An iterative time-domain algorithm for reconstructing three-dimensional (3-D) objects is presented, using normalized microwave data. The incident waveform information is excluded from the cost functional by normalizing the observed and calculated fields in the frequency domain. The exciting pulse used in the reconstruction can be freely selected by considering the bandwidth of the received data. Two numerical examples are shown to demonstrate that the proposed method can rebuild an inhomogeneous object from noisy data where different waveforms in the observation and reconstruction are used. Two normalized data sets from synthetic observed data and calculated data for a known model are illustrated too.
2. Zaeytijd, D., J. Franchois, A. C. Eyraud, and J. M. Geffrin, "Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method --- Theory and experiment," IEEE Trans. on Antennas Propagat., Vol. 55, No. 11, 3279-3292, 2007.
3. Otto, G. P. and W. C. Chew, "Microwave inverse scattering-local shape function imaging for improved resolution of strong scatterers," IEEE Trans. Microwave Theory Tech., Vol. 42, No. 1, 137-141, 1994.
4. Franchois, A. and C. Pichot, "Microwave imaging-complex permittivity reconstruction with a Levenberg-Marquardt method," IEEE Trans. Antennas Propagat., Vol. 45, No. 2, 203-214, 1997.
5. Van Dongen, K. W. A. and W. M. D. Wright, "A full vectorial contrast source inversion scheme for three-dimensional acoustic imaging of both compressibility and density profiles," The Journal of the Acoustical Society of America, Vol. 121, 1538-1549, 2007.
6. Bucci, O. M., L. Crocco, T. Isernia, and V. Pascazio, "Inverse scattering problems with multifrequency data: Reconstruction capabilities and solution strategies," IEEE Trans. Geosci. Remote Sensing, Vol. 38, No. 4, 1749-1756, 2000.
7. Cui, T. J., Y. Qin, Y. Ye, J. Wu, G. L. Wang, and W. C. Chew, "Efficient low-frequency inversion of 3-D buried objects with large contrasts," IEEE Trans. Geosci. Remote Sensing, Vol. 44, No. 1, 3-9, 2006.
8. Pastorino, M., A. Massa, and S. Caorsi, "A microwave inverse scattering technique for image reconstruction based on a genetic algorithm," IEEE Trans. Instrumentation and Measurement, Vol. 49, No. 3, 573-578, 2000.
9. Isernia, T., V. Pascazio, and R. Pierri, "On the local minima in a tomographic imaging technique," IEEE Trans. Geosci. Remote Sensing, Vol. 39, No. 7, 1596-1607, 2001.
10. Caorsi, S., M. Donelli, D. Franceschini, and A. Massa, "An iterative multiresolution approach for microwave imaging applications," Microwave Opt. Technol. Lett., Vol. 32, No. 5, 352-356, 2002.
11. Joachimowicz, N., C. Pichot, and J. Hugonin, "Inverse scattering: an iterative numerical method for electromagnetic imaging," IEEE Trans. Antennas Propagat., Vol. 39, No. 12, 1742-1752, 1991.
12. Lin, J.-H. and W. C. Chew, "Solution of the three-dimensional electromagnetic inverse problem by the local shape function and the conjugate gradient fast Fourier transform methods," J. Opt. Soc. Am. A, Vol. 14, No. 11, 3037-3045, 1997.
13. Abubakar, A., P. M. van den Berg, and B. Kooij, "A conjugate gradient contrast source technique for 3D profile inversion," IEICE Trans. Electron. E83-C, 1864-1874, 2000.
14. Song, L. P. and Q. H. Liu, "Fast three-dimensional electromagnetic nonlinear inversion in layered media with a novel scattering approximation," Inverse Problems, Vol. 20, 171-194, 2004.
15. Moghaddam, M. and W. C. Chew, "Study of some practical issues in inversion with the Born iterative method using time-domain data," IEEE Trans. Antennas Propagt., Vol. 41, No. 2, 177-184, 1993.
16. Fhager, A., P. Hashemzadeh, and M. Persson, "Reconstruction quality and spectral content of an electromagnetic time-domain inversion algorithm," IEEE Trans. on Biomedical Eng., Vol. 53, 1594-1604, 2006.
17. He, S., P. Fuks, and G. W. Larson, "Optimization approach to time-domain electromagnetic inverse problem for a stratified dispersive and dissipative slab," IEEE Trans. Antennas Propagat., Vol. 44, No. 9, 1277-1282, 1996.
18. Yu, W. H. and R. Mittra, "A nonlinear optimization technique for reconstructing dielectric scatterers with possible high contrasts," Microwave Opt. Technol. Lett., Vol. 14, No. 2, 268-271, 1997.
19. Gustafsson, M. and S. He, "An optimization approach to two-dimensional time domain electromagnetic inverse problems," Radio Sci., Vol. 35, 525-536, 2000.
20. Takenaka, T., H. Zhou, and T. Tanaka, "Inverse scattering for a three-dimensional object in the time domain," J. Opt. Soc. Am. A, Vol. 20, No. 10, 1867-1874, 2003.
21. Zhou, H., M. Sato, T. Takenaka, and G. Li, "Reconstruction from antenna transformed radar data using a time-domain reconstruction method," IEEE Trans. Geosci. Remote Sensing, Vol. 45, No. 3, 689-696, 2007.
22. Tanaka, T., N. Kuroki, and T. Takenaka, "Filtered forward-backward time-stepping method applied to reconstruction of dielectric cylinders," J. Electromagn. Waves Appl., Vol. 17, No. 2, 253-270, 2003.
23. Zhou, H., D. L. Qiu, and T. Takenaka, "Reconstructing properties of subsurface from Ground-penetrating radar data," Progress In Electromagnetics Research Symposium 2007, 1009-1014, Beijing, China, March 26-30, 2007.
24. Daniels, D. J., Surface-penetrating Radar, UK Instit Elect Eng., London, 1996.
25. Broquetas, A., et al., "Cylindrical geometry: A further step in active microwave tomography," IEEE Trans. Microwave Theory Tech., Vol. 39, No. 5, 836-844, 1991.
26. Bloemenkamp, R. F., A. Abubakar, and P. M. van den Berg, "Inversion of experimental multi-frequency data using the contrast source inversion method," Inverse Problems, Vol. 17, 1611-1622, 2001.