State space models in process tomography - Approximation of state noise covariance

Inverse Problems in Engineering

Volumn 9, Issue 5, 2001, Pages 561-585

  Seppanen A ^a   Vauhkonen, M ^a   Somersalo, E ^b   Kaipio, J P ^a  

^a UNIVERSITY OF EASTERN FINLAND   (Finland)

^b AALTO UNIVERSITY   (Finland)

Author keywords

Electrical impedance tomography (EIT); Process tomography; State estimation

Indexed keywords

EID: 0038697819     PISSN: 10682767     EISSN: None     Source Type: Journal    
DOI: 10.1080/174159701088027781     Document Type: Article

References (27)

1. Anderson, B. D. O. and Moore, J. B., Optimal Filtering. Prentice Hall, 1979.
2. Arridge, S. R. (1999). Optical tomography in medical imaging. Inv. Probl., 15, R41-R93.
3. Barber, D. C. and Brown, B. H. (1984). Applied potential tomography. J. Phys. E: Sci. Instrum., 17, 723-733.
4. Baroudi, D., Kaipio, J. P. and Somersalo, E. (1998). Dynamical electric wire tomography: Time series approach. Inv. Probl., 14, 799-813.
5. Cheng, K.-S., Isaacson, D., Newell, J. C. and Gisser, D. G. (1989). Electrode models for electric current computed tomography. IEEE Trans. Biomed. Eng., 36, 918-924.
6. Chorin, A. J. and Marsden, J. E., A Mathematical Introduction to Fluid Mechanics. Springer-Verlag, 1993.
7. George, D. L., Torczynski, J. R., Shollenberger, K. A., O'Hern, T. J. and Ceccio, S. L. (2000). Validation of electrical-impedance tomography for measurement of material distribution in two-phase flows. Int. J. Multiphase Flow, 26, 549-581.
8. Heikkinen, L. M., Vauhkonen, M., Savolainen, T., Leinonen, K. and Kaipio, J. P. (2000). Electrical process tomography with known internal structures and resistivities. Inv. Prob. Eng., In press.
9. Järvenpää, S., A finite element model for the inverse conductivity problem. Phil. Lic. thesis, University of Helsinki, Finland, 1996.
10. Kaipio, J. P., Kolehmainen, V., Somersalo, E. and Vauhkonen, M. (2000). Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography. Inv. Probl., 16, 1487-1522.
11. Kaipio, J. P., Karjalainen, P. A., Somersalo, E. and Vauhkonen, M. (1999). State estimation in time-varying electrical impedance tomography. Ann. New York Acad. Sci., 873, 430-439.
12. Kaipio, J. P., Kolehmainen, V., Vauhkonen, M. and Somersalo, E. (1998). Construction of nonstandard smoothness priors. Department of Applied Physics Report series, 5/98.
13. Kaipio, J. P., Kolehmainen, V., Vauhkonen, M. and Somersalo, E., Inverse problems with structural prior information. Inv. Probl., 15, 713-729.
14. Karjalainen, P. A., Vauhkonen, M. and Kaipio, J. P., Dynamic reconstruction in SPET. In: Proc. 19th Int. Conf. IEEE Eng. Med. Biol. Society, pages 777-780, Chicago, October 30-November 2, 1997.
15. Kloeden, P. E. and Platen, E. (1999). Numerical Solution of Stochastic Differential Equations. Springer-Verlag, 1999.
16. Melsa, J. L. and Cohn, D. L., Decision and Estimation Theory. McGraw-Hill, 1978.
17. Øksendal, B. (1998). Stochastic Differential Equations. Springer-Verlag.
18. Seppänen, A., Vauhkonen, M., Vauhkonen, P. J., Somersalo, E. and Kaipio, J. P., State estimation with fluid dynamical evolution models in process tomography -EIT application. Technical Report 6/2000, University of Kuopio, Department of Applied Physics, 2000. http://venda.uku.fi/research/IP/publications/deptrep/ fluiddyneit.pdf.
19. Seppänen, A., Vauhkonen, M., Vauhkonen, P. J., Somersalo, E. and Kaipio, J. P., State estimation with fluid dynamical evolution models in process tomography -an application with impedance tomography. Inv. Probl., 17, 467-484.
20. Somersalo, E., Cheney, M. and Isaacson, D. (1992). Existence and uniqueness for electrode models for electric current computed tomography. SIAM J. Appl. Math., 52, 1023-1040.
21. Stoer, J. and Bulirsch, R. (1980). Introduction to Numerical Analysis. Springer-Verlag.
22. Vauhkonen, M., Electrical Impedance Tomography and Prior Information. Ph. D. thesis, University of Kuopio, Kuopio, Finland, 1997.
23. Vauhkonen, M., Karjalainen, P. A. and Kaipio, J. P. (1998). A Kalman filter approach to track fast impedance changes in electrical impedance tomography. IEEE Trans. Biomed. Eng., 45, 486-493.
24. Vauhkonen, P. J., Vauhkonen, M. and Kaipio, J. P., Fixed-lag smoothing and state estimation in dynamic electrical impedance tomography. Int. J. Numer. Methods Eng., 50, 2195-2209.
25. Vauhkonen, P. J., Vauhkonen, M., Mäkinen, T., Karjalainen, P. A. and Kaipio, J. P. (2000). Dynamic electrical impedance tomography-phantom studies. Inv. Prob. Eng., 8, 495-510.
26. Vauhkonen, P. J., Vauhkonen, M., Savolainen, T. and Kaipio, J. P., Three-dimensional electrical impedance tomography based on the complete electrode model. IEEE Trans. Biomed. Eng., 46, 1150-1160.
27. Williams, R. A. and Beck, M. S. Editors Process Tomography, Principles, Techniques and Applications, Butterworth-Heinemann Ltd, Oxford, 1995.