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2016-01-11
Absolute Imaging of Low Conductivity Material Distributions Using Nonlinear Reconstruction Methods in Magnetic Induction Tomography
By
Progress In Electromagnetics Research, Vol. 155, 1-18, 2016
Abstract
Magnetic Induction Tomography (MIT) is a newly developing technique of electrical tomography that in principle is able to map the electrical conductivity distribution in the volume of objects. The image reconstruction problem in MIT is similar to electrical impedance tomography (EIT) in the sense that both seek to recover the conductivity map, but differ remarkably in the fact that data being inverted in MIT is derived from induction theory and related sources of noise are different. Progress in MIT image reconstruction is still limited, and so far mainly linear algorithms have been implemented. In difference imaging, step inversion was demonstrated for recovering perturbations within conductive media, but at the cost of producing qualitative images, whilst in absolute imaging, linear iterative algorithms have mostly been employed but mainly offering encouraging results for imaging isolated high conductive targets. In this paper, we investigate the possibility of absolute imaging in 3D MIT within a target for low conductivity application (σ < 5 Sm-1). For this class of problems, the MIT image reconstruction exhibits non-linearity and ill-posedness that cannot be treated with linear algorithms. We propose to implement for the first time in MIT two effective inversion methods known in non-linear optimization as Levenberg Marquardt (LMM) and Powell's Dog Leg (PDLM) methods. These methods employ damping and trust region techniques for controlling convergence and improving minimization of the objective function. An adaptive version of Gauss Newton is also presented (AGNM), which implements a damping mechanism to the regularization parameter. Here, the level of penalty is varied during the iterative process. As a comparison between the methods, different criteria are examined from image reconstructions using the LMM, PDLM and AGNM. For test examples, volumetric image reconstruction of a perturbation within homogeneous cylindrical background is considered. For inversion, an independent finite element FEM software package Maxwell by Ansys is employed to generate simulated data using a model of a 16 channel MIT system. Numerical results are employed to show different performance characteristics between the methods based on convergence, stability and sensitivity to the choice of the regularization parameter. To demonstrate the effect of scalability of absolute imaging in MIT for more realistic problems, a human head model with an internal anomaly is used to produce reconstructions for different finer resolutions. AGNM is adopted here and employs the Krylov subspace method to replace the computationally demanding direct inversion of the regularized Hessian.
Citation
Bachir Dekdouk, Christos Ktistis, David W. Armitage, and Anthony J. Peyton, "Absolute Imaging of Low Conductivity Material Distributions Using Nonlinear Reconstruction Methods in Magnetic Induction Tomography," Progress In Electromagnetics Research, Vol. 155, 1-18, 2016.
doi:10.2528/PIER15071705
References

1. Griffiths, H., "Magnetic induction tomography," Measurement Science & Technology, Vol. 12, 1126-1131, 2001.
doi:10.1088/0957-0233/12/8/319

2. Peyton, A. J., Z. Z. Yu, G. Lyon, S. AlZeibak, J. Ferreira, J. Velez, F. Linhares, A. R. Borges, H. L. Xiong, N. H. Saunders, and M. S. Beck, "An overview of electromagnetic inductance tomography: Description of three different systems," Measurement Science & Technology, Vol. 7, 261-271, 1996.
doi:10.1088/0957-0233/7/3/006

3. Ke, L., X. Lin, and Q. Du, "An improved back-projection algorithm for magnetic induction tomography image reconstruction," Advanced Materials Research, Vol. 647, 630-635, 2013.
doi:10.4028/www.scientific.net/AMR.647.630

4. Korjenevsky, A., V. Cherepenin, and S. Sapetsky, "Magnetic induction tomography: Experimental realization," Physiological Measurement, Vol. 21, 89-94, 2000.
doi:10.1088/0967-3334/21/1/311

5. Merwa, R., K. Hollaus, P. Brunner, and H. Scharfetter, "Solution of the inverse problem of magnetic induction tomography (MIT)," Physiological Measurement, Vol. 26, S241-S250, 2005.
doi:10.1088/0967-3334/26/2/023

