volume | PIER Journals

Abstract

An efficient method is proposed in this paper to reconstruct the shape of a two-dimensional perfectly electrically conducting (PEC) target using limited scattered information. Based on the physical optics approximation, a Fourier transform relation has been obtained between the PEC target and the scattered fields. In theory, all scattered-field data are required for the reconstruction in the whole angle range (from 0 to 2π) and in the whole frequency range (from 0 to ∞). However, such data are impossible in practical applications. In this paper, we have discussed the influence of limited frequencies and limited incident angles on the imaging, where a Pade interpolation technique has been developed to obtain the scattered information in the whole angle range from limited-angle information. In order to overcome the ill-posed problem in the interpolation, the Tikhonov regularization has been used. Reconstruction examples are given to validate the efficiency of the proposed approach.

1. Lewis, R. M., "Physical optics inverse diffraction," IEEE Trans. Ant. Propagat., Vol. 17, No. 3, 308-314, 1969.
doi:10.1109/TAP.1969.1139417 Google Scholar

2. Das, Y., "On radar target shape estimation using algorithms for reconstruction from projections," IEEE Trans. Ant. Propagat., Vol. 26, No. 2, 274-279, 1978.
doi:10.1109/TAP.1978.1141825 Google Scholar

3. Bennett, C. L., "Time domain inverse scattering," IEEE Trans. Ant. Propagat., Vol. 29, No. 2, 213-219, 1981.
doi:10.1109/TAP.1981.1142556 Google Scholar

4. Bojarski, N. N., "A survey of the physical optics inverse scattering identity," IEEE Trans. Ant. Propagat., Vol. 30, 980-989, 1982.
doi:10.1109/TAP.1982.1142890 Google Scholar

5. Boerner, W. M., C. M. Ho, and B. Y. Foo, "Use of Radon's projection theory in electromagnetic inverse scattering," IEEE Trans. Ant. Propagat., Vol. 2, No. 3, 336-341, 1981.
doi:10.1109/TAP.1981.1142581 Google Scholar

6. Rothwell, E. J., K. M. Chen, D. P. Nyquist, and J. E. Ross, "Time-domain imaging of airborne targets using ultra-wideband or short-pulse radar," IEEE Trans. Ant. Propagat., Vol. 43, No. 3, 327-329, 1995.
doi:10.1109/8.372006 Google Scholar

7. Dai, Y. C., E. J. Rothwell, K. M. Chen, and D. P. Nyquist, "Time-domain imaging of radar targets using algorithms for reconstruction from projections," IEEE Trans. Ant. Propagat., Vol. 45, No. 8, 1227-1235, 1997.
doi:10.1109/8.611241 Google Scholar

8. Chan, C. K. and N. H. Farhat, "Frequency swept tomographic imaging of three-dimensional perfectly conducting objects," IEEE Trans. Ant. Propagat., Vol. 29, No. 3, 312-319, 1981.
doi:10.1109/TAP.1981.1142571 Google Scholar

9. Young, J. D., "Radar imaging from ramp response signatures," IEEE Trans. Ant. Propagat., Vol. 24, No. 5, 276-282, 1976.
doi:10.1109/TAP.1976.1141346 Google Scholar

10. Dural, G. and D. L. Moffatt, "SARimaging to identify basic scattering mechanisms," IEEE Trans. Ant. Propagat., Vol. 42, No. 1, 99-110, 1994.
doi:10.1109/8.272307 Google Scholar

11. Cui, T. J. and W. C. Chew, "Study of resolution and super resolution in electromagnetic imaging for half-space problems," IEEE Trans. Ant. Propagat., Vol. 52, No. 6, 1398-1411, 2004.
doi:10.1109/TAP.2004.829847 Google Scholar

12. Belkebir, K., A. Baussard, and D. Premel, "Edge-preserving regularization scheme applied to modified gradient method to reconstruct two-dimensional targets from data laboratorycontrolled," Progress In Electromagnetics Research, Vol. 54, 1-17, 2005.
doi:10.2528/PIER04073003 Google Scholar

13. Persson, K. and M. Gustafsson, "Reconstruction of equivalent currents using a near-field data transformation — with radome," Applications Progress In Electromagnetics Research, Vol. 54, 179-198, 2005.
doi:10.2528/PIER04111602 Google Scholar

14. Bermani, E., A. Boni, A. Kerhet, and A. Massa, "Kernels evaluation of SVM-based estimators for inverse scattering problems," Progress In Electromagnetics Research, Vol. 53, 167-188, 2005.
doi:10.2528/PIER04090801 Google Scholar

15. Chen, X., K. Huang, and X.-B. Xu, "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 Google Scholar

16. Thomas, V., J. Yohannan, A. Lonappan, G. Bindu, and K. T. Mathew, "Localization of the investigation domain in electromagnetic imaging of buried 2-D dielectric pipelines with circular cross section," Progress In Electromagnetics Research, Vol. 61, 111-131, 2006.
doi:10.2528/PIER05110801 Google Scholar

17. Cockrel, C. R. and F. B. Beck, "Asymptotic waveform evaluation (AWE) technique for frequency domain electromagnetic analysis," NASA Technical Memorandum 110292, No. 11, 1996. Google Scholar

18. Tikhonov, A. N. and V. Y. Arsenin, Solution of Ill-Posed Problems, V. H. Winston and Sons, 1977.

19. Cui, T. J., Y. Qin, G. L. Wang, and W. C. Chew, "Low-frequency detection of 2D buried objects using high-order extended Born approximations," Inverse Problems, Vol. 20, 41, 2004.
doi:10.1088/0266-5611/20/6/S04 Google Scholar

Dr. Jing Wu

Professor Tie-Jun Cui