We consider MUltiple SIgnal Classification (MUSIC)-type imaging of perfectly conducting cracks arising in inverse scattering problems. We first explore the structure of a MUSIC-type imaging function by finding a relationship between it and the Bessel function of order zero of the first kind. Then, we design multi-frequency based MUSIC-type imaging in order to improve the traditional one, and establish a relationship with the Bessel function of integer order of the first kind. Some numerical experiments are presented to support the results of our investigation.
1. Ammari, , H., Mathematical Modeling in Biomedical Imaging II: Optical, Ultrasound, and Opto-acoustic Tomographies, Vol. 2035, Lecture Notes in Mathematics: Mathematical Biosciences Subseries, Springer-Verlag, Berlin, 2011, 2011.
2. Ammari, , H., , J. Garnier, V. Jugnon, and H. Kang, "Stability and resolution analysis for a topological derivative based imaging functional," SIAM J. Control. Optim., Vol. 50, 48-76, 2012. doi:10.1137/100812501
3. Ammari, , H., , J. Garnier, H. Kang, W.-K. Park, and K. Salna, "Imaging schemes for perfectly conducting cracks," SIAM J. Appl. Math., Vol. 71, 68-91, 2011. doi:10.1137/100800130
4. Ammari, , H., , E. Iakovleva, and D. Lesselier, "A MUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency," SIAM Multiscale Modeling Simulation, Vol. 3, 597-628, 2005. doi:10.1137/040610854
5. Ammari, , H., H. Kang, H. Lee, and W.-K. Park, "Asymptotic imaging of perfectly conducting cracks," SIAM J. Sci. Comput. , Vol. 32, 894-922, 2010. doi:10.1137/090749013
6. Bencheikh, , M. L. , Y. Wang, and , "Combined esprit-rootMUSIC for DOA-DOD estimation in polarimetric bistatic MIMO radar," Progress In Electromagnetics Research Letters, Vol. 22, 109-117, 2011. doi:10.2528/PIERC11050205
8. Catapano, , I., F. Soldovieri, and L. Crocco, "On the feasibility of the linear sampling method for 3D GPR surveys," Progress In Electromagnetics Research, Vol. 118, 185-203, 2011. doi:10.2528/PIER11042704
9. Chang, , Y.-L., , C.-Y. Chiang, and K.-S. Chen, "SAR image simulation with application to target recognition," Progress In Electromagnetics Research, Vol. 119, 35-57, 2011. doi:10.2528/PIER11061507
10. Chen, X., Y. Zhong, and , "MUSIC electromagnetic imaging with enhanced resolution for small inclusions," Inverse Problems,, Vol. 25, 015008, 2009.. doi:10.1088/0266-5611/25/1/015008
12. Colton, D., H. Haddar, and P. Monk, "The linear sampling method for solving the electromagnetic inverse scattering problem," SIAM J. Sci. Comput., Vol. 24, , 719-731, 2002. doi:10.1137/S1064827501390467
13. Griesmaier, R., "Multi-frequency orthogonality sampling for inverse obstacle scattering problems," Inverse Problems,, Vol. 27, 085005, 2011. doi:10.1088/0266-5611/27/8/085005
14. Gu, X. and Y. Zhang, "Resolution threshold analysis of MUSIC algorithm in radar range imaging," Progress In Electromagnetics Research B, Vol. 31, 297-321, 2011.
15. Hasar, , U. C. and J. J. Barroso, "Retrieval approach for determination of forward and backward wave impedances of bianisotropic metamaterials," Progress In Electromagnetics Research,, Vol. 112, 109-124, 2011.
16. Hou, , S., K. Huang, K. SAlna, and H. Zhao, "A phase and space coherent direct imaging method," J. Opt. Soc. Am., Vol. 125, 227-238, 2009.
17. Joh, , Y.-D., Y. M. Kwon, J. Y. Huh, and W.-K. Park, "Structure analysis of single- and multi-frequency subspace migrations in inverse scattering problems," Progress In Electromagnetics Research, Vol. 136, 607-622, 2013.
