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Modulated luminescence tomography
Determining an obstacle by far-field data measured at a few spots
1. | Department of Computing Sciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 |
2. | School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an,710049 |
References:
[1] |
F. Cakoni, D. Colton and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering, SIAM, Philadelphia, PA, 2011.
doi: 10.1137/1.9780898719406. |
[2] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, $2^{nd}$ edition, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-662-03537-5. |
[3] |
D. Colton and B. D. Sleeman, Uniqueness theorems for the inverse problem of acoustic scattering, IMA J. Appl. Math., 31 (1983), 253-259.
doi: 10.1093/imamat/31.3.253. |
[4] |
G. Dassios and R. Kleinman, Low Frequency Scattering, Clarendon Press, Oxford, 2000. |
[5] |
G. Hu, X. Liu and B. Zhang, Unique determination of a perfectly conducting ball by a finite number of electric far field data, J. Math. Anal. Appl., 352 (2009), 861-871.
doi: 10.1016/j.jmaa.2008.09.016. |
[6] |
V. Isakov, Inverse Problems for Partial Differential Equations, Volume 127, Springer, 1998.
doi: 10.1007/978-1-4899-0030-2. |
[7] |
A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford University Press, Oxford, 2008. |
[8] |
J. Li, H. Y. Liu, Z. Shang and H. Sun, Two single-shot methods for locating multiple electromagnetic scatterers, SIAM J. Appl. Math., 73 (2013), 1721-1746.
doi: 10.1137/130907690. |
[9] |
J. Li, H. Y. 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. |
[10] |
H. Y. Liu and J. Zou, Zeros of Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering, IMA J. Appl. Math., 72 (2007), 817-831.
doi: 10.1093/imamat/hxm013. |
[11] |
J. Li, H. Y. 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. |
[12] |
J. Li and J. Zou, A direct sampling method for inverse scattering using far-field data, Inverse Problems and Imaging, 7 (2013), 757-775.
doi: 10.3934/ipi.2013.7.757. |
[13] |
J. Li, H. Y. Liu and J. Zou, Multilevel linear sampling method for inverse scattering problems, SIAM Journal on Scientific Computing, 30 (2008), 1228-1250.
doi: 10.1137/060674247. |
[14] |
J. Li, H. Y. Liu and J. Zou, Strengthened linear sampling method with a reference ball, SIAM Journal on Scientific Computing, 31 (2009), 4013-4040.
doi: 10.1137/080734170. |
[15] |
J. Li, H. Y. Liu and J. Zou, Locating multiple multiscale acoustic scatterers, SIAM Multiscale Modeling and Simulations, 12 (2014), 927-952.
doi: 10.1137/13093409X. |
[16] |
H. Y. Liu and J. Zou, On uniqueness in inverse acoustic and electromagnetic obstacle scattering problems, Journal of Physics: Conference Series, 124 (2008), 012006.
doi: 10.1088/1742-6596/124/1/012006. |
[17] |
R. Potthast, Point Sources and Multipoles in Inverse Scattering Theory, Chapman & Hall/CRC Research Notes in Mathematics, 427, Chapman & Hall/CRC, Boca Raton, FL, 2001.
doi: 10.1201/9781420035483. |
show all references
References:
[1] |
F. Cakoni, D. Colton and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering, SIAM, Philadelphia, PA, 2011.
doi: 10.1137/1.9780898719406. |
[2] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, $2^{nd}$ edition, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-662-03537-5. |
[3] |
D. Colton and B. D. Sleeman, Uniqueness theorems for the inverse problem of acoustic scattering, IMA J. Appl. Math., 31 (1983), 253-259.
doi: 10.1093/imamat/31.3.253. |
[4] |
G. Dassios and R. Kleinman, Low Frequency Scattering, Clarendon Press, Oxford, 2000. |
[5] |
G. Hu, X. Liu and B. Zhang, Unique determination of a perfectly conducting ball by a finite number of electric far field data, J. Math. Anal. Appl., 352 (2009), 861-871.
doi: 10.1016/j.jmaa.2008.09.016. |
[6] |
V. Isakov, Inverse Problems for Partial Differential Equations, Volume 127, Springer, 1998.
doi: 10.1007/978-1-4899-0030-2. |
[7] |
A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford University Press, Oxford, 2008. |
[8] |
J. Li, H. Y. Liu, Z. Shang and H. Sun, Two single-shot methods for locating multiple electromagnetic scatterers, SIAM J. Appl. Math., 73 (2013), 1721-1746.
doi: 10.1137/130907690. |
[9] |
J. Li, H. Y. 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. |
[10] |
H. Y. Liu and J. Zou, Zeros of Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering, IMA J. Appl. Math., 72 (2007), 817-831.
doi: 10.1093/imamat/hxm013. |
[11] |
J. Li, H. Y. 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. |
[12] |
J. Li and J. Zou, A direct sampling method for inverse scattering using far-field data, Inverse Problems and Imaging, 7 (2013), 757-775.
doi: 10.3934/ipi.2013.7.757. |
[13] |
J. Li, H. Y. Liu and J. Zou, Multilevel linear sampling method for inverse scattering problems, SIAM Journal on Scientific Computing, 30 (2008), 1228-1250.
doi: 10.1137/060674247. |
[14] |
J. Li, H. Y. Liu and J. Zou, Strengthened linear sampling method with a reference ball, SIAM Journal on Scientific Computing, 31 (2009), 4013-4040.
doi: 10.1137/080734170. |
[15] |
J. Li, H. Y. Liu and J. Zou, Locating multiple multiscale acoustic scatterers, SIAM Multiscale Modeling and Simulations, 12 (2014), 927-952.
doi: 10.1137/13093409X. |
[16] |
H. Y. Liu and J. Zou, On uniqueness in inverse acoustic and electromagnetic obstacle scattering problems, Journal of Physics: Conference Series, 124 (2008), 012006.
doi: 10.1088/1742-6596/124/1/012006. |
[17] |
R. Potthast, Point Sources and Multipoles in Inverse Scattering Theory, Chapman & Hall/CRC Research Notes in Mathematics, 427, Chapman & Hall/CRC, Boca Raton, FL, 2001.
doi: 10.1201/9781420035483. |
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