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Progress In Electromagnetics Research
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MICROWAVE TOMOGRAPHY EMPLOYING AN ADJOINT NETWORK BASED SENSITIVITY MATRIX

By D. G. Drogoudis, G. A. Kyriacou, and J. N. Sahalos

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Abstract:
A reconstruction algorithm for two- and three- dimen-sional microwave imaging is proposed. The present effort is focused on the reconstruction of conductivity (σ) and permittivity (εr) distri-butions aiming at a technique serving medical imaging, while perme-ability imaging can be easily incorporated to serve geophysical geophysical prospecting as well. This work constitutes the most recent one within the effort of extending our Modified Perturbation Method (MPM) from static to high and now microwave frequencies. MPM is an approximate method based on an exact Sensitivity or Jacobian matrix for an iterative update of an initial (σ, εr) guess until convergence. This method is proved almost immune of the problem inherent ill-posedness, but its robustness is actually gained by paying a penalty of compromised accuracy in the final achieved image. However, this image can be fine tuned by formulating and solving an exact inverse problem. Regarding the involved Jacobian matrix, this is evaluated through closed form expressions obtained through an Adjoint Network Theorem in conjuction with the electromagnetics reciprocity theorem. The field distributions required for its evaluation are readily available from the always required forward problem solutions on the assumed (σ, εr) distributions. Herein, the finite element method along with absorbing boundary conditions are employed for the forward problem electromagnetic simulation.

Citation:
D. G. Drogoudis, G. A. Kyriacou, and J. N. Sahalos, "Microwave tomography employing an adjoint network based sensitivity matrix," Progress In Electromagnetics Research, Vol. 94, 213-242, 2009.
doi:10.2528/PIER09060808
http://www.jpier.org/PIER/pier.php?paper=09060808

References:
1. Keller, G. V., "Electrical properties of rocks and minerals," Handbook of Physical Constemts,, 553-770, S. P. Calrk (ed.), N. Y. Geological Society of America, 1988.

2. Pethig, R., "Dielectric properties of biological materials: Biophysical and medical applications," IEEE Transactions on Electrical Insulation, Vol. 19, 453-474, 1984.
doi:10.1109/TEI.1984.298769

3. Gabriel, C., S. Gabriel, and E. Corthout, "The dielectric properties of biological tissues: Parts 1, 2 and 3," Phys. Med. Biol., Vol. 41, 2231-2249, 1996.
doi:10.1088/0031-9155/41/11/001

4. Fang, Q., P. M. Meaney, S. D. Geimer, A. V. Streltsov, and K. D. Paulsen, "Microwave image reconstruction from 3-D fields coupled to 2-D parameter estimation," IEEE Trans. Medica Imaging., Vol. 23, No. 4, 475-484, 2004.
doi:10.1109/TMI.2004.824152

5. Meaney, P. M., K. D. Paulsen, A. Hartov, and R. K. Crane, "Microwave imaging for tissue assessment: Initial evaluation in multitarget tissue-equivalent phantoms," IEEE Trans. Biomed. Eng., Vol. 43, 878-890, 1996.
doi:10.1109/10.532122

6. Meaney, P., K. Paulsen, and T. Ryan, "Two-dimensional hybrid element image reconstruction for TM illumination," IEEE Trans. Antennas and Propagation, Vol. 43, 239-247, 1995.
doi:10.1109/8.371992

7. Semenov, S., R. Svenson, A. Bulyshev, A. Souvorov, A. Nazarov, Y. Sizov, A. Pavlovsky, V. Borisov, B. Voinov, G. Simonova, A. Starostin, V. Posukh, G. Tatsis, and V. Baranov, "Three-dimensional microwave tomography: Experimental prototype of the system and vector born reconstruction method," IEEE Trans. Biomed. Eng., Vol. 46, 937-946, 1999.
doi:10.1109/10.775403

8. Rekanos, I. T., M. S. Efraimidou, and T. D. Tsiboukis, "Microwave imaging: Inversion of scattered near-field measurements," IEEE Trans. Magnetics, Vol. 37, 3294-3297, 2001.
doi:10.1109/20.952598

9. Joachimowicz, N., C. Pichot, and J. Hugonin, "Inverse scattering: An iterative numerical method for electromagnetic imaging," IEEE Trans. Antennas and Propagation, Vol. 39, 1742-1753, 1991.
doi:10.1109/8.121595

10. Meaney, P. M., K. D. Paulsen, B. W. Pogue, and M. I. Miga, "Microwave image reconstruction utilizing log-magnitude and unwrapped phase to improve high-contrast object recovery," IEEE Trans. Medical Imaging., Vol. 20, No. 2, 104-116, 2001.
doi:10.1109/42.913177