6. Scharfetter, H., K. Hollaus, J. Rosell-Ferrer, and R. Merwa, "Single-step 3-D image reconstruction in magnetic induction tomography: Theoretical limits of spatial resolution and contrast to noise ratio," Annals of Biomedical Engineering, Vol. 34, 1786-1798, 2006.
doi:10.1007/s10439-006-9177-6

7. Scharfetter, H., P. Brunner, and R. Merwa, "Magnetic induction tomography: Single-step solution of the 3-D inverse problem for differential image reconstruction," International Journal of Information and Systems Sciences, Vol. 2, 585-606, 2006.

8. Vauhkonen, M., M. Hamsch, and C. H. Igney, "A measurement system and image reconstruction in magnetic induction tomography," Physiological Measurement, Vol. 29, S445-S454, 2008.
doi:10.1088/0967-3334/29/6/S37

9. Ma, X., A. J. Peyton, S. R. Higson, A. Lyons, and S. J. Dickinson, "Hardware and software design for an electromagnetic induction tomography (EMT) system for high contrast metal process applications," Measurement Science & Technology, Vol. 17, 111-118, 2006.
doi:10.1088/0957-0233/17/1/018

10. Wei, H.-Y. and M. Soleimani, "Four dimensional reconstruction using magnetic induction tomography: Experimental study," Progress In Electromagnetics Research, Vol. 129, 17-32, 2012.
doi:10.2528/PIER12032403

11. Wei, H.-Y. and M. Soleimani, "Volumetric magnetic induction tomography," Measurement Science and Technology, Vol. 23, No. 4, 055401, 2012.
doi:10.1088/0957-0233/23/5/055401

12. Wei, H.-Y. and M. Soleimani, "Three-dimensional magnetic induction tomography imaging using a matrix free Krylov subspace inversion algorithm," Progress In Electromagnetics Research, Vol. 122, 29-45, 2012.
doi:10.2528/PIER11091513

13. Watson, S., R. J.Williams, W. Gough, and H. Griffiths, "A magnetic induction tomography system for samples with conductivities below 10 Sm-1," Measurement Science & Technology, Vol. 19, No. 4, 11, 2008.
doi:10.1088/0957-0233/19/4/045501

14. Soleimani, M. and W. R. B. Lionheart, "Absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method," IEEE Transactions on Medical Imaging, Vol. 25, 1521-1530, 2006.
doi:10.1109/TMI.2006.884196

15. Soleimani, M., W. R. B. Lionheart, A. J. Peyton, X. D. Ma, and S. R. Higson, "A three-dimensional inverse finite-element method applied to experimental eddy-current imaging data," IEEE Transactions on Magnetics, Vol. 42, 1560-1567, 2006.
doi:10.1109/TMAG.2006.871255

16. Hansen, P. C. and D. P. O'Leary, "The use of the L-curve in the regularization of discrete ill-posed systems," SIAM J. Sci. Comput, Vol. 14, No. 5, 1487-1503, 1993.
doi:10.1137/0914086

17. Goharian, M., M. Soleimani, and G. R. Moran, "A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data," Progress In Electromagnetics Research, Vol. 94, 19-32, 2009.
doi:10.2528/PIER09052003

18. Goharian, M., A. Jegatheesan, and G. R. Moran, "Dogleg trust-region application in electrical impedance tomography," Physiological Measurement, Vol. 28, 555-572, 2007.
doi:10.1088/0967-3334/28/5/009

19. Tan, C., G. Xu, Y. Li, Y. Xuand, and G. Su, "Boundary image reconstruction based on the nonmonotonic and self-adaptive trust region method for electrical impedance tomography," Physiological Measurement, Vol. 34, 951-962, 2013.
doi:10.1088/0967-3334/34/8/951

20. Tan, C., Y. Xuand, and F. Dong, "Determining the boundary of inclusions with known conductivities using a Levenberg-Marquardt algorithm by electrical resistance tomography," Measurement Science & Technology, Vol. 22, 104005, 2011.
doi:10.1088/0957-0233/22/10/104005

