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Fast imaging of electromagnetic scatterers by a two-stage multilevel sampling method
1. | Faculty of Science, South University of Science and Technology of China, Shenzhen, 518055 |
2. | Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China |
3. | Department of Computing Sciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China |
References:
[1] |
H. Ammari and H. Kang, Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics, 1846, Springer-Verlag, Berlin, 2004.
doi: 10.1007/b98245. |
[2] |
H. Ammari and H. Kang, Polarization and Moment Tensors. With Applications to Inverse Problems and Effective Medium Theory, Applied Mathematical Sciences, Springer, New York, 2007. |
[3] |
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, NewYork, 1965.
doi: 10.1119/1.1972842. |
[4] |
H. Ammari and J.-C. Nédélec, Low-frequency electromagnetic scattering, SIAM J. Math. Anal., 31 (2000), 836-861.
doi: 10.1137/S0036141098343604. |
[5] |
H. Ammari, H. Kang, E. Kim and J. Lee, The generalized polarization tensors for resolved imaging. Part II: Shape and electromagnetic parameters reconstruction of an electromagnetic inclusion from multistatic measurements, Math. Comp., 81 (2012), 839-860.
doi: 10.1090/S0025-5718-2011-02534-2. |
[6] |
F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory: An Introduction, Springer, 2006. |
[7] |
F. Cakoni, D. Colton and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering, Philadelphia: SIAM, 2011.
doi: 10.1137/1.9780898719406. |
[8] |
X. Chen and Y. Zhong, MUSIC electromagnetic imaging with enhanced resolution for small inclusions, Inverse Problems, 25 (2009), 12 pp.
doi: 10.1088/0266-5611/25/1/015008. |
[9] |
D. Colton, J. Coyle and P. Monk, Recent developments in inverse acoustic scattering theory, SIAM Rev., 42 (2000), 369-414.
doi: 10.1137/S0036144500367337. |
[10] |
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. |
[11] |
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, John Wiley & Sons, New York, 1983. |
[12] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Cambridge: Cambridge University Press, 1998.
doi: 10.1007/978-3-662-03537-5. |
[13] |
J. Li, H. Liu, Z. Shang and H. Sun, Two single-shot methods for locating multiple electromagnetic scatterers, SIAM J. Appl. Mat., 73 (2013), 1721-1746.
doi: 10.1137/130907690. |
[14] |
J. Li, H. Liu and Q. Wang, Locating multiple multiscale electromagnetic scatterers by a single far-field measurement, SIAM J. Imaging Sci., 6 (2013), 2285-2309.
doi: 10.1137/130920356. |
[15] |
J. Li, H. Liu and Q. Wang, Enhanced multilevel linear sampling methods for inverse scattering problems, J. Comput. Phys., 22 (2014), 554-571.
doi: 10.1016/j.jcp.2013.09.048. |
[16] |
J. Li, H. Liu and J. Zou, Multilevel linear sampling method for inverse scattering problems, SIAM J. Sci. Comp., 30 (2008),1228-1250.
doi: 10.1137/060674247. |
[17] |
J-C. Nédélec, Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems, volume 144, Springer, 2001.
doi: 10.1007/978-1-4757-4393-7. |
[18] |
C. G. Someda, Electromagnetic Waves, Boca Raton, FL: CRC Press, 2nd edition, 2006. |
[19] |
J. Li and J. Zou, A direct sampling method for inverse scattering using far-field data, Inverse Problems & Imaging, 7 (2013).
doi: 10.3934/ipi.2013.7.757. |
[20] |
M. Ikehata, Reconstruction of obstacles from boundary measurements, Wave Motion, 3 (1999), 205-223.
doi: 10.1016/S0165-2125(99)00006-2. |
[21] |
A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford University Press, Oxford, 2008. |
[22] |
R. Potthast, A survey on sampling and probe methods for inverse problems, Inverse Problems, 22 (2006), R1-R47.
doi: 10.1088/0266-5611/22/2/R01. |
[23] |
G. Uhlmann, Inside Out: Inverse Problems and Applications, MSRI Publications, 47, Cambridge University Press, 2003.
doi: 10.1090/conm/333. |
show all references
References:
[1] |
H. Ammari and H. Kang, Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics, 1846, Springer-Verlag, Berlin, 2004.
doi: 10.1007/b98245. |
[2] |
H. Ammari and H. Kang, Polarization and Moment Tensors. With Applications to Inverse Problems and Effective Medium Theory, Applied Mathematical Sciences, Springer, New York, 2007. |
[3] |
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, NewYork, 1965.
