-
Previous Article
Gaussian Markov random field priors for inverse problems
- IPI Home
- This Issue
-
Next Article
Inverse diffusion from knowledge of power densities
Near-field imaging of the surface displacement on an infinite ground plane
1. | Department of Mathematics, Zhejiang University, Hangzhou, China |
2. | Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, United States |
References:
[1] |
H. Ammari, G. Bao and A. W. Wood, An integral equation method for the electromagnetic scattering from cavities, Math. Meth. Appl. Sci., 23 (2000), 1057-1072.
doi: 10.1002/1099-1476(200008)23:12<1057::AID-MMA151>3.0.CO;2-6. |
[2] |
H. Ammari, G. Bao and A. W. Wood, Analysis of the electromagnetic scattering from a cavity, Japan J. Indust. Appl. Math., 19 (2002), 301-310.
doi: 10.1007/BF03167458. |
[3] |
H. Ammari, J. Garnier and K. Sølna, Resolution and stability analysis in full-aperture, linearized conductivity and wave imaging, Proc. Amer. Math. Soc., to appear. |
[4] |
M. Born and E. Wolf, "Principles of Optics," (6th ed.), Cambridge University Press, 1980.
doi: 10.1017/CBO9781139644181. |
[5] |
P. Carney and J. Schotland, Inverse scattering for near-field microscopy, Appl. Phys. Lett., 77 (2000), 2798-800.
doi: 10.1063/1.1320844. |
[6] |
D. Colton and R. Kress, "Integral Equation Methods in Scattering Theory," Pure and Applied Mathematics, Wiley, New York, 1983. |
[7] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory," Applied Mathematical Sciences, 93, Springer-Verlag, Berlin, 1998. |
[8] |
D. Courjon and C. Bainier, Near field microscopy and near field optics, Rep. Prog. Phys., 57 (1994), 989-1028. |
[9] |
G. Derveaux, G. Papanicolaou and C. Tsogka, Resolution and denoising in near-field imaging, Inverse Problems, 22 (2006), 1437-1456.
doi: 10.1088/0266-5611/22/4/017. |
[10] |
H. W. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems," Mathematics and Its Application, Kluwer Academic Pubishers, New York, 1996.
doi: 10.1007/978-94-009-1740-8. |
[11] |
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, American Mathematical Society, 1997. |
[12] |
A. Kirsch, "An Introduction to the Mathematical Theory of Inverse Problems," Applied Mathematical Sciences, 120, Springer-Verlag, New York, 1996.
doi: 10.1007/978-1-4612-5338-9. |
[13] |
R. Kress and T. Tran, Inverse scattering for a locally perturbed half-plane, Inverse Problems, 16 (2000), 1541-1559.
doi: 10.1088/0266-5611/16/5/323. |
[14] |
L. Landweber, An iteration formula for Fredholm integral equations of the first kind, Am. J. Math., 73 (1951), 615-624.
doi: 10.2307/2372313. |
[15] |
L Novotny and B. Hecht, "Principles of Nano-Optics," Cambridge University Press, 2006. |
[16] |
L. Rayleigh, On the theory of optical images with special reference to the optical microscope, Phil. Mag., 5 (1896), 167-195. |
[17] |
F. Reitich and C. Turc, High-order solutions of three-dimensional roughsurface scattering problems at high-frequencies. I: The scalar case, Waves Random and Complex Media, 15 (2005), 1-16.
doi: 10.1080/17455030500053393. |
[18] |
J. Sun, P. Carney and J. Schotland, Near-field scanning optical tomography: A nondestructive method for three-dimensional nanoscale imaging, IEEE J. Sel. Top. Quant., 12 (2006), 1072-1082.
doi: 10.1109/JSTQE.2006.879567. |
[19] |
A. V. Tikhonov, On the solution of incorrectly formulated problems and the regularization method, Soviet Math. Doklady, 4 (1963), 1035-1038. |
[20] |
A. Willers, The Helmholtz equation in disturbed half-spaces, Math. Meth. Appl. Sci., 9 (1987), 312-323.
doi: 10.1002/mma.1670090124. |
[21] |
B. Zhang and S. N. Chandler-Wilde, Integral equation methods for scattering by infinite rough surfaces, Math. Meth. Appl. Sci., 26 (2003), 463-488.
