A new computationally efficient algorithm for reconstruction of lossy and inhomogeneous 1-D media by using inverse scattering method in time domain is proposed. In this algorithm, cosine Fourier series expansion is utilized in conjunction with finite difference time domain (FDTD) and particle swarm optimization (PSO) methods. The performance of the proposed algorithm is studied for several 1-D permittivity and conductivity profile reconstruction cases. Various types of regularization terms are examined and compared with each other in the presented method. It is shown that the number of unknowns in optimization routine is reduced to about 1/3 as compared with conventional methods which leads to a considerable reduction in the amount of computations, while the precision of the solutions would not be affected significantly. Another advantage of the proposed expansion method is that, since only a limited number of terms are taken in the expansion, the divergence of the algorithm is far less likely to occur. Sensitivity analysis of the suggested method to the number of expansion terms in the algorithm is studied, as well.
"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
1. Bindu, G., A. Lonappan, V. Thomas, C. K. Aanandan, and K. T. Mathew, "Active microwave imaging for breast cancer detection," Progress In Electromagnetics Research, Vol. 58, 149-169, 2006. doi:10.2528/PIER05081802
2. Colton, D. and P. B. Monk, "Target identification of coated objects," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 4, 1232-1242, 2006. doi:10.1109/TAP.2006.872564
3. Semenov, S. Y., V. G. Posukh, A. E. Bulyshev, Y. E. Sizov, and P. N. Repin, "Microwave tomographic imaging of the heart in intact swine," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 874-890, 2006. doi:10.1163/156939306776149897
4. Rosenthal, A. and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber bragg gratings," IEEE Journal of Quantum Electronics, Vol. 39, No. 8, 1018-1026, 2003. doi:10.1109/JQE.2003.814365
5. Chen, X. and K. Huang, "Microwave imaging of buried inhomogeneous objects using parallel genetic algorithm combined with FDTD method," Progress In Electromagnetics Research, Vol. 53, 283-298, 2005. doi:10.2528/PIER04102902
6. Popovic, M. and A. Taflove, "Two-dimensional FDTD inversescattering scheme for determination of near-surface material properties at microwave frequencies," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 2, 2366-2373, 2004. doi:10.1109/TAP.2004.832515
7. Huang, C. H., Y. F. Chen, and C. C. Chiu, "Permittivity distribution reconstruction of dielectric objects by a cascaded method," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 2, 145-159, 2007. doi:10.1163/156939307779378790
8. Colton, D. and L. Paivarinta, "The uniqueness of a solution to an inverse scattering problem for electromagnetic waves," Arc. Ration. Mech. Anal., Vol. 119, 59-70, 1992. doi:10.1007/BF00376010
9. Isakov, V., "Uniqueness and stability in multidimensional inverse problems," Inverse Problems, Vol. 9, 579-621, 1993. doi:10.1088/0266-5611/9/6/001
10. Sheen, D. and D. Shepelsky, "Uniqueness in the simultaneous reconstruction of multiparameters of a transmission line," Progress In Electromagnetics Research, Vol. 21, 153-172, 1999. doi:10.2528/PIER98072001
11. Abubakar, A., P. M. Van Den Berg, T. M. Habashy, and H. Braunisch, "A multiplicative regularization approach for deblurring problems," IEEE Transactions on Image Processing, Vol. 13, No. 11, 1524-1532, 2004. doi:10.1109/TIP.2004.836172
12. Chung, Y. S., C. Cheon, and S. Y. Hahn, "Reconstruction of dielectric cylinders using FDTD and topology optimization technique," IEEE Transactions on Magnetics, Vol. 36, No. 4, 956-959, 2000. doi:10.1109/20.877600
13. Rekanos, I. T. and A. Raisanen, "Microwave imaging in the time domain of buried multiple scatterers by using an FDTDbased optimization technique," IEEE Transactions on Magnetics, Vol. 39, No. 3, 1381-1384, 2003. doi:10.1109/TMAG.2003.810526
14. Abubakar, A., T. M. Habashy, and P. M. Van Den Berg, "Nonlinear inversion of multi-frequency microwave Fresnel data using the multiplicative regularized contrast source inversion," Progress In Electromagnetics Research, Vol. 62, 193-201, 2006. doi:10.2528/PIER06042205
15. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd edition, Artech House, 2005.
16. Tikhonov, A. N. and V. Arsenine, Solutions of Ill-Posed Problem, Winston, New York, 1977.
17. Hansen, P. C., Rank Deficient and discrete Ill-posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia, 1998.
18. Abubakar, A. and P. M. Van Den Berg, "Total variation as a multiplicative constraint for solving inverse problems," IEEE Transactions on Image Processing, Vol. 10, No. 9, 1384-1392, 2001. doi:10.1109/83.941862
19. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 2, 397-407, 2004. doi:10.1109/TAP.2004.823969
20. Lee, K. C. and J. Y. Jhang, "Application of particle swarm algorithm to the optimization of unequally spaced antenna arrays," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2001-2012, 2006. doi:10.1163/156939306779322747
21. Chen, T. B., Y. L. Dong, Y. C. Jiao, and F. S. Zhang, "Synthesis of circular antenna array using crossed particle swarm optimization algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1785-1795, 2006. doi:10.1163/156939306779292273
22. Meyer, T., A. Jostingmeier, and A. S. Omar, "Microwave imaging using a novel regularization scheme," Proceedings of the Antennas and Propagation Society International Symposium, Vol. 3, 175-178, 2003.