This paper presents a computational approach to the two-dimensional time domain inverse scattering problem of a dielectric cylinder based on the finite difference time domain (FDTD) method and the particle swarm optimization (PSO) to determine the shape, location and permittivity of a dielectric cylinder. A pulse is incident upon a homogeneous dielectric cylinder with unknown shape and dielectric constant in free space andthe scattered fieldis recorded outside. By using the scattered field, the shape and permittivity of the dielectric cylinder are reconstructed. The subgridding technique is implemented in the FDTD code for modeling the shape of the cylinder more closely. In order to describe an unknown cylinder with arbitrary shape more effectively, the shape function is expandedb y closedcubicspline function insteadof frequently used trigonometric series. The inverse problem is resolved by an optimization approach, and the global searching scheme PSO is then employedto search the parameter space. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In addition, the effects of Gaussian noise on the reconstruction results are investigated. Numerical results show that even the measured scattered E fields are contaminated with some Gaussian noise, PSO can still yield good reconstructed quality.
2. Ma, J., W. C. Chew, C. C. Lu, and J. Song, "Image reconstruction from TE scattering data using equation of strong permittivity fluctuation ," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 6, 860-867, 2000.
doi:10.1109/8.865217
3. Otto, G. P. and W. C. Chew, "Microwave inverse scattering-local shape function imaging for improvedresolution of strong scatterers ," IEEE Transactions on Microwave Theory and Techniques , Vol. 42, No. 1, 137-142, 1994.
doi:10.1109/22.265541
4. Chiu, C. C. and Y. W. Kiang, "Microwave imaging of multiple conducting cylinders," IEEE Transactions on Antennas and Propagation, Vol. 40, No. 8, 933-941, 1992.
doi:10.1109/8.163431
5. Chien, W. and C. C. Chiu, "Using NU-SSGA to reduce the searching time in inverse problem of a buriedmetallic object," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 10, 3128-3134, 2005.
doi:10.1109/TAP.2005.856362
6. Qing, A., "An experimental study on electromagnetic inverse scattering of a perfectly conducting cylinder by using the real-coded genetic algorithm ," Microwave and Optical Technology Letters, Vol. 30, 315-320, 2001.
doi:10.1002/mop.1301
7. Caorsi, S., A. Massa, and M. Pastorino, "A computational technique basedon a real-codedgenetic algorithm for microwave imaging purposes ," IEEE Transactions on Geoscience and Remote Sensing , Vol. 38, No. 4, 1697-1708, 2000.
doi:10.1109/36.851968
8. Takenaka, T., Z. Q. Meng, T. Tanaka, and W. C. Chew, "Local shape function combinedwith genetic algorithm appliedto inverse scattering for strips ," Microwave and Optical Technology Letters, Vol. 16, 337-341, 1997.
doi:10.1002/(SICI)1098-2760(19971220)16:6<337::AID-MOP5>3.0.CO;2-L
9. Wei, C., "Inverse scattering of an un-uniform conductivity scatterer buriedin a three-layer structure ," Progress In Electromagnetics Research, Vol. 82, 1-18, 2008.
10. Huang, C.-H., Y.-F. Chen, and C.-C. Chiu, "Permittivity distribution reconstruction of dielectric objects by a cascaded method," Journal of Electromagnetic Waves & Applications, Vol. 21, No. 2, 145-159, 2007.
doi:10.1163/156939307779378790
11. Thomas, V., C. Gopakumar, J. Yohannan, A. Lonappan, G. Bindu, A. V. P. Kumar, V. Hamsakutty, and K. T. Mathew, "A novel technique for localizing the scatterer in inverse profiling of two dimensional circularly symmetric dielectric scatterers using degree of symmetry and neural networks," Journal of Electromagnetic Waves & Applications, Vol. 19, No. 15, 2113-2121, 2005.
doi:10.1163/156939305775570477
12. Yagle, A. E. and J. L. Frolik, "On the feasibility of impulse reflection response data for the two-dimensional inverse scattering problem," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 12, 1551-1564, 1996.
doi:10.1109/8.546241
13. Yu, W., Z. Peng, and L. Jen, "The time-domain born iterative method for two-dimensional inhomogeneous lossy dielectric," Journal of Microwaves, Vol. 11, No. 12, 1995.
14. Chaturvedi, P. and R. G. Plumb, "Electromagnetic imaging of undergroundtargets using constrainedoptimization," IEEE Transactions on Geoscience and Remote Sensing, Vol. 33, No. 3, 551-561, 1995.
doi:10.1109/36.387572
15. Moghaddam, M. and W. C. Chew, "Study of some practical issues in inversion with the Born iterative methodusing time-domain data ," IEEE Transactions on Antennas and Propagation, Vol. 41, No. 2, 177-184, 1993.
doi:10.1109/8.214608
16. Weedon, W. H., Broadband microwave inverse scattering: Theory andexp eriment, Ph.D. dissertation, University of Illinois at Urbana-Champaign, 1994.
