Level-Set Method Applied to Magnetic Induction Tomography Using Experimental Data

Magnetic induction tomography (MIT) can be used to probe electrical conductivity variation of an object. It offers a nondestructive and contactless means of imaging the internal conductivity distribution of the object. The forward problem in MIT is a general eddy current problem, which is required to estimate the measured data for a given conductivity distribution. The edge finite-element method with a formulation using a magnetic vector potential has been implemented to solve the forward problem. Conductivity reconstruction in MIT is a nonlinear and ill-posed inverse problem. The regularization techniques are required to incorporate a priori knowledge of the conductivity distribution for a stable solution of this inverse problem. This article presents a conductivity interface reconstruction technique, which has an inherent regularization property. Instead of calculating the conductivity distribution in the whole region of interest, the interface between two different conductivities is reconstructed. A narrowband level-set method has been implemented to describe the interfaces. An iterative optimization scheme has been used to modify the interface estimation in each iteration step, so that the predicated forward solution is closed to the measured data. The results are presented using experimental data representative of an application of MIT in molten metal flow visualization.

References
1. H. Griffiths. Measurement Science and Technology 12(8):1126–1131 (2001). 2. A. J. Peyton, Z. Z. Yu, G. Lyon, S. Al-Zeibak, J. Ferreira, J. Velez, F. Linhares, A. R. Borges, H. L. Xiong, N. H. Saunders, and M. S. Beck. Meas. Sci. Technol. 7:261–271 (1996). 3. M. Soleimani. Image and Shape Reconstruction Methods in Magentic Induction and Electrical Impedance Tomography, PhD thesis, University of Manchester (2005). 4. R. Binns, A. R. A. Lyons, A. J. Peyton, and W. D. N Pritchard. Meas. Sci. Technol. 12:1132–1138 (2001). 5. M. Soleimani, W. R. B. Lionheart, A. J. Peyton, and X. Ma. In Proc., 7th Biennial ASME Conference Engineering Systems Design and Analysis, ESDA 04 (2004). 6. H. Huang, T. Takagi, and H. Fukutomi. IEEE Trans. MAG. 36(4):1719–1723 (2000). 7. Y. Li, L. Udpa, and S. S Udpa. IEEE Trans. MAG. 40(2):410–417 (2004). 8. M. Soleimani and W. R. B. Lionheart. IEEE Trans. Mag. 41(4):1274–1279 (2005). 9. R. Merwa, K. Hollaus, P. Brunner, and H. Scharfetter. Physiol. Meas. 26(2):S241–S250 (2005). 10. N. Polydorides and W. R. B. Lionheart. Meas. Sci. Technol. 13:1871–1883 (2002). 11. S. Osher and J. Sethian. J. Comp. Phy. 56:12–49 (1988). 12. S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer, New York, (2003). 13. J. A. Sethian. Level Set Methods and Fast Marching Methods, 2nd ed. Cambridge University Press, Cambridge (1999). 14. O. Dorn, E. L. Miller, and C. M. Rappaport. Inverse Problems 16:1119–1156 (2000). LEVEL-SET METHOD APPLIED TO MAGNETIC INDUCTION TOMOGRAPHY 11 15. O. Dorn and D. Lesselier. Inverse Problems 22:R67–R131 (2006). 16. F. Santosa. ESAIM: Control, Optimization and Calculus of Variations 1:17–33 (1996). 17. A. Luminita Vese and T. F. Chan. International Journal of Computer Vision 50:271–293 (2002). 18. X.-C. Tai and T. F. Chan. Internat. J. Numerical Analysis Modeling 1(1):2547 (2004). 19. X. Ma, S. R. Higson, A. Lyons, and A. J. Peyton, In 4th World Congress on Industrial Process Tomography, Aizu, Japan (2005). 20. M. Soleimani, W. R. B. Lionheart, Cl. H. Riedel, and O. Dssel. In Proc. 3rd World Congress on Industrial Process Tomography, pp. 275–280 (2003). 21. A. Bossavit. Computational Electromagnetism. Academic Press, Boston, (1998). 22. O. Biro. Computer Methods in Applied Mechanics and Engineering 169:391–405 (1999). 23. W. R. B. Lionheart, M. Soleimani, and A. J. Peyton. In Proc. 3rd World Congress on Industrial Process Tomography, pp. 239–244 (2003). 24. M. Soleimani. Insight 48(1):39–44 (2006). 25. J. Qi-Nian. Math. Computation 69(232):1603–1623 (2000). 26. V. A. Morozov. Methods for Solving Incorrectly Posed Problems. Springer-Verlag, New York (1984).
Metrics
Usage Shares
Total Views
11 Page Views
Total Shares
0 Tweets
11
0 PDF Downloads
0
0 Facebook Shares
Total Usage
11