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Fast imaging of electromagnetic scatterers by a two-stage multilevel sampling method
The factorization method for scatterers with different physical properties
1. | Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China |
References:
[1] |
O. Bondarenko, A. Kirsch and X. Liu, The Factorization method for inverse acoustic scattering in a layered medium, Inverse Problems, 29 (2013), 045010.
doi: 10.1088/0266-5611/29/4/045010. |
[2] |
O. Bondarenko and X. Liu, The Factorization method for inverse obstacle scattering with conductive boundary condition, Inverse Problems, 29 (2013), 095021.
doi: 10.1088/0266-5611/29/9/095021. |
[3] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd Edition, Springer, 2012.
doi: 10.1007/978-1-4614-4942-3. |
[4] |
N. Grinberg and A. Kirsch, The Linear sampling method in inverse obstacle scattering for impedance boundary conditions, Journal of Inverse and Ill-Posed Problems, 10 (2002), 171-185.
doi: 10.1515/jiip.2002.10.2.171. |
[5] |
N. Grinberg and A. Kirsch, The factorization method for obstacles with a-prior separated sound-soft and sound-hard parts, Math. Comput. in Simul., 66, (2004), 267-279.
doi: 10.1016/j.matcom.2004.02.011. |
[6] |
A. Kirsch, Charaterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), 1489-1512.
doi: 10.1088/0266-5611/14/6/009. |
[7] |
A. Kirsch, Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory, Inverse Problems, 15 (1999), 413-429.
doi: 10.1088/0266-5611/15/2/005. |
[8] |
A. Kirsch, The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media, Inverse Problems, 18 (2002), 1025-1040.
doi: 10.1088/0266-5611/18/4/306. |
[9] |
A. Kirsch, An introduction to the Mathematical Theory of Inverse Problems, 2nd Edition, Springer, 2011.
doi: 10.1007/978-1-4419-8474-6. |
[10] |
A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford University Press, 2008. |
[11] |
A. Kirsch and X. Liu, The factorization method for inverse acoustic scattering by a penetrable anisotropic obstacle, Math. Meth. Appl. Sci., 37 (2014), 1159-1170.
doi: 10.1002/mma.2877. |
[12] |
A. Kirsch and X. Liu, Direct and inverse acoustic scattering by a mixed-type scatterer, Inverse Problems, 29 (2013), 065005.
doi: 10.1088/0266-5611/29/6/065005. |
[13] |
A. Kirsch and X. Liu, A modification of the factorization method for the classical acoustic inverse scattering problems, Inverse Problems, 30 (2014), 035013.
doi: 10.1088/0266-5611/30/3/035013. |
[14] |
A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Problems Imaging, 3 (2009), 123-138.
doi: 10.3934/ipi.2009.3.123. |
[15] |
X. Liu, The factorization method for cavities, Inverse Problems, 30 (2014), 015006.
doi: 10.1088/0266-5611/30/1/015006. |
[16] |
W. Mclean, Strongly Elliptic Systems and Boundary Integral Equation, Cambridge University Press, Cambridge, 2000. |
[17] |
D. L. Nguyen, Spectral Methods for Direct and Inverse Scattering from Periodic Structures, PhD thesis, Ecole Polytechnique X, Paris, 2012. |
[18] |
J. Yang, B. Zhang and H. Zhang, The factorization method for reconstructing a penetrable obstacle with unknown buried objects, SIAM J. Appl. Math., 73 (2013), 617-635.
doi: 10.1137/120883724. |
show all references
References:
[1] |
O. Bondarenko, A. Kirsch and X. Liu, The Factorization method for inverse acoustic scattering in a layered medium, Inverse Problems, 29 (2013), 045010.
doi: 10.1088/0266-5611/29/4/045010. |
[2] |
O. Bondarenko and X. Liu, The Factorization method for inverse obstacle scattering with conductive boundary condition, Inverse Problems, 29 (2013), 095021.
doi: 10.1088/0266-5611/29/9/095021. |
[3] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd Edition, Springer, 2012.
doi: 10.1007/978-1-4614-4942-3. |
[4] |
N. Grinberg and A. Kirsch, The Linear sampling method in inverse obstacle scattering for impedance boundary conditions, Journal of Inverse and Ill-Posed Problems, 10 (2002), 171-185.
doi: 10.1515/jiip.2002.10.2.171. |
[5] |
N. Grinberg and A. Kirsch, The factorization method for obstacles with a-prior separated sound-soft and sound-hard parts, Math. Comput. in Simul., 66, (2004), 267-279.
doi: 10.1016/j.matcom.2004.02.011. |
[6] |
A. Kirsch, Charaterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), 1489-1512.
doi: 10.1088/0266-5611/14/6/009. |
[7] |
A. Kirsch, Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory, Inverse Problems, 15 (1999), 413-429.
doi: 10.1088/0266-5611/15/2/005. |
[8] |
A. Kirsch, The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media, Inverse Problems, 18 (2002), 1025-1040.
doi: 10.1088/0266-5611/18/4/306. |
[9] |
A. Kirsch, An introduction to the Mathematical Theory of Inverse Problems, 2nd Edition, Springer, 2011.
doi: 10.1007/978-1-4419-8474-6. |
[10] |
A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford University Press, 2008. |
[11] |
A. Kirsch and X. Liu, The factorization method for inverse acoustic scattering by a penetrable anisotropic obstacle, Math. Meth. Appl. Sci., 37 (2014), 1159-1170.
doi: 10.1002/mma.2877. |
[12] |
A. Kirsch and X. Liu, Direct and inverse acoustic scattering by a mixed-type scatterer, Inverse Problems, 29 (2013), 065005.
doi: 10.1088/0266-5611/29/6/065005. |
[13] |
A. Kirsch and X. Liu, A modification of the factorization method for the classical acoustic inverse scattering problems, Inverse Problems, 30 (2014), 035013.
doi: 10.1088/0266-5611/30/3/035013. |
[14] |
A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Problems Imaging, 3 (2009), 123-138.
doi: 10.3934/ipi.2009.3.123. |
[15] |
X. Liu, The factorization method for cavities, Inverse Problems, 30 (2014), 015006.
doi: 10.1088/0266-5611/30/1/015006. |
[16] |
W. Mclean, Strongly Elliptic Systems and Boundary Integral Equation, Cambridge University Press, Cambridge, 2000. |
[17] |
D. L. Nguyen, Spectral Methods for Direct and Inverse Scattering from Periodic Structures, PhD thesis, Ecole Polytechnique X, Paris, 2012. |
[18] |
J. Yang, B. Zhang and H. Zhang, The factorization method for reconstructing a penetrable obstacle with unknown buried objects, SIAM J. Appl. Math., 73 (2013), 617-635.
doi: 10.1137/120883724. |
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