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.
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
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,
13. J. A. Sethian. Level Set Methods and Fast Marching Methods, 2nd ed. Cambridge University Press,
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).