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Overlapping domain decomposition methods for linear inverse problems
Near-field imaging of obstacles
1. | Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States, United States |
References:
[1] |
G. Bao, T. Cui and P. Li, Inverse diffraction grating of Maxwell's equations in biperiodic structures, Optics Express, 22 (2014), 4799-4816.
doi: 10.1364/OE.22.004799. |
[2] |
G. Bao and P. Li, Inverse medium scattering problems in near-field optics, J. Comput. Math., 25 (2007), 252-265. |
[3] |
G. Bao and P. Li, Numerical solution of inverse scattering for near-field optics, Optics Lett., 32 (2007), 1465-1467.
doi: 10.1364/OL.32.001465. |
[4] |
G. Bao and P. Li, Near-field imaging of infinite rough surfaces, SIAM J. Appl. Math., 73 (2013), 2162-2187.
doi: 10.1137/130916266. |
[5] |
G. Bao and P. Li, Near-field imaging of infinite rough surfaces in dielectric media, SIAM J. Imaging Sci., 7 (2014), 867-899.
doi: 10.1137/130944485. |
[6] |
G. Bao and P. Li, Convergence analysis in near-field imaging, Inverse Problems, 30 (2014), 085008, 26PP.
doi: 10.1088/0266-5611/30/8/085008. |
[7] |
G. Bao and J. Lin, Imaging of reflective surfaces by near-field optics, Optics Lett., 37 (2012), 5027-5029.
doi: 10.1364/OL.37.005027. |
[8] |
G. Bao and J. Lin, Near-field imaging of the surface displacement on an infinite ground plane, Inverse Probl. Imag., 7 (2013), 377-396.
doi: 10.3934/ipi.2013.7.377. |
[9] |
O. Bruno and F. Reitich, Numerical solution of diffraction problems: A method of variation of boundaries, J. Opt. Soc. Am. A, 10 (1993), 1168-1175.
doi: 10.1364/JOSAA.10.001168. |
[10] |
F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory: An Introduction, Springer, Berlin, 2006. |
[11] |
P. Carney and J. Schotland, Near-field tomography, in Inside Out: Inverse Problems and Applications (ed. G. Uhlmann), Cambridge University Press, 47 (2003), 133-168. |
[12] |
T. Cheng, P. Li and Y. Wang, Near-field imaging of perfectly conducting grating surfaces, J. Opt. Soc. Am. A, 30 (2013), 2473-2481.
doi: 10.1364/JOSAA.30.002473. |
[13] |
D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, 12 (1996), 383-393.
doi: 10.1088/0266-5611/12/4/003. |
[14] |
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Wiley, New York, 1983. |
[15] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-662-03537-5. |
[16] |
D. Courjon, Near-field Microscopy and Near-field Optics, Imperial College Press, London, 2003.
doi: 10.1088/0034-4885/57/10/002. |
[17] |
D. Courjon and C. Bainier, Near field microscopy and near field optics, Rep. Prog. Phys., 57 (1994), 989-1028.
doi: 10.1088/0034-4885/57/10/002. |
[18] |
F. Hettlich, Frechét derivatives in inverse obstacle scattering, Inverse Problems, 11 (1995), 371-382.
doi: 10.1088/0266-5611/11/2/007. |
[19] |
M. Ikehata, Reconstruction of an obstacle from the scattering amplitude at a fixed frequency, Inverse Problems, 14 (1998), 949-954.
doi: 10.1088/0266-5611/14/4/012. |
[20] |
A. Kirsch, The domain derivative and two applications in inverse scattering theory, Inverse Problems, 9 (1993), 81-96.
doi: 10.1088/0266-5611/9/1/005. |
[21] |
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. |
[22] |
NIST Digital Library of Mathematical Functions., http://dlmf.nist.gov/, Release 1.0.6 of 2013-05-06. |
[23] |
R. Kress, Newton's method for inverse obstacle scattering meets the method of least squares, Inverse Problems, 19 (2003), S91-S104.
