To save the computation time and improve the accuracy of reconstruction results by support vector machine (SVM), a multi-output least square SVM (LS-SVM) algorithm is proposed to reconstruct the position of a 2-D perfect electric conductor cylinder below a rough surface. Firstly, the scattered electromagnetic field at a number of observation positions is calculated by the method of moment to generate the training and testing data. Then the multi-output LS-SVM is trained to reconstruct the coordinate of the object center. Numerical results show that this approach is accurate and efficient even with some additive Gaussian noise.
2. Li, F. H., Q. H. Liu, and L. P. Song, "Three-dimensional reconstruction of objects buried in layered media using born and distorted born iterative methods," IEEE Trans. on Geoscience and Remote Sensing Letters, Vol. 1, No. 2, 107-111, 2004.
3. Wang, X., C.-F. Wang, and Y.-B. Gan, "Electromagnetic scattering from a circular target above or below rough surface," Progress In Electromagnetics Research, Vol. 40, 207-227, 2003.
4. Ji, , W. J., , C. M. Tong, and P. W. Yan, "Fast calculation of EM scattering from randomly rough surface with buried PEC target," Chinese Journal of Radio Science, Vol. 24, No. 5, 939-965, 2009.
5. Firoozabadi, R., E. L. Miller, and C. M. Rappaport, "New inverse method for simultaneous reconstruction of object buried beneath rough ground and the ground surface structure using SAMM forward model," Proceedings of SPIE, Vol. 5674, 382-393, 2005.
6. Cai, J. L., et al., "Inversion of PEC targets below dielectric rough surface based on hybrid multi-phase particle swarm optimization," System Engineering and Electronics, Vol. 34, No. 12, 2433-2437, 2012.
7. Cmielewski, O., H. Tortel, and A. Litman, "A two-step procedure for characterizing obstacles under a rough surface from bistatic measurements," IEEE Trans. on Geoscience and Remote Sensing, Vol. 45, No. 9, 2850-2858, September 2007.
8. Altuncu, Y., O. Ozdemir, and I. Akduman, "Imaging of dielectric objects buried under an arbitrary rough surface," IEEE International Geoscience and Remote Sensing Symposium, IGARSS, 2954-2957, 2006.
9. Vapnik, V. N., The Nature of Statistical Learning Theory, 2nd Ed., Springer-Verlag, New York, 1995.
10. Bermani, E., A. Boni, S. Caorsi, and A. Massa, "An innovative real-time technique for buried object detection," IEEE Transactions on Geoscience and Remote Sensing, Vol. 41, No. 4, 927-931, 2003.
11. Wu, H. B., J. J. Yao, and S. Y. He, "Parameters extraction of the two-dimensional object above or on a rough surface based on the electromagnetic simulation," Journal of Wuhan University, Natural Science Edition, Vol. 55, No. 6, 705-709, 2009.
12. Bermani, E., A. Boni, A. Kerhet, and A. Massa, "Kernal evaluation of SVM based estimation for inverse scattering problems," Progress In Electromagnetics Research, Vol. 53, 167-188, 2005.
13. Wang, F. F. and Y. R. Zhang, "The support vector machine for dielectric target detection through a wall," Progress In Electromagnetics Research Letters, Vol. 23, 119-128, 2011.
14. Zhang, Q. H, B. X. Xiao, and G. Q. Zhu, "Inverse scattering by dielectric circular cylinder using support vector machine approach," Microwave and Optical Technology Letters, Vol. 49, No. 2, 372-375, 2007.
15. Cai, J. L., C. M. Tong, and W. J. Zhong, "Reconstruction of dielectric cylinder by multi-output least square support vector machine," Cross Straight Quad-region Radio Science and Wireless Technology Conference (CSQRWC), Vol. 1, 160-163, 2011.
16. Platt, J., Fast Training of Support Vector Machines Using Sequential Minimal Optimization, Advances in Kernel Methods-support Vector Learning, MIT Press, Cambridge, MA, 1999.
17. Donelli, , M. and A. Massa, "Computational approach based on a particle swarm optimization for microwave imaging of two dimensional dielectric scatters," IEEE trans. on Microwave Theory and Techniques, Vol. 53, No. 5, 1761-1776, 2005.