doi: 10.1119/1.1972842. |
[4] |
H. Ammari and J.-C. Nédélec, Low-frequency electromagnetic scattering, SIAM J. Math. Anal., 31 (2000), 836-861.
doi: 10.1137/S0036141098343604. |
[5] |
H. Ammari, H. Kang, E. Kim and J. Lee, The generalized polarization tensors for resolved imaging. Part II: Shape and electromagnetic parameters reconstruction of an electromagnetic inclusion from multistatic measurements, Math. Comp., 81 (2012), 839-860.
doi: 10.1090/S0025-5718-2011-02534-2. |
[6] |
F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory: An Introduction, Springer, 2006. |
[7] |
F. Cakoni, D. Colton and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering, Philadelphia: SIAM, 2011.
doi: 10.1137/1.9780898719406. |
[8] |
X. Chen and Y. Zhong, MUSIC electromagnetic imaging with enhanced resolution for small inclusions, Inverse Problems, 25 (2009), 12 pp.
doi: 10.1088/0266-5611/25/1/015008. |
[9] |
D. Colton, J. Coyle and P. Monk, Recent developments in inverse acoustic scattering theory, SIAM Rev., 42 (2000), 369-414.
doi: 10.1137/S0036144500367337. |
[10] |
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. |
[11] |
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, John Wiley & Sons, New York, 1983. |
[12] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Cambridge: Cambridge University Press, 1998.
doi: 10.1007/978-3-662-03537-5. |
[13] |
J. Li, H. Liu, Z. Shang and H. Sun, Two single-shot methods for locating multiple electromagnetic scatterers, SIAM J. Appl. Mat., 73 (2013), 1721-1746.
doi: 10.1137/130907690. |
[14] |
J. Li, H. Liu and Q. Wang, Locating multiple multiscale electromagnetic scatterers by a single far-field measurement, SIAM J. Imaging Sci., 6 (2013), 2285-2309.
doi: 10.1137/130920356. |
[15] |
J. Li, H. Liu and Q. Wang, Enhanced multilevel linear sampling methods for inverse scattering problems, J. Comput. Phys., 22 (2014), 554-571.
doi: 10.1016/j.jcp.2013.09.048. |
[16] |
J. Li, H. Liu and J. Zou, Multilevel linear sampling method for inverse scattering problems, SIAM J. Sci. Comp., 30 (2008),1228-1250.
doi: 10.1137/060674247. |
[17] |
J-C. Nédélec, Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems, volume 144, Springer, 2001.
doi: 10.1007/978-1-4757-4393-7. |
[18] |
C. G. Someda, Electromagnetic Waves, Boca Raton, FL: CRC Press, 2nd edition, 2006. |
[19] |
J. Li and J. Zou, A direct sampling method for inverse scattering using far-field data, Inverse Problems & Imaging, 7 (2013).
doi: 10.3934/ipi.2013.7.757. |
[20] |
M. Ikehata, Reconstruction of obstacles from boundary measurements, Wave Motion, 3 (1999), 205-223.
doi: 10.1016/S0165-2125(99)00006-2. |
[21] |
A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford University Press, Oxford, 2008. |
[22] |
R. Potthast, A survey on sampling and probe methods for inverse problems, Inverse Problems, 22 (2006), R1-R47.
doi: 10.1088/0266-5611/22/2/R01. |
[23] |
G. Uhlmann, Inside Out: Inverse Problems and Applications, MSRI Publications, 47, Cambridge University Press, 2003.
doi: 10.1090/conm/333. |
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