17. Weedon, W. H. and W. C. Chew, "Time-domain inverse scattering using the local shape function (LSF) method," Inverse Problem, Vol. 9, 551-564, 1993.
doi:10.1088/0266-5611/9/5/005
18. Rekanos, I. T., "Time-domain inverse scattering using lagrange multipliers: An iterative FDTD-basedoptimization technique," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 2, 271-289, 2003.
doi:10.1163/156939303322235824
19. Kang, N. W., Y. S. Chung, C. Cheon, and H. K. Jung, "A new 2-D image reconstruction algorithm basedon FDTD and design sensitivity analysis," IEEE Transactions on Microwave Theory and Techniques, Vol. 50, No. 12, 2734-2740, 2002.
doi:10.1109/TMTT.2002.805294
20. Takenaka, T., H. Jia, and T. Tanaka, "Microwave imaging of electrical property distributions by a forward-backward time-stepping method ," Journal of Electromagnetic Waves Application, Vol. 14, 1609-1625, 2000.
doi:10.1163/156939300X00383
21. He, S., P. Fuks, and G. W. Larson, "An optimization approach to time-domain electromagnetic inverse problem for a stratified dispersive and dissipative slab," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 9, 1277-1282, 1996.
doi:10.1109/8.535386
22. Zhong, X.-M., C. Liao, and W. Chen, "Image reconstruction of arbitrary cross section conducting cylinder using UWB pulse," Journal of Electromagnetic Waves Application, Vol. 21, No. 1, 25-34, 2007.
doi:10.1163/156939307779391786
23. Chen, X., D. Liang, and K. Huang, "Microwave imaging 3-D buriedob jects using parallel genetic algorithm combined with FDTD technique," Journal of Electromagnetic Waves Application, Vol. 20, No. 13, 1761-1774, 2006.
doi:10.1163/156939306779292264
24. Huang, C. H., S. H. Chen, C. L. Li, and C. C. Chiu, Time domain inverse scattering of an embedded cylinder with arbitrary shape using nearly resonant technique, 2004 International Conference on Electromagnetic Applications and Compatibility, Taipei, Taiwan, 2004.
25. Bermani, E., S. Caorsi, and M. Raffetto, "Geometric andd ielectric characterization of buried cylinders by using simple time-domain electromagnetic data and neural networks ," Microwave and Optical Technology Letters, Vol. 24, No. 1, 24-31, 2000.
doi:10.1002/(SICI)1098-2760(20000105)24:1<24::AID-MOP9>3.0.CO;2-U
26. Isakov, V., "Uniqueness andstabilit y in multidimensional inverse problems ," Inverse Problems, Vol. 9, No. 6, 579-621, 1993.
doi:10.1088/0266-5611/9/6/001
27. Kirsch, A. and R. Kress, "Uniqueness in inverse obstacle scattering," Inverse Problems, Vol. 9, 285-299, 1993.
doi:10.1088/0266-5611/9/2/009
28. Colton, D. and L. Paivarinta, "The uniqueness of a solution to an inverse scattering problem for electromagnetic waves," Archive for Rational Mechanics and Analysis, Vol. 119, No. 1, 59-70, 1992.
doi:10.1007/BF00376010
29. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, New York, 1992.
30. Eberhart, R. C. and J. Kennedy, "A new optimizer using particle swarm theory," Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 39-43, Japan, 1995.
doi:10.1109/MHS.1995.494215
31. Donelli, M. and A. Massa, "Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 5, 1761-1776, 2005.
doi:10.1109/TMTT.2005.847068
32. 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
33. Caorsi, S., M. Donelli, A. Lommi, and A. Massa, "Location and imaging of two-dimensional scatterers by using a particle swarm algorithm," Journal of Electromagnetic Waves & Applications, Vol. 18, No. 4, 481-494, 2004.
doi:10.1163/156939304774113089
34. Huang, T. and A. S. Mohan, "Application of particle swarm optimization for microwave imaging of lossy dielectric objects," 2005 IEEE Antenna and Propagation Society International Symposium Digest , 852-855, 2005.
35. Semnani and M. Kamyab, "Truncated cosine fourier series expansion methodfor solving 2-din verse scattering problems," Progress In Electromagnetics Research, Vol. 81, 73-97, 2008.
doi:10.2528/PIER07122404
36. Taflove, A. and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, Boston, MA, 2000.
37. Chevalier, M. W., R. J. Luebbers, and V. P. Cable, "FDTD local gridwith materical traverse," IEEE Trans. Antennas and Propagation, Vol. 45, No. 3, 1997.
doi:10.1109/8.558656
38. De Boor, C., A Practical Guide to Splines, Springer-Verlag, New York, 1978.
39. Li, C.-L., C.-W. Liu, and S.-H. Chen, "Optimization of a PML absorber's conductivity profile using FDTD," Microwave and Optical Technology Letters, Vol. 37, No. 5, 69-73, 2003.
40. Yee, K., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media ," IEEE Transactions on Antennas and Propagation, Vol. 14, No. 3, 302-307, 1966.
doi:10.1109/TAP.1966.1138693
Submit
