| PIER | |
| Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |
Home > Vol. 94 > pp. 213-242
MICROWAVE TOMOGRAPHY EMPLOYING AN ADJOINT NETWORK BASED SENSITIVITY MATRIXBy D. G. Drogoudis, G. A. Kyriacou, and J. N. SahalosAbstract: 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:
References:
2. Pethig, R., "Dielectric properties of biological materials: Biophysical and medical applications," IEEE Transactions on Electrical Insulation, Vol. 19, 453-474, 1984. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 24. Mauriello, P. and D. Patella, "Geoelectrical anomalies imaged by polar and dipolar probability tomography," Progress In Electromagnetics Research, Vol. 87, 63-88, 2008. 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. 27. Mauriello, P. and D. Patella, "Resistivity tensor probability tomography," Progress In Electromagnetics Research B, Vol. 8, 129-146, 2008. 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. 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. 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. 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.
|