Acta mathematica scientia, Series B >
MUSIC ALGORITHM FOR LOCATING POINT-LIKE SCATTERERS CONTAINED IN A SAMPLE ON FLAT SUBSTRATE
Received date: 2009-10-16
Revised date: 2011-08-25
Online published: 2012-07-20
Supported by
This work was supported by the National Natural Science Foundation of China (10971083, 10801063) and the School of Mathematical Sciences Foundation of Jilin University.
In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reconstruction problem can be reduced to a calculation of Green function corresponding to the background medium. In addition, we use an explicit formulation of Green function in the MUSIC algorithm to simplify the calculation when the cross-section of sample is a half-disc. Numerical experiments are included to demonstrate the feasibility of this method.
DONG He-Ping , MA Fu-Ming , ZHANG De-Yue . MUSIC ALGORITHM FOR LOCATING POINT-LIKE SCATTERERS CONTAINED IN A SAMPLE ON FLAT SUBSTRATE[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1647 -1661 . DOI: 10.1016/S0252-9602(12)60131-3
[1] Devaney A J. Super-resolution processing of multi-static data using time reversal and MUSIC.
http://www.ece.neu.edu/faculty/devaney/ajd/preprints.htm
[2] Devaney A J, Marengo E A, Gruber F K. Time-reversal-based imaging and inverse scattering of multiply scattering point targets. J Acoust Soc Am, 2005, 118: 3129–3138
[3] Kirsch A. The MUSIC algorithm and the factorization method in inverse scattering theory for inhomoge-neous media. Inverse Problems, 2002, 18: 1025–1040
[4] Prada C, Manneville S, Spoliansky D, Fink M. Decomposition of the time reversal operator: Detection and selective focusing on two scatterers. J Acoust Soc Am, 1996, 99: 2067–2076
[5] Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering Theory. 2nd ed. Berlin: Springer, 1998
[6] Colton D, Monk P. A linear sampling method for the detection of leukemia using microwaves. SIAM J Appl Math, 1998, 58: 926–941
[7] Duffy D G. Green’s Functions with Applications. Chapman & Hall/CRC, 2001
[8] Cakoni F, Colton D. Qualitative Methods in Inverse Scattering Theory. Berlin: Springer, 2006
[9] Ammari H, Iakovleva E, Moskow S. Recovery of small inhomogeneities from the scattering amplitude at a fixed frequency. SIAM J Math Anal, 2003, 34: 882–900
[10] Ammari H, Iakovleva E, Lesselier D. AMUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency. Multiscale Model Simul, 2005, 3: 597–628
[11] Ammari H, Iakovleva E, Lesselier D. Two numerical methods for recovering small inclusions from the scattering amplitude at a fixed frequency. SIAM J Sci Comput, 2005, 27: 130–158
[12] Ammari H, Iakovleva E, Lesselier D, Perruson G. MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions. SIAM J Sci Comput, 2007, 29: 674–709
[13] Ammari H, Griesmaier R, Hanke M. Identification of small inhomogeneities: Asymptotic factorization. Math Comput, 2007, 76: 1425–1448
[14] Ammari H, Kang H. Reconstruction of Small Inhomogeneities from Boundary Measurements. Berlin: Springer, 2004
[15] Dong H P, Ma F M. Reconstruction of the shape of object with near field measurements in a half-plane. Science in China Series A: Mathematics, 2008, 51: 1059–1070
[16] Cheney M. The linear sampling method and the MUSIC algorithm. Inverse Problems, 2001, 17: 591–595
[17] Fink M, Prada C. Acoustic time-reversal mirrors. Inverse Problems, 2001, 17: R1–R38
[18] Park W K, Lesselier D. MUSIC-type imaging of a thin penetrable inclusion from its multi-static response matrix. Inverse Problems, 2009, 25: 075002
[19] Park W K, Lesselier D. Electromagnetic MUSIC-Type Imaging of Perfectly Conducting, Arc-Like Cracks at Single Frequency. Journal of Computational Physics, 2009, 228(21): 8093–8111
[20] Chen X D, Zhong Y. MUSIC electromagnetic imaging with enhanced resolution for small inclusions. Inverse Problems, 2009, 25: 015008
[21] Hou S, Huang K, Sølna K, Zhao H. A phase and space coherent direct imaging method. J Acoust Soc Am, 2009, 125: 227–238
[22] Park W K. On the imaging of thin dielectric inclusions buried within a half-space. Inverse Problems, 2010, 26: 074008
[23] Ammari H. An Introduction to Mathematics of Emerging Biomedical Imaging. Mathematics and Appli-cations, Volume 62. Berlin: Springer, 2008
[24] Ammari H, Kang H, Kim E, Louati K, Vogelius M. A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements. Numerische Mathematik, 2008, 108: 501–528
[25] Ammari H, Garnier J, Kang H, Park W K, Sølna K. Imaging schemes for perfectly conducting cracks. SIAM J Appl Math, 2011, 71: 68–91
[26] Ammari H, Garnier J, Sølna K. A statistical approach to optimal target detection and localization in the presence of noise. Waves in Random and Complex Media, 2012, 22(1): 40–65
[27] Liu Taiping, Zeng Yanni. On Green's function for hyperbolic-parabolic systems. Acta Mathematica Scientia, 2009, 29(6): 1556–1572
/
| 〈 |
|
〉 |