18. Kirsch, , A. and Ritter S., "A linear sampling method for inverse scattering from an open arc," Inverse Problems, Vol. 16, 89-105, 2000. doi:10.1088/0266-5611/16/1/308
19. Kress, R., "Inverse scattering from an open arc," Math. Methods Appl. Sci., Vol. 18, 267-293, 1995. doi:10.1002/mma.1670180403
20. Ma, , Y.-K., , P.-S. Kim, and W.-K. Park, "Analysis of topological derivative function for a fast electromagnetic imaging of perfectly conducing cracks," Progress In Electromagnetics Research, Vol. 122, 311-325, 2012.. doi:10.2528/PIER11092901
21. Nazarchuk, Z. T., "Singular Integral Equations in Diffraction Theory," Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences , Vol. 210, 1994..
22. Park, , W.-K., "Non-iterative imaging of thin electromagnetic inclusions from multi-frequency response matrix," Progress In Electromagnetics Research, Vol. 106, 225-241, 2010. doi:10.2528/PIER10052506
23. Park, W.-K., "On the imaging of thin dielectric inclusions buried within a half-space ," Inverse Problems, Vol. 26, 074008, 2010. doi:10.1088/0266-5611/26/7/074008
24. Park, , W.-K., "On the imaging of thin dielectric inclusions via topological derivative concept," Progress In Electromagnetics Research, Vol. 110, 237-252, 2010. doi:10.2528/PIER10101305
25. Park, , W.-K., , "Topological derivative strategy for one-step iteration imaging of arbitrary shaped thin, curve-like electromagnetic inclusions," J. Comput. Phys., Vol. 231, 1426-1439, 2012. doi:10.1016/j.jcp.2011.10.014
26. Park, , W.-K. , D. Lesselier, and , "Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency," J. Comput. Phys., Vol. 228, 8093-8111, 2009. doi:10.1016/j.jcp.2009.07.026
27. Park, , W.-K. and D. Lesselier, "Fast electromagnetic imaging of thin inclusions in half-space affected by random scatterers," Waves Random Complex Media, Vol. 22, 3-23, 2012. doi:10.1080/17455030.2010.536854
28. Park, , W.-K., D. Lesselier, and , "MUSIC-type imaging of a thin penetrable inclusion from its far-field multi-static response matrix," Inverse Problems, Vol. 25, 075002, 2009.. doi:10.1088/0266-5611/25/7/075002
29. Pouramadi, M., M. Nakhkash, and A. A. Tadion, "Application of Mdl criterion for microwave imaging by MUSIC algorithm," Progress In Electromagnetics Research B, Vol. 40, 261-278, 2012.
31. Solimene, R., A. Dell'Aversano, and G. Leone, "Interferometric time reversal MUSIC for small scatterer localization," Progress In Electromagnetics Research, Vol. 131, 243-258, 2012.
32. Wei, , S.-J., , X.-L. Zhang, and J. Shi, "Linear array SAR imaging via compressed sensing," Progress In Electromagnetics Research,, Vol. 117, 299-319, 2011.
33. Yang, , M. , G. Zhang, and , "Unsupervised target detection in SAR images using scattering center model and mean shift clustering algorithm," Progress In Electromagnetics Research Letters, Vol. 35, 11-18, 2012.
34. Yu, L. and Y. Zhang, "A 3D target imaging algorithm based on two-pass circular SAR observations," Progress In Electromagnetics Research,, Vol. 122, 341-360, 2012. doi:10.2528/PIER11101901
35. Zhang, , M., , Y. W. Zhao, H. Chen, and W.-Q. Jiang, "SAR imaging simulation for composite model of ship on dynamic ocean ccene," Progress In Electromagnetics Research, Vol. 113, 395-412, 2011. doi:10.2528/PIER11071501
36. Zhang, , X., G. Feng, and D. Xu, "Blind direction of angle and time delay estimation algorithm for uniform linear array employing multi-invariance MUSIC," Progress In Electromagnetics Research Letters, Vol. 13, 11-20, 2010. doi:10.2528/PIERL09102611
37. Zhang, W., , A. Hoorfar, and L. Li, "Through-the-wall target localization with time reversal MUSIC method," Progress In Electromagnetics Research, Vol. 106, 75-89, 2010. doi:10.2528/PIER10052408