doi: 10.1088/0266-5611/19/6/056. |
[24] |
R. Kress and W. Rundell, A quasi-Newton method in inverse obstacle scattering, Inverse Problems, 10 (1994), 1145-1157.
doi: 10.1088/0266-5611/10/5/011. |
[25] |
P. Li and J. Shen, Analysis of the scattering by an unbounded rough surface, Math. Meth. Appl. Sci., 35 (2012), 2166-2184.
doi: 10.1002/mma.2560. |
[26] |
A. Malcolm and D. P. Nicholls, A field expansions method for scattering by periodic multilayered media, J. Acout. Soc. Am., 129 (2011), 1783-1793.
doi: 10.1121/1.3531931. |
[27] |
A. Malcolm and D. P. Nicholls, A boundary perturbation method for recovering interface shapes in layered media, Inverse Problems, 27 (2011), 095009, 18pp.
doi: 10.1088/0266-5611/27/9/095009. |
[28] |
D. P. Nicholls and F. Reitich, Shape deformations in rough surface scattering: Cancellations, conditioning, and convergence, J. Opt. Soc. Am. A, 21 (2004), 590-605.
doi: 10.1364/JOSAA.21.000590. |
[29] |
D. P. Nicholls and F. Reitich, Shape deformations in rough surface scattering: improved algorithms, J. Opt. Soc. Am. A, 21 (2004), 606-621.
doi: 10.1364/JOSAA.21.000606. |
[30] |
D. P. Nicholls and J. Shen, A Stable High-Order Method for Two-Dimensional Bounded-Obstacle Scattering, SIAM J. Sci. Comput., 28 (2006), 1398-1419.
doi: 10.1137/050632920. |
[31] |
R. Potthast, Stability estimates and reconstructions in inverse acoustic scattering using singular sources, J. Comp. Appl. Math., 114 (2000), 247-274.
doi: 10.1016/S0377-0427(99)00201-0. |
[32] |
R. Schmidt, Multiple emitter location and signal parameter estimation, IEEE Trans. Antennas Propag., 34 (1986), 276-280.
doi: 10.1109/TAP.1986.1143830. |
show all references
References:
[1] |
G. Bao, T. Cui and P. Li, Inverse diffraction grating of Maxwell's equations in biperiodic structures, Optics Express, 22 (2014), 4799-4816.
doi: 10.1364/OE.22.004799. |
[2] |
G. Bao and P. Li, Inverse medium scattering problems in near-field optics, J. Comput. Math., 25 (2007), 252-265. |
[3] |
G. Bao and P. Li, Numerical solution of inverse scattering for near-field optics, Optics Lett., 32 (2007), 1465-1467.
doi: 10.1364/OL.32.001465. |
[4] |
G. Bao and P. Li, Near-field imaging of infinite rough surfaces, SIAM J. Appl. Math., 73 (2013), 2162-2187.
doi: 10.1137/130916266. |
[5] |
G. Bao and P. Li, Near-field imaging of infinite rough surfaces in dielectric media, SIAM J. Imaging Sci., 7 (2014), 867-899.
doi: 10.1137/130944485. |
[6] |
G. Bao and P. Li, Convergence analysis in near-field imaging, Inverse Problems, 30 (2014), 085008, 26PP.
doi: 10.1088/0266-5611/30/8/085008. |
[7] |
G. Bao and J. Lin, Imaging of reflective surfaces by near-field optics, Optics Lett., 37 (2012), 5027-5029.
doi: 10.1364/OL.37.005027. |
[8] |
G. Bao and J. Lin, Near-field imaging of the surface displacement on an infinite ground plane, Inverse Probl. Imag., 7 (2013), 377-396.
doi: 10.3934/ipi.2013.7.377. |
[9] |
O. Bruno and F. Reitich, Numerical solution of diffraction problems: A method of variation of boundaries, J. Opt. Soc. Am. A, 10 (1993), 1168-1175.