21. Kleefeld, A. and M. Reißel, "The Levenberg-Marquardt method applied to a parameter estimation problem arising from electrical resistivity tomography," Applied Mathematics and Computation, Vol. 217, 4490-4501, 2011.
doi:10.1016/j.amc.2010.10.052

22. Ren, S., F. Dong, Y. Xuand, and C. Tan, "Reconstruction of the three-dimensional inclusion shapes using electrical capacitance tomography," Measurement Science & Technology, Vol. 25, 025403-025419, 2014.
doi:10.1088/0957-0233/25/2/025403

23. Nielsen, H. B., "Damping parameter in Marquardt's method,", Report IMM-REP-1999-05, Department of Mathematical Modelling, 31 pages, DTU, 1999.

24. Nocedal, J. and S. J. Wright, Numerical Optimization, Springer, ISBN 978-0-387-40065-5, 1999.
doi:10.1007/b98874

25. Frandsen, P. E., K. Jonasson, H. B. Nielsen, and O. Tingleff, Unconstrained Optimization, 3rd Ed., IMM, DTU, 2004.

26. Gazzola, S. and J. Nagy, "Generalized Arnoldi-Tikhonov method for sparse reconstruction," SIAM J. Sci. Comput., Vol. 36, No. 2, B225-B247, 2014.
doi:10.1137/130917673

27. Biro, O. and K. Preis, "On the use of the magnetic vector potential in the Finite Element Analysis of 3 dimensional eddy currents," IEEE Transactions on Magnetics, Vol. 25, 3145-3159, 1989.
doi:10.1109/20.34388

28. Hollaus, K., C. Magele, R. Merwa, and H. Scharfetter, "Numerical simulation of the eddy current problem in magnetic induction tomography for biomedical applications by edge elements," IEEE Transactions on Magnetics, Vol. 40, 623-626, 2004.
doi:10.1109/TMAG.2004.825424

29. Morris, A., H. Griffiths, and W. Gough, "A numerical model for magnetic induction tomographic measurements in biological tissues," Physiological Measurement, Vol. 22, 113-119, 2001.
doi:10.1088/0967-3334/22/1/315

30. Pham, M. H. and A. J. Peyton, "A model for the forward problem in magnetic induction tomography using boundary integral equations," IEEE Transactions on Magnetics, Vol. 44, 2262-2267, 2008.
doi:10.1109/TMAG.2008.2003142

31. Dekdouk, B., W. Yin, C. Ktistis, D.W. Armitage, and A. J. Peyton, "A method to solve the forward problem in magnetic induction tomography based on the weakly coupled field approximation," IEEE Trans. Biomed. Eng., Vol. 57, No. 4, 914-921, 2009.
doi:10.1109/TBME.2009.2036733

32. Dyck, D. N., D. A. Lowther, and E. M. Freeman, "A method of computing the sensitivity of electromagnetic quantities to changes in materials and sources," IEEE Transactions on Magnetics, Vol. 30, 3415-3418, 1994.
doi:10.1109/20.312672

33. Gabriel, S., R. W. Lau, and C. Gabriel, "The dielectric properties of biological tissues. 2 Measurements in the frequency range 10 Hz to 20 GHz," Physics in Medicine and Biology, Vol. 41, 2251-2269, 1996.
doi:10.1088/0031-9155/41/11/002

34. Madsen, K., H. B. Nielsen, and O. Tingleff, Methods for Non-linear Least Sqaures Problems, 2nd Ed., 2004.

35. Horesh, L., "Some novel approaches in modelling and image reconstruction for multi-frequency electrical impedance tomography of the human brain,", PhD Thesis, 137-173, UCL, 2006.

36. Polydorides, N., W. R. B. Lionheart, and H. McCann, "Krylov subspace iterative techniques: On the detection of brain activity with electrical impedance tomography," IEEE Transactions on Medical Imaging, Vol. 21, 596-603, 2002.
doi:10.1109/TMI.2002.800607