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The Gauss-Newton inversion (GNI), an iterative algorithm, is developed from the frequency domain to the time domain in order to simultaneously reconstruct the electrical permittivity and electric conductivity of a two-dimensional object of interest by directly using the ultra-wideband time-domain measurement data. The resulting forward problem is solved by the finite difference time domain method, while the ill-posedness of the corresponding inverse problem is restrained by an adaptive regularization technique at each iteration. Furthermore, the modified GNI algorithm is applied to four types of numerical examples where a noise model is considered, and the simulated results preliminarily demonstrate its feasibility and robustness. The reconstructed images present super resolution, thus it is expected to be used in the engineering practice such as the detection of the early-stage breast cancer.
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Keywords:
- electromagnetic inverse scattering /
- Gauss-Newton inversion (GNI) /
- finite difference time domain (FDTD) /
- regularization
[1] Wang Y M, Chew W C 1989 Int. J. Imaging Syst. Technol. 1 100
[2] Chew W C, Wang Y M 1990 IEEE Trans. Med. Imaging 9 218
[3] Yu W H, Peng Z Q, Ren L 1995 J. Microw. 11 97 (in Chinese) [余文华, 彭仲秋, 任朗 1995 微波学报 11 97]
[4] Nie Z P, Zhang Y R 1998 IEEE Trans. Geosci. Remote Sens. 36 749
[5] Takenaka T, Jia H, Tanaka T 2000 J. Electromagn. Waves Appl. 14 1609
[6] Liu G D, Zhang Y R 2010 Acta Phys. Sin. 59 6969 (in Chinese) [刘广东, 张业荣 2010 物理学报 59 6969]
[7] Ali M A, Moghaddam M 2010 IEEE Trans. Antennas Propag. 58 2327
[8] Mojabi P, LoVetri J 2011 IEEE Trans. Antennas Propag. 59 2954
[9] Wang F F, Zhang Y R 2012 Acta Phys. Sin. 61 084101 (in Chinese) [王芳芳, 张业荣 2012 物理学报 61 084101]
[10] Wang F F, Zhang Y R 2012 Chin. Phys. B 21 050204
[11] Chiu C C, Sun C H, Li C L, Huang C H 2013 IEEE Trans. Geosci. Remote Sens. 51 2302
[12] Ge D B, Yan Y B 2005 Finite-Difference Time-Domain Method for Electromagnetic Waves (2nd ed.) (Xi’an: Xidian University Press) (in Chinese) [葛德彪, 闫玉波 2005 电磁波时域有限差分法(第二版)(西安: 西安电子科技大学出版社)]
[13] Gennarelli G, Soldovieri F 2013 IEEE Geosci. Remote Sens. Lett. 10 1085
[14] Dai Y H 2003 Math. Comput. 17 1317
[15] Abubakar A, Habashy T, Druskin V, Knizhnerman L, Alumbaugh D 2008 Geophysics 73 165
[16] Liu G D, Zhang Y R 2011 Acta Phys. Sin. 60 074303 (in Chinese) [刘广东, 张业荣 2011 物理学报 60 074303]
[17] Xiao X, Xu L, Liu B Y 2013 Acta Phys. Sin. 62 044105 (in Chinese) [肖夏, 徐立, 刘冰雨 2013 物理学报 62 044105]
[18] Shahzad A, O’Halloran M, Jones E, Glavin M 2013 IEEE Trans. Antennas Wireless Propag. Lett. 12 500
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[1] Wang Y M, Chew W C 1989 Int. J. Imaging Syst. Technol. 1 100
[2] Chew W C, Wang Y M 1990 IEEE Trans. Med. Imaging 9 218
[3] Yu W H, Peng Z Q, Ren L 1995 J. Microw. 11 97 (in Chinese) [余文华, 彭仲秋, 任朗 1995 微波学报 11 97]
[4] Nie Z P, Zhang Y R 1998 IEEE Trans. Geosci. Remote Sens. 36 749
[5] Takenaka T, Jia H, Tanaka T 2000 J. Electromagn. Waves Appl. 14 1609
[6] Liu G D, Zhang Y R 2010 Acta Phys. Sin. 59 6969 (in Chinese) [刘广东, 张业荣 2010 物理学报 59 6969]
[7] Ali M A, Moghaddam M 2010 IEEE Trans. Antennas Propag. 58 2327
[8] Mojabi P, LoVetri J 2011 IEEE Trans. Antennas Propag. 59 2954
[9] Wang F F, Zhang Y R 2012 Acta Phys. Sin. 61 084101 (in Chinese) [王芳芳, 张业荣 2012 物理学报 61 084101]
[10] Wang F F, Zhang Y R 2012 Chin. Phys. B 21 050204
[11] Chiu C C, Sun C H, Li C L, Huang C H 2013 IEEE Trans. Geosci. Remote Sens. 51 2302
[12] Ge D B, Yan Y B 2005 Finite-Difference Time-Domain Method for Electromagnetic Waves (2nd ed.) (Xi’an: Xidian University Press) (in Chinese) [葛德彪, 闫玉波 2005 电磁波时域有限差分法(第二版)(西安: 西安电子科技大学出版社)]
[13] Gennarelli G, Soldovieri F 2013 IEEE Geosci. Remote Sens. Lett. 10 1085
[14] Dai Y H 2003 Math. Comput. 17 1317
[15] Abubakar A, Habashy T, Druskin V, Knizhnerman L, Alumbaugh D 2008 Geophysics 73 165
[16] Liu G D, Zhang Y R 2011 Acta Phys. Sin. 60 074303 (in Chinese) [刘广东, 张业荣 2011 物理学报 60 074303]
[17] Xiao X, Xu L, Liu B Y 2013 Acta Phys. Sin. 62 044105 (in Chinese) [肖夏, 徐立, 刘冰雨 2013 物理学报 62 044105]
[18] Shahzad A, O’Halloran M, Jones E, Glavin M 2013 IEEE Trans. Antennas Wireless Propag. Lett. 12 500
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