volume | PIER Journals

Abstract

Truncated cosine Fourier series expansion method is applied for reconstruction of lossy and inhomogeneous 2-D media by using inverse scattering method in time domain. In this method, the unknown parameters are expanded in a cosine Fourier series and coefficients of this expansion are optimized in particle swarm optimization (PSO) routine with the aid of finite difference time domain (FDTD) method as an electromagnetic (EM) solver. The performance of the algorithm is studied for several 2-D permittivity and conductivity profile reconstruction cases. It is shown that since only a limited number of terms are retained in the expansion, using the proposed method guarantees the well-posedness of the problem and uniqueness of the solution and various types of regularization may be used to only have more precise reconstruction. It is also shown that the number of unknowns in optimization routine is reduced more than 75 percent as compared with conventional methods which leads to a considerable reduction in the amount of computations with negligible adverse effect on the precision of reconstruction. Sensitivity analysis of the suggested method to the number of expansion terms in the algorithm is studied, as well.

1. Bindu, G., A. Lonappan, V. Thomas, C. K. Aanandan, and K. T. Mathew, "Activ e 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, "Micro wave tomographic imaging of the heart in intact swine," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 873-890, 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, "P ermittivity 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. Tikhonov, A. N. and V. Arsenine, Solutions of Ill-posed Problem, Winston, New York, 1977.

12. Hansen, P . C., Rank Deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia, 1998.

13. 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

14. 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

15. 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

16. 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

17. 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

18. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd edition, Artec h House, 2005.

19. 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

20. Meyer, T.A. Jostingmeier, and A. S. Omar, "Micr owave imaging using a novel regularization scheme," Proceedings of the Antennas and Propagation Society International Symposium, Vol. 3, 175-178, 2003.

21. Khalaj-Amirhosseini, M., "Reconstruction of inhomogeneous dielectrics at microwave frequencies," Progress In Electromagnetics Research, Vol. 77, 75-84, 2007.
doi:10.2528/PIER07080202

22. 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

23. 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

24. Chen, T. B., Y. L. Dong, Y. C. Jiao, and F. S. Zhang, "Syn thesis 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

Dr. Abbas Semnani

Dr. Manouchehr Kamyab