doi: 10.1002/mma.361. |
show all references
References:
[1] |
H. Ammari, G. Bao and A. W. Wood, An integral equation method for the electromagnetic scattering from cavities, Math. Meth. Appl. Sci., 23 (2000), 1057-1072.
doi: 10.1002/1099-1476(200008)23:12<1057::AID-MMA151>3.0.CO;2-6. |
[2] |
H. Ammari, G. Bao and A. W. Wood, Analysis of the electromagnetic scattering from a cavity, Japan J. Indust. Appl. Math., 19 (2002), 301-310.
doi: 10.1007/BF03167458. |
[3] |
H. Ammari, J. Garnier and K. Sølna, Resolution and stability analysis in full-aperture, linearized conductivity and wave imaging, Proc. Amer. Math. Soc., to appear. |
[4] |
M. Born and E. Wolf, "Principles of Optics," (6th ed.), Cambridge University Press, 1980.
doi: 10.1017/CBO9781139644181. |
[5] |
P. Carney and J. Schotland, Inverse scattering for near-field microscopy, Appl. Phys. Lett., 77 (2000), 2798-800.
doi: 10.1063/1.1320844. |
[6] |
D. Colton and R. Kress, "Integral Equation Methods in Scattering Theory," Pure and Applied Mathematics, Wiley, New York, 1983. |
[7] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory," Applied Mathematical Sciences, 93, Springer-Verlag, Berlin, 1998. |
[8] |
D. Courjon and C. Bainier, Near field microscopy and near field optics, Rep. Prog. Phys., 57 (1994), 989-1028. |
[9] |
G. Derveaux, G. Papanicolaou and C. Tsogka, Resolution and denoising in near-field imaging, Inverse Problems, 22 (2006), 1437-1456.
doi: 10.1088/0266-5611/22/4/017. |
[10] |
H. W. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems," Mathematics and Its Application, Kluwer Academic Pubishers, New York, 1996.
doi: 10.1007/978-94-009-1740-8. |
[11] |
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, American Mathematical Society, 1997. |
[12] |
A. Kirsch, "An Introduction to the Mathematical Theory of Inverse Problems," Applied Mathematical Sciences, 120, Springer-Verlag, New York, 1996.
doi: 10.1007/978-1-4612-5338-9. |
[13] |
R. Kress and T. Tran, Inverse scattering for a locally perturbed half-plane, Inverse Problems, 16 (2000), 1541-1559.
doi: 10.1088/0266-5611/16/5/323. |
[14] |
L. Landweber, An iteration formula for Fredholm integral equations of the first kind, Am. J. Math., 73 (1951), 615-624.
doi: 10.2307/2372313. |
[15] |
L Novotny and B. Hecht, "Principles of Nano-Optics," Cambridge University Press, 2006. |
[16] |
L. Rayleigh, On the theory of optical images with special reference to the optical microscope, Phil. Mag., 5 (1896), 167-195. |
[17] |
F. Reitich and C. Turc, High-order solutions of three-dimensional roughsurface scattering problems at high-frequencies. I: The scalar case, Waves Random and Complex Media, 15 (2005), 1-16.
doi: 10.1080/17455030500053393. |
[18] |
J. Sun, P. Carney and J. Schotland, Near-field scanning optical tomography: A nondestructive method for three-dimensional nanoscale imaging, IEEE J. Sel. Top. Quant., 12 (2006), 1072-1082.
doi: 10.1109/JSTQE.2006.879567. |
[19] |
A. V. Tikhonov, On the solution of incorrectly formulated problems and the regularization method, Soviet Math. Doklady, 4 (1963), 1035-1038. |
[20] |
A. Willers, The Helmholtz equation in disturbed half-spaces, Math. Meth. Appl. Sci., 9 (1987), 312-323.
doi: 10.1002/mma.1670090124. |
[21] |
B. Zhang and S. N. Chandler-Wilde, Integral equation methods for scattering by infinite rough surfaces, Math. Meth. Appl. Sci., 26 (2003), 463-488.
