volume | PIER Journals

Abstract

In this paper, a novel algorithm based on an equivalent current source is proposed to reconstruct objects buried in a multilayered medium. First, a radiating current source, one part of the equivalent current source, is obtained directly in closed-form from scattering data via the signal-subspace method. Secondly, a nonradiating current source, the other part of the equivalent current source, is represented with the linear superposition of vectors in the noise-subspace. Finally, the objects and equivalent current source are reconstructed efficiently by solving an optimization problem in a lower dimensional linear space with the conjugate gradient (CG) method. To test the new method, the effects of the frequency of incident wave, array aperture size, and SNR are studied in detail. Numerical results show that the proposed method has a high capacity to reconstruct objects buried in a multilayered medium.

1. Cui, T. J. and W. C. Chew, "Novel diffraction tomography algorithm for imaging two-dimensional targets buried under a lossy earth," IEEE Transactions on Geoscience Remote Sensing, Vol. 38, No. 4, 2033-2041, Jul. 2000.

2. Meincke, P., "Linear GPR inversion for lossy soil and a planar air-soil interface," IEEE Transactions on Geoscience Remote Sensing, Vol. 39, No. 12, 2713-2721, Dec. 2001.
doi:10.1109/36.975005

3. Galdi, V., D. A. Castanon, and L. B. Felsen, "Multifrequency reconstruction of moderately rough interfaces via quasi-ray Gaussian beams," IEEE Transactions on Geoscience and Sensing, Vol. 40, No. 2, 453-460, Feb. 2003.
doi:10.1109/36.992810

4. Zhang, Z. Q. and Q. H. Liu, "3-D nonlinear image reconstruction for microwave biomedical imaging," IEEE Transactions on Biomedical Engineering, Vol. 51, No. 3, 544-548, Mar. 2004.
doi:10.1109/TBME.2003.821052

5. Song, L. P., Q. H. Liu, F. Li, and Z. Q. Zhang, "Reconstruction of three-dimensional objects in layered media: Numerical experiments," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 4, 1556-1561, Apr. 2005.
doi:10.1109/TAP.2004.842585

6. Song, L. P. and Q. H. Liu, "Ground-penetrating radar landmine imaging: Two-dimensional seismic migration and three-dimensional inverse scattering in layered media," Radio Science, Vol. 40, No. 1, RS1S90.1-RS1S90.1, Feb. 2005.
doi:10.1029/2004RS003087

7. Cui, T. J. and W. C. Chew, "Diffraction tomographic algorithm for the detection of three-dimensional objects buried in a lossy half-space," IEEE Transactions on Antennas and Propagation, Vol. 50, No. 1, 42-49, Jan. 2002.
doi:10.1109/8.992560

8. Deming, R. and A. J. Devaney, "Diffraction tomography for multi-monostatic ground penetrating radar imaging," Inverse Problems, Vol. 13, 29-45, 1997.
doi:10.1088/0266-5611/13/1/004

9. Wang, Y. M. and W. C. Chew, "An iterative solution of the two-dimensional electromagnetic inverse scattering problems," Int. J. Imaging Syst. Tech., Vol. 1, No. 1, 100-108, 1989.
doi:10.1002/ima.1850010111

10. Chew, W. C. and Y. M. Wang, "Reconstruction of two-dimensional permittivity distribution using the distorted born iteration method," IEEE Transactions on Medical Imaging, Vol. 9, No. 2, 218-225, Jun. 1990.
doi:10.1109/42.56334

11. Van den Berg, P. M. and R. E. Kleinman, "A contrast source inversion method," Inverse Problems, Vol. 13, No. 6, 1607-1620, Jul. 1997.
doi:10.1088/0266-5611/13/6/013

12. Van den Berg, P. M., A. L. van Broehoven, and A. Abubakar, "Extended contrast source inversion," Inverse Problems, Vol. 15, No. 5, 1325-1344, Jun. 1999.
doi:10.1088/0266-5611/15/5/315

13. Chen, X., "Subspace-based optimization method for solving inverse-scattering problems," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 1, 42-49, Jan. 2010.
doi:10.1109/TGRS.2009.2025122

14. Chen, X., "Application of signal-subspace and optimization methods in reconstructing extended scatterers," Journal of the Optical Society of America A, Vol. 26, No. 4, 1022-1026, Mar. 2009.
doi:10.1364/JOSAA.26.001022

15. Xu, X. M. and Q. H. Liu, "The BCGS-FFT method for electromagnetic scattering from inhomogeneous objects in a planarly layered-medium," IEEE Antennas and Wireless Propagation Letters, Vol. 1, No. 1, 77-80, Feb. 2002.
doi:10.1109/LAWP.2002.802549

16. Millard, X. and Q. H. Liu, "Fast volume integral equation solver for electromagnetic scattering from large inhomogeneous objects in planarly layered-media," IEEE Transaction on Antennas and Propagation, Vol. 51, No. 9, 2393-2401.
doi:10.1109/TAP.2003.816311

17. Simsek, E., J. Liu, and Q. H. Liu, "A spectral integral method (SIM) for layered media," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 6, 1742-1749, Jun. 2006.
doi:10.1109/TAP.2006.875500

18. Chew, W. C. and J. H. Lin, "A frequency-hopping approach for microwave imaging of large inhomogeneous bodies," IEEE Microwave Guided Wave Letter, Vol. 5, No. 12, 439-441, Dec. 1995.
doi:10.1109/75.481854

19. Bertero, M. and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics Publishing, Bristol, U.K., 1998.
doi:10.1887/0750304359

20. Persico, R., R. Bernini, and F. Soldovieri, "The role of the measurement configuration in inverse scattering from buried objects under the born approximation," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 6, Jun. 2005.
doi:10.1109/TAP.2005.848468

21. Soldovieri, F. and R. Solimene, "Through-wall imaging via a linear inverse scattering algorithm," IEEE Geoscience Remote Sensing Letters, Vol. 4, No. 4, Oct. 2007.

Dr. Peng Zhang

Dr. Peng Fei

Dr. Xin Wen

Dr. Feng Nian