doi: 10.1364/JOSAA.10.001168. |
[10] |
F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory: An Introduction, Springer, Berlin, 2006. |
[11] |
P. Carney and J. Schotland, Near-field tomography, in Inside Out: Inverse Problems and Applications (ed. G. Uhlmann), Cambridge University Press, 47 (2003), 133-168. |
[12] |
T. Cheng, P. Li and Y. Wang, Near-field imaging of perfectly conducting grating surfaces, J. Opt. Soc. Am. A, 30 (2013), 2473-2481.
doi: 10.1364/JOSAA.30.002473. |
[13] |
D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, 12 (1996), 383-393.
doi: 10.1088/0266-5611/12/4/003. |
[14] |
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Wiley, New York, 1983. |
[15] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-662-03537-5. |
[16] |
D. Courjon, Near-field Microscopy and Near-field Optics, Imperial College Press, London, 2003.
doi: 10.1088/0034-4885/57/10/002. |
[17] |
D. Courjon and C. Bainier, Near field microscopy and near field optics, Rep. Prog. Phys., 57 (1994), 989-1028.
doi: 10.1088/0034-4885/57/10/002. |
[18] |
F. Hettlich, Frechét derivatives in inverse obstacle scattering, Inverse Problems, 11 (1995), 371-382.
doi: 10.1088/0266-5611/11/2/007. |
[19] |
M. Ikehata, Reconstruction of an obstacle from the scattering amplitude at a fixed frequency, Inverse Problems, 14 (1998), 949-954.
doi: 10.1088/0266-5611/14/4/012. |
[20] |
A. Kirsch, The domain derivative and two applications in inverse scattering theory, Inverse Problems, 9 (1993), 81-96.
doi: 10.1088/0266-5611/9/1/005. |
[21] |
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. |
[22] |
NIST Digital Library of Mathematical Functions., http://dlmf.nist.gov/, Release 1.0.6 of 2013-05-06. |
[23] |
R. Kress, Newton's method for inverse obstacle scattering meets the method of least squares, Inverse Problems, 19 (2003), S91-S104.
doi: 10.1088/0266-5611/19/6/056. |
[24] |
R. Kress and W. Rundell, A quasi-Newton method in inverse obstacle scattering, Inverse Problems, 10 (1994), 1145-1157.
doi: 10.1088/0266-5611/10/5/011. |
[25] |
P. Li and J. Shen, Analysis of the scattering by an unbounded rough surface, Math. Meth. Appl. Sci., 35 (2012), 2166-2184.
doi: 10.1002/mma.2560. |
[26] |
A. Malcolm and D. P. Nicholls, A field expansions method for scattering by periodic multilayered media, J. Acout. Soc. Am., 129 (2011), 1783-1793.
doi: 10.1121/1.3531931. |
[27] |
A. Malcolm and D. P. Nicholls, A boundary perturbation method for recovering interface shapes in layered media, Inverse Problems, 27 (2011), 095009, 18pp.
doi: 10.1088/0266-5611/27/9/095009. |
[28] |
D. P. Nicholls and F. Reitich, Shape deformations in rough surface scattering: Cancellations, conditioning, and convergence, J. Opt. Soc. Am. A, 21 (2004), 590-605.
doi: 10.1364/JOSAA.21.000590. |
[29] |
D. P. Nicholls and F. Reitich, Shape deformations in rough surface scattering: improved algorithms, J. Opt. Soc. Am. A, 21 (2004), 606-621.
doi: 10.1364/JOSAA.21.000606. |
[30] |
D. P. Nicholls and J. Shen, A Stable High-Order Method for Two-Dimensional Bounded-Obstacle Scattering, SIAM J. Sci. Comput., 28 (2006), 1398-1419.
doi: 10.1137/050632920. |
[31] |
R. Potthast, Stability estimates and reconstructions in inverse acoustic scattering using singular sources, J. Comp. Appl. Math., 114 (2000), 247-274.
doi: 10.1016/S0377-0427(99)00201-0. |
[32] |
R. Schmidt, Multiple emitter location and signal parameter estimation, IEEE Trans. Antennas Propag., 34 (1986), 276-280.
doi: 10.1109/TAP.1986.1143830. |
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