11. Kyriacou, G., C. Koukourlis, and J. Sahalos, "A reconstruction algorithm of electrical impedance tomography with optimal configuration of the driven electrodes ," IEEE Trans. Medical Imaging., Vol. 12, 430-438, 1993.
doi:10.1109/42.241870

12. Drogoudis, D. G., G. Trichopoulos, G. A. Kyriacou, and J. N. Sahalos, "A modified perturbation method for three-dimensional time harmonic impedance tomography," PIERS Online, Vol. 1, No. 2, 151-155, 2005.
doi:10.2529/PIERS041210144331

13. Drogoudis, D. G., G. A. Kyriacou, and J. N. Sahalos, "A sensitivity matrix based microwave tomography exploiting an adjoint network theorem," PIERS Online, Vol. 3, No. 8, 1217-1221, 2007.
doi:10.2529/PIERS070220140417

14. Drogoudis, D. G., G. A. Kyriacou, and J. N. Sahalos, "A three dimensional microwave tomography employing an adjoint network theorem based sensitivity matrix ," IEEE Trans. Magnetics, Vol. 45, No. 3, 1686-1689, 2009.
doi:10.1109/TMAG.2009.2012782

15. Jin, J., The Finite Element Method in Electromagnetics, John Wiley & Sons, New York, 1993.

16. Zhu, Y. and A. C. Cangellaris, Multigrid Finite Element Methods for Electromagnetic Field Modeling, John Wiley & Sons, 2006.

17. Oldenburg, D. W., "Practical strategies for the solution of large-scale electromagnetic inverse problems," Radio Science, Vol. 29, 1081-1099, 1994.
doi:10.1029/94RS00746

18. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, 1989.

19. Hansen, P. C., Rank-deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia, PA, 1997.

20. Semnani, A. and M. Kamyab, "Truncated cosine fourier series expansion methodfor solving 2-D inverse scattering problems," Progress In Electromagnetics Research, Vol. 81, 73-97, 2008.
doi:10.2528/PIER07122404

21. Semnani, A. and M. Kamyab, "An enhanced method for inverse scattering problems using Fourier series expansion in conjunction with FDTD and PSO," Progress In Electromagnetics Research, Vol. 76, 45-64, 2007.
doi:10.2528/PIER07061204

22. Shyu, J. J., C.-H. Chan, M.-W. Hsiung, P.-N. Yang, H.-W. Chen, and W.-C. Kuo, "Diagnosis of articular cartilage damage by polarization sensitive optical coherence tomography and the extracted optical properties," Progress In Electromagnetics Research, Vol. 91, 365-376, 2009.
doi:10.2528/PIER09022602

23. Soleimani, M., C. 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

24. Mauriello, P. and D. Patella, "Geoelectrical anomalies imaged by polar and dipolar probability tomography," Progress In Electromagnetics Research, Vol. 87, 63-88, 2008.
doi:10.2528/PIER08092201

25. Děková, J., "Identification of defects in materials with surface conductivity distribution," PIERS Online, Vol. 4, No. 1, 11-15, 2008.

26. Tarvainen, T., M. Vauhkonen, V. Kolehmainen, J. P. Kaipio, and S. R. Arridge, "Utilizing the radiative transfer equation in optical tomography," PIERS Online, Vol. 4, No. 6, 655-660, 2008.
doi:10.2529/PIERS071219142458

27. Mauriello, P. and D. Patella, "Resistivity tensor probability tomography," Progress In Electromagnetics Research B, Vol. 8, 129-146, 2008.
doi:10.2528/PIERB08051604

28. Zainud-Deen, S. H., W. M. Hassen, E. El deen Ali, and K. H. Awadalla, "Breast cancer detection using a hybrid finite difference frequency domain and particle swarm optimization techniques," Progress In Electromagnetics Research B, Vol. 3, 35-46, 2008.
doi:10.2528/PIERB07112703

29. Chen, X., D. Liang, and K. Huang, "Microwave imaging 3-D buried objects using parallel genetic algorithm combined with FDTD technique," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1761-1774, 2006.
doi:10.1163/156939306779292264

30. Bermani, E., A. Boni, A. Kerhet, and A. Massa, "Kernels evaluation of svm-based estimators for inverse scattering problems," Progress In Electromagnetics Research, Vol. 53, 167-188, 2005.
doi:10.2528/PIER04090801

31. Roger, A. and F. Chapel, "Iterative methods for inverse problems," Progress In Electromagnetics Research, Vol. 5, 423-454, 1991.

32. Fang, Q., "Computational methods for microwave medical imaging,", PhD Thesis, Dartmouth College Hanover, New Hampshire, 2004.


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