volume | PIER Journals

Abstract

Magnetic induction tomography (MIT) attempts to image the passive electromagnetic properties (PEP) of an object by measuring the mutual inductances between pairs of coils placed around its periphery. In recent years, there has been an increase in applications of non-contact magnetic induction tomography. When finite element-based reconstruction methods are used, that rely on the inversion of a derivative operator, the large size of the Jacobian matrix poses a challenge since the explicit formulation and storage of the Jacobian matrix could be in general not feasible. This problem is aggravated further in applications for example when the number of coils is increased and in three-dimension. Krylov subspace methods such as conjugate gradient (CG) methods are suitable for such large scale inverse problems. However, these methods require use of the Jacobian matrix, which can be large scale. This paper presents a matrix-free reconstruction method, that addresses the problems of large scale inversion and reduces the computational cost and memory requirements for the reconstruction. The idea behind the matrix-free method is that information about the Jacobian matrix could be available through matrix times vector products so that the creation and storage of big matrices can be avoided. Furthermore the matrix vector multiplications were performed in multiple core fashion so that the computational time can decrease even further. The method was tested for the simulated and experimental data from lab experiments, and substantial benefits in computational times and memory requirements have been observed.

1. Griffiths, H., "Magnetic induction tomography," Institute of Physics Publishing Meas. Sci. Technol., Vol. 12, 1126-1131, Dec. 2001.
doi:10.1088/0957-0233/12/8/319

2. Ma, X., A. J. Peyton, S. R. Higson, A. Lyons, and S. J. Dickinson, "Hardware and software design for an electromagnetic induction tomography system applied to high contrast metal process applications," Meas. Science and Technology, Vol. 17, No. 1, 111-118, 2006.
doi:10.1088/0957-0233/17/1/018

3. Korjenevsky, A., V. Cherepenin, and S. Sapetsky, "Magnetic induction tomography: Experimental realization," Physiol. Meas., Vol. 21, No. 1, 89-94, 2000.
doi:10.1088/0967-3334/21/1/311

4. Hanson, P. C., Rank-deficient and Discrete Ill-posed Problems, SIAM, 1998.

5. Peyton, A. J., Z. Z. Yu, and G. M. Lyon, "An overview of electromagnetic inductance tomography: Description of three different systems," Measurement Science & Technology, Vol. 7, No. 3, 261-271, Mar. 1996.
doi:10.1088/0957-0233/7/3/006

6. Watson, S., R. J. Williams, W. A. Gough, and H. Griffiths, "A magnetic induction tomography system for samples with conductivities less than 10 s m^-1," Meas. Sci. Technol., Vol. 19, 045501-11, 2008.

7. Soleimani, M., "Simultaneous reconstruction of permeability and conductivity in magnetic induction tomography," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 5/6, 785-798, 2009.
doi:10.1163/156939309788019822

8. Soleimani, M., N. Mitchell, R. Banasiak, R. Wajman, and A. Adler, "Four-dimensional electrical capacitance tomography imaging using experimental data," Progress In Electromagnetics Research, Vol. 90, 171-186, 2009.
doi:10.2528/PIER09010202

9. Banasiak, R., R. Wajman, D. Sankowski, and M. Soleimani, "Three-dimensional nonlinear inversion of electrical capacitance tomography data using a complete sensor model," Progress In Electromagnetics Research, Vol. 100, 219-234, 2010.
doi:10.2528/PIER09111201

10. 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

11. Catapano, I., F. Soldovieri, and L. Crocco, "On the feasibility of the linear sampling method for 3D GPR surveys," Progress In Electromagnetics Research, Vol. 118, 185-203, 2011.
doi:10.2528/PIER11042704

12. Flores-Tapia, D., M. O'Halloran, and S. Pistorius, "A bimodal reconstruction method for breast cancer imaging," Progress In Electromagnetics Research, Vol. 118, 461-486, 2011.
doi:10.2528/PIER11050408

13. Asimakis, N. P., I. S. Karanasiou, and N. K. Uzunoglu, "Non-invasive microwave radiometric system for intracranial applications: A study using the conformal L-notch microstrip patch antenna," Progress In Electromagnetics Research, Vol. 117, 83-101, 2011.

14. Litman, A., J. M. Geffrin, and H. Tortel, "On the calibration of a multistatic scattering matrix measured by a fixed circular array of antennas," Progress In Electromagnetics Research, Vol. 110, 1-21, 2010.
doi:10.2528/PIER10090302

15. Parise, M., "Fast computation of the forward solution in controlled- source electromagnetic sounding problems," Progress In Electromagnetics Research, Vol. 111, 119-139, 2011.
doi:10.2528/PIER10101409

16. Biro, O., "Edge element formulations of eddy current problems," Comput. Methods Appl. Mech. Engrg., Vol. 169, 391-405, 1999.
doi:10.1016/S0045-7825(98)00165-0

17. Soleimani, M., "Sensitivity maps in three-dimensional magnetic induction tomography," Insight, Vol. 48, No. 1, 39-44, Jan. 2006.
doi:10.1784/insi.2006.48.1.39

18. Soleimani, M. and W. R. B. Lionheart, "Image reconstruction in three-dimensional magnetostatic permeability tomography," IEEE Transactions on Magnetics, Vol. 41, No. 4, 1274-1279, 2005.
doi:10.1109/TMAG.2005.845158

19. Zacharopoulos, A. D., P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Adndersson-Engels, "A matrix-free algorithm for multiple wavelength fluorescene tomography," Optics Express, Vol. 17, No. 5, 3025-3035, 2009.
doi:10.1364/OE.17.003042

20. Li, M., A. bubakar, J. Liu, G. Pan, and T. M. Habashy, "A compressed implicit jacobian scheme for 3D electromagnetic data inversion," Geophysics, Vol. 76, No. 3, F173-F183, 2011.
doi:10.1190/1.3569482

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

Dr. Hsin-Yu Wei

Prof. Manuchehr Soleimani