synthetic data are provided to illustrate the reconstruction performance of the proposed algorithm.

전기 임피던스 단층촬영법은 표적의 경계면에서 여러 개의 전극을 통하여 전류를 주입하고 저항률의 함수로써 경계면에 유기되는 전압을 구하고, 경계면에 유기된 전압 값으로부터 표적 내부의 저항률 분포를 추정하여 표적의 영상을 복원하는 비교적 새로운 영상복원법이다. 본 논문에서는, 상태방정식과 측정방정식으로 구성되는 동적 모델에 기초하여, 시간에 따라 변하는 저항률 분포를 온라인으로 추정하기 위해 확장 칼만 필터를 이용한 전기 임피던스 단층촬영법의 영상복원 알고리즘을 제안하였다. 또한, Tikhonov 조정 기법에 근거한 제약조건을 비용함수에 추가하여 역문제의 부정치성을 완화시켰다. 제안된 영상복원 알고리즘의 성능을 검증하기 위해 16 채널에 대한 컴퓨터 시뮬레이션을 수행하였으며, 시간에 따른 표적의 저항률 분포의 변화가 심한 경우에도 비교적 양호한 복원성능을 나타내었다.

Keywords

References

  1. J. G. Webster, Electrical Impedance Tomography, Adam Hilger, 1990
  2. M. Cheney, D. Isaacson, and J. C. Newell, 'Electrical Impedance Tomography,' SIAM Review, Vol. 41, No.1, pp. 85-101, 1999 https://doi.org/10.1137/S0036144598333613
  3. C. G. Xie, N. Reinecke, M.S. Beck, D, mewes, and R. A. Williams, 'Electrical Tomography Techniques for Process Engineering Applications,' The chemical Engineering Journal, Vol. 56, pp. 127-133, 1995 https://doi.org/10.1016/0923-0467(94)02907-5
  4. R. W. M. Smith, I. L. Freeston, and B. H. Brown, 'A Real-Time Electrical Impedance Tomography System for Clinical Use Design and Preliminary Results,' IEEE Transactions on Biomedical Engineering, Vol. 42, No.2, pp. 133-140, 1995 https://doi.org/10.1109/10.341825
  5. S. L. Ceccio and D. L. George, 'Review of Electrical Impedance Techniques for the Measurement of Multiphase Flows,' Journal of Fluids Engineering, Vol. 118, pp. 391-399, 1996
  6. T. Murai, and Y. Kagawa, 'Electrical Impedance Computed Tomography Based on a Finite element Model,' IEEE Transactions on Biomedical Engineering, Vol. 32, No.3, pp.177-184, 1985 https://doi.org/10.1109/TBME.1985.325526
  7. H. Akaike, 'A New Look at Statistical Model Identification,' IEEE Transactions on Automatic Control, Vol. 19, No.6, pp. 716-723, 1974 https://doi.org/10.1109/TAC.1974.1100705
  8. L. Ovacik, O.C. Jones 'Development of an Electrical Impedance Computed Tomographic Two-Phase Flows Analyzer,' Final Report for the U.S. Department of Energy, Energy Research Office, Nuclear Engineering research Program, Contract Number DEFG079OERl3032, Rensselaer Polytechnic Institute, 1998
  9. C. Cohen-Bacrie, Y. Goussard, and R. Guardo, 'Regularized Reconstruction in Electrical Impedance Tomography Using a Variance Uniformization Constraint,' IEEE Transactions on Medical Imaging, Vol. 16, No.5, pp. 170-179, 1997 https://doi.org/10.1109/42.640745
  10. M. Vauhkonen, 'Electrical Impedance Tomography and Prior Information,' Doctoral Dissertation, Dept. Applied Physic, University Kuopio, 1997
  11. M. Vauhkonen, D. Vadasz, P. A Karjalainen, E. Somersalo, and J. P. Kaipio, 'Tikhonov Regularization and Prior Information in Electrical Impedance Tomography,' IEEE Transactions on Biomedical Engineering, Vol. 17, No.2, 1998 https://doi.org/10.1109/42.700740
  12. M. Vauhkonen, D. Vadasz, P. A. Karjalainen, and J. P. Kaipio, 'Subspace Regularization Method for Electrical Impedance Tomography,' 1st International Conference on Bioelectromagnetism, Tampere, Finland, pp. 9-13, 1996
  13. T. J. Yorkey, J. G. Webster, and W. J. Tompkins, 'Comparing Reconstruction Algorithms for Electrical Impedance Tomography,' IEEE Transactions on Biomedical Engineering, Vol.34, No.11, pp. 843-852, 1987 https://doi.org/10.1109/TBME.1987.326032
  14. M. Vauhkonen, P. A. Karjalainen, and J. P. Kaipio, 'A Kalman Filter Approach to Track Fast Impedance Changes in Electrical Impedance Tomography,' IEEE Transactions on Biomedical Engineering, Vol.45, No.4, pp. 486-493, 1998 https://doi.org/10.1109/10.664204