PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 136 > pp. 607-622

STRUCTURE ANALYSIS OF SINGLE- AND 2 MULTI-FREQUENCY SUBSPACE MIGRATIONS IN 3 INVERSE SCATTERING PROBLEMS

By Y.-D. Joh, Y. M. Kwon, J. Y. Huh, and W.-K. Park

Full Article PDF (404 KB)

Abstract:
We carefully investigate the structure of single- and multi frequency imaging functions, that are usually employed in inverse scattering problems. Based on patterns of the singular vectors of the Multi-Static Response (MSR) matrix, we establish a relationship between imaging functions and the Bessel function. This relationship indicates certain properties of imaging functions and the reason behind enhancement in the imaging performance by multiple frequencies. Several numerical simulations with a large amount of noisy data are performed in order to support our investigation.

Citation:
Y.-D. Joh, Y. M. Kwon, J. Y. Huh, and W.-K. Park, "Structure Analysis of Single- and 2 Multi-Frequency Subspace Migrations in 3 Inverse Scattering Problems," Progress In Electromagnetics Research, Vol. 136, 607-622, 2013.
doi:10.2528/PIER12120313
http://www.jpier.org/PIER/pier.php?paper=12120313

References:
1. Álvarez, D., O. Dorn, N. Irishina, and M. Moscoso, "Crack reconstruction using a level-set strategy," J. Comput. Phys., Vol. 228, 5710-5721, 2009.
doi:10.1016/j.jcp.2009.04.038

2. Ammari, H., "Mathematical Modeling in Biomedical Imaging II: Optical, Ultrasound, and Opto-Acoustic Tomographies," Lecture Notes in Mathematics: Mathematical Biosciences Subseries, Vol. 2035, Springer-Verlag, Berlin, 2011.

3. 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

4. Ammari, H., J. Garnier, H. Kang, W.-K. Park, and K. Sølna, "Imaging schemes for perfectly conducting cracks," SIAM J. Appl. Math., Vol. 71, 68-91, 2011.
doi:10.1137/100800130

5. Ammari, H. and H. Kang, "Reconstruction of Small Inhomogeneities from Boundary Measurements," Lecture Notes in Mathematics, Vol. 1846, Springer-Verlag, Berlin, 2004.

6. 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

7. Chen, X., "Subspace-based optimization method in electric impedance tomography ," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 11-12, 1397-1406, 2009.
doi:10.1163/156939309789476301

8. Cheney, M., "The linear sampling method and the MUSIC algorithm," Inverse Problems, Vol. 17, 591-595, 2001.
doi:10.1088/0266-5611/17/4/301

9. Delbary, F., K. Erhard, R. Kress, R. Potthast, and J. Schulz, "Inverse electromagnetic scattering in a two-layered medium with an application to mine detection," Inverse Problems, Vol. 24, 015002, 2008.
doi:10.1088/0266-5611/24/1/015002

10. Donelli, M., "A rescue radar system for the detection of victims trapped under rubble based on the independent component analysis algorithm," Progress In Electromagnetic Research M, Vol. 19, 173-181, 2011.
doi:10.2528/PIERM11061206

11. Donelli, M., I. J. Craddock, D. Gibbins, and M. Sarafianou, "A three-dimensional time domain microwave imaging method for breast cancer detection based on an evolutionary algorithm," Progress In Electromagnetic Research M, Vol. 18, 179-195, 2011.

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.

13. Dorn, O. and D. Lesselier, "Level set methods for inverse scattering," Inverse Problems, Vol. 22, R67-R131, 2006.
doi:10.1088/0266-5611/22/4/R01

14. 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

15. Hou, S., K. Huang, K. Sølna, and H. Zhao, "A phase and space coherent direct imaging method," J. Acoust. Soc. Am., Vol. 125, 227-238, 2009.
doi:10.1121/1.3035835

16. Kwon, O., J. K. Seo, and J.-R. Yoon, "A real-time algorithm for the location search of discontinuous conductivities with one measurement," Commun. Pur. Appl. Math., Vol. 55, 1-29, 2002.
doi:10.1002/cpa.3009

17. Lesselier, D. and B. Duchene, "Buried, 2-D penetrable objects illuminated by line sources: FFT-based iterative