In this paper, the reconstruction problem of inaccessible objects buried into a three-part space with locally rough interfaces is solved by Distorted Born Iterative Method (DBIM). DBIM requires the calculation of the background electric field and Green's function in every iteration step via the solution of the direct scattering problem. Here, they are calculated numerically by using the buried object approach (BOA) which is very useful in the solutions of the problems including stratified media with locally rough interfaces. Various numerical applications have been performed to demonstrate the applicability and efficiency of the method. The method was found to be very successful in reconstructing moderate contrast objects when they were buried in the middle space. In this case, the method works effectively even if the buried objects and interface roughnesses have complex geometric structures. Moreover, the multiplicity of buried objects has no negative effect on the reconstruction results. Nevertheless, the results of reconstruction deteriorate when objects are buried in the bottom space. However, the accuracies of them are still on an acceptable level in this situation.
1. Pierri, R. and G. Leone, "Inverse scattering of dielectric cylinders by a second-order Born approximation," IEEE Trans. Geosci. Remote Sens., Vol. 37, No. 1, 374-382, 1999. doi:10.1109/36.739072
2. Haddadin, O. S. and E. S. Ebbini, "Imaging strongly scattering media using a multiple frequency distorted Born iterative method," IEEE Trans. Ultrason., Ferroelectr., Freq. Control, Vol. 45, No. 6, 1485-1496, 1998. doi:10.1109/58.738288
3. Chew, W. C. and Y. M. Wang, "Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method," IEEE Trans. Med. Imag., Vol. 9, No. 2, 218-225, 1990. doi:10.1109/42.56334
4. Zhang, L., W. Li, and F. Li, "Tomographic reconstruction using the distorted Rytov iterative method with phaseless data," IEEE Geosci. Remote Sens. Lett., Vol. 5, No. 3, 479-483, 2008. doi:10.1109/LGRS.2008.919818
5. Chew, W. C. and Q. Liu, "Inversion of induction tool measurements using the distorted Born iterative method and CG-FFHT," IEEE Trans. Geosci. Remote Sens., Vol. 32, No. 4, 878-884, 1994. doi:10.1109/36.298015
6. Zheng, H., C. Wang, and E. Li, "Modification of enhanced distorted Born iterative method for the 2D inverse problem," IET Microw. Antenna P., Vol. 10, No. 10, 1036-1042, 2016. doi:10.1049/iet-map.2015.0239
7. Lavarello, R. and M. Oelze, "A study on the reconstruction of moderate contrast targets using the distorted Born iterative method," IEEE Trans. Ultrason., Ferroelectr., Freq. Control, Vol. 55, No. 1, 112-124, 2008. doi:10.1109/TUFFC.2008.621
8. Lavarello, R. J. and M. L. Oelze, "Tomographic reconstruction of three-dimensional volumes using the distorted Born iterative method," IEEE Trans. Med. Imag., Vol. 28, No. 10, 1643-1653, 2009. doi:10.1109/TMI.2009.2026274
9. Hesford, A. J. and W. C. Chew, "Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole algorithm," The Journal of the Acoustical Society of America, Vol. 128, No. 2, 679-690, 2010. doi:10.1121/1.3458856
10. Cui, T. J., W. C. Chew, A. A. Aydiner, and S. Chen, "Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method," IEEE Trans. Geosci. Remote Sens., Vol. 39, No. 2, 339-346, 2001. doi:10.1109/36.905242
11. Tu, H., W. Chien, C. Chiu, and T. Hu, "Comparison of two different shape descriptions in the half-space inverse problem," SBMO/IEEE MTT-S International Conference on Microwave and Optoelectronics, 158-161, 2005.
12. Chiu, C. and Y. Kiang, "Electromagnetic inverse scattering of a conducting cylinder buried in a lossy half-space," IEEE Trans. Antennas Propag., Vol. 40, No. 12, 1562-1565, 1992. doi:10.1109/8.204747
13. Caorsi, S., G. L. Gragnani, and M. Pastorino, "Numerical electromagnetic inverse-scattering solutions for two-dimensional infinite dielectric cylinders buried in a lossy half-space," IEEE Trans. Microw. Theory Techn., Vol. 41, No. 2, 352-357, 1993. doi:10.1109/22.216482
14. Mahmoud, S. F., S. M. Ali, and J. R. Wait, "Electromagnetic scattering from a buried cylindrical inhomogeneity inside a lossy earth," Radio Sci., Vol. 16, No. 6, 1285-1298, 1981. doi:10.1029/RS016i006p01285
15. Delbary, F., K. Erhard, R. Kress, R. Potthast, and J. Schulz, "Inverse electromagnetic scattering in a two-layered medium with an application to mine detection," Inverse Probl., Vol. 24, No. 10, 1-26, 2008.
16. Li, F., Q. H. Liu, and L. P. Song, "Three-dimensional reconstruction of objects buried in layered media using born and distorted Born iterative methods," IEEE Geosci. Remote Sens. Lett., Vol. 1, No. 2, 107-111, 2004. doi:10.1109/LGRS.2004.826562
17. Zhang, P., P. Fei, X. Wen, and F. Nian, "Reconstruction of objects buried in layered media based on an equivalent current source," Progress In Electromagnetics Research M, Vol. 44, 171-182, 2015. doi:10.2528/PIERM15081807
18. Galdi, V., H. Feng, D. Castaon, W. C. Karl, and L. B. Felsen, "Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams," IEEE Trans. Antennas Propag., Vol. 51, No. 9, 2304-2318, 2003. doi:10.1109/TAP.2003.816363
19. Firoozabadi, R., E. L. Miller, C. M. Rappaport, and A. W. Morgenthaler, "Subsurface sensing of buried objects under a randomly rough surface using scattered electromagnetic field data," IEEE Trans. Geosci. Remote Sens., Vol. 45, No. 1, 104-117, 2007. doi:10.1109/TGRS.2006.883462
20. El-Shenawee, M., C. M. Rappaport, E. Miller, and M. Silevitch, "Three-dimensional subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: Use of the steepest descent fast multipole method," IEEE Trans. Geosci. Remote Sens., Vol. 39, No. 6, 1174-1182, 2001. doi:10.1109/36.927436
21. Ozdemir, O. and Y. Altuncu, "A reconstruction of dielectric objects buried under a rough surface," 13. International Workshop on Optimization and Inverse Problems in Electromagnetism, 2014.
22. Altuncu, Y., "Reconstruction of 3D dielectric objects buried under 2D rough urfaces by using contrast source inversion method," 13. International Workshop on Optimization and Inverse Problems in Electromagnetism, 2014.
23. Tetik, E. and I. Akduman, "3D imaging of dielectric objects buried under a rough surface by using CSI," International Journal of Antennas and Propagation, Vol. 2015, 1-8, 2015. doi:10.1155/2015/179304
24. Hadamard, J., Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale University Press, New Haven, 1923.
25. Sung Chan, J. and U. Jin Choi, "Convergence analyses of the born iterative method and the distorted born iterative method," Numerical Functional Analysis and Optimization, Vol. 20, No. 3-4, 301-316, 2007.
26. Gilmore, C., P. Mojabi, and J. LoVetri, "Comparison of an enhanced distorted Born iterative method and the multiplicative-regularized contrast source inversion method," IEEE Trans. Antennas Propag., Vol. 57, No. 8, 2341-2351, 2009. doi:10.1109/TAP.2009.2024478
27. Van den Berg, P. M., A. L. Van Broekhoven, and A. Abubakar, "Extended contrast source inversion," Inverse Probl., Vol. 15, 1325-1344, 1996.
28. Van den Berg, P. M. and R. E. Kleinman, "A contrast source inversion method," Inverse Probl., Vol. 13, 1607-1620, 1997. doi:10.1088/0266-5611/13/6/013
29. Abubakar, A., P. M. Van den Berg, and J. J. Mallorqui, "Imaging of biomedical data using a multiplicative regularized contrast source inversion method," IEEE Trans. Microw. Theory Techn., Vol. 50, No. 7, 1761-1771, 2002. doi:10.1109/TMTT.2002.800427
30. Bozza, G. and M. Pastorino, "An inexact Newton-based approach to microwave imaging within the contrast source formulation," IEEE Trans. Antennas Propag., Vol. 57, No. 4, 1122-1132, 2009. doi:10.1109/TAP.2009.2015820
31. Bloemenkamp, R. F., A. Abubakar, and P. M. Van den Berg, "Inversion of experimental multifrequency data using the contrast source inversion method," Inverse Probl., Vol. 17, 1611-1622, 2001. doi:10.1088/0266-5611/17/6/305
33. Ye, X. and X. Chen, "Subspace-based distorted-born iterative method for solving inverse scattering problems," IEEE Trans. Antennas Propag., Vol. 65, No. 12, 7224-7232, 2017. doi:10.1109/TAP.2017.2766658
34. Altuncu, Y., A. Yapar, and I. Akduman, "On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface," IEEE Trans. Geosci. Remote Sens., Vol. 44, No. 6, 1435-1443, 2006. doi:10.1109/TGRS.2006.870436
35. Tikhonov, A. N. and V. Y. Arsenin, Solution of Ill-posed Problems, Winston and Sons., Washington, 1977.