Vol. 166
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2019-10-09
Reconstruction of Two-Dimensional Objects Buried into Three-Part Space with Locally Rough Interfaces via Distorted Born Iterative Method
By
Progress In Electromagnetics Research, Vol. 166, 23-41, 2019
Abstract
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.
Citation
Yasemin Altuncu, Tulun Durukan, and Riza Erhan Akdogan, "Reconstruction of Two-Dimensional Objects Buried into Three-Part Space with Locally Rough Interfaces via Distorted Born Iterative Method," Progress In Electromagnetics Research, Vol. 166, 23-41, 2019.
doi:10.2528/PIER19072203
References

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

32. Chen, X., "Subspace-based optimization method for solving inverse-scattering problems," IEEE Trans. Geosci. Remote Sens., Vol. 48, No. 1, 42-49, 2010.
doi:10.1109/TGRS.2009.2025122

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.

36. Kirsch, A., An Introduction to the Mathematical Theory of Inverse Problem, Springer, New York, 1996.
doi:10.1007/978-1-4612-5338-9