doi: 10.1002/mma.361. |
[1] |
Peijun Li, Yuliang Wang. Near-field imaging of obstacles. Inverse Problems and Imaging, 2015, 9 (1) : 189-210. doi: 10.3934/ipi.2015.9.189 |
[2] |
Deyue Zhang, Yukun Guo, Fenglin Sun, Hongyu Liu. Unique determinations in inverse scattering problems with phaseless near-field measurements. Inverse Problems and Imaging, 2020, 14 (3) : 569-582. doi: 10.3934/ipi.2020026 |
[3] |
Xiaoxu Xu, Bo Zhang, Haiwen Zhang. Uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data at a fixed frequency. Inverse Problems and Imaging, 2020, 14 (3) : 489-510. doi: 10.3934/ipi.2020023 |
[4] |
Ming Li, Ruming Zhang. Near-field imaging of sound-soft obstacles in periodic waveguides. Inverse Problems and Imaging, 2017, 11 (6) : 1091-1105. doi: 10.3934/ipi.2017050 |
[5] |
Lei Zhang, Luming Jia. Near-field imaging for an obstacle above rough surfaces with limited aperture data. Inverse Problems and Imaging, 2021, 15 (5) : 975-997. doi: 10.3934/ipi.2021024 |
[6] |
Michael V. Klibanov. A phaseless inverse scattering problem for the 3-D Helmholtz equation. Inverse Problems and Imaging, 2017, 11 (2) : 263-276. doi: 10.3934/ipi.2017013 |
[7] |
Giovanni Bozza, Massimo Brignone, Matteo Pastorino, Andrea Randazzo, Michele Piana. Imaging of unknown targets inside inhomogeneous backgrounds by means of qualitative inverse scattering. Inverse Problems and Imaging, 2009, 3 (2) : 231-241. doi: 10.3934/ipi.2009.3.231 |
[8] |
Deyue Zhang, Yue Wu, Yinglin Wang, Yukun Guo. A direct imaging method for the exterior and interior inverse scattering problems. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022025 |
[9] |
Huai-An Diao, Peijun Li, Xiaokai Yuan. Inverse elastic surface scattering with far-field data. Inverse Problems and Imaging, 2019, 13 (4) : 721-744. doi: 10.3934/ipi.2019033 |
[10] |
Jingzhi Li, Jun Zou. A direct sampling method for inverse scattering using far-field data. Inverse Problems and Imaging, 2013, 7 (3) : 757-775. doi: 10.3934/ipi.2013.7.757 |
[11] |
Jun Lai, Ming Li, Peijun Li, Wei Li. A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers. Inverse Problems and Imaging, 2018, 12 (3) : 635-665. doi: 10.3934/ipi.2018027 |
[12] |
Roland Griesmaier. Reciprocity gap music imaging for an inverse scattering problem in two-layered media. Inverse Problems and Imaging, 2009, 3 (3) : 389-403. doi: 10.3934/ipi.2009.3.389 |
[13] |
Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the half-space inverse scattering problem with phaseless data. Inverse Problems and Imaging, 2017, 11 (5) : 901-916. doi: 10.3934/ipi.2017042 |
[14] |
Karzan Berdawood, Abdeljalil Nachaoui, Rostam Saeed, Mourad Nachaoui, Fatima Aboud. An efficient D-N alternating algorithm for solving an inverse problem for Helmholtz equation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 57-78. doi: 10.3934/dcdss.2021013 |
[15] |
Peter Monk, Virginia Selgas. Near field sampling type methods for the inverse fluid--solid interaction problem. Inverse Problems and Imaging, 2011, 5 (2) : 465-483. doi: 10.3934/ipi.2011.5.465 |
[16] |
S. L. Ma'u, P. Ramankutty. An averaging method for the Helmholtz equation. Conference Publications, 2003, 2003 (Special) : 604-609. doi: 10.3934/proc.2003.2003.604 |
[17] |
Kaitlyn (Voccola) Muller. SAR correlation imaging and anisotropic scattering. Inverse Problems and Imaging, 2018, 12 (3) : 697-731. doi: 10.3934/ipi.2018030 |
[18] |
John C. Schotland, Vadim A. Markel. Fourier-Laplace structure of the inverse scattering problem for the radiative transport equation. Inverse Problems and Imaging, 2007, 1 (1) : 181-188. doi: 10.3934/ipi.2007.1.181 |
[19] |
Yuan Li, Shou-Fu Tian. Inverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation. Communications on Pure and Applied Analysis, 2022, 21 (1) : 293-313. doi: 10.3934/cpaa.2021178 |
[20] |
Wei-Kang Xun, Shou-Fu Tian, Tian-Tian Zhang. Inverse scattering transform for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (9) : 4941-4967. doi: 10.3934/dcdsb.2021259 |
2021 Impact Factor: 1.483
Tools
Metrics
Other articles
by authors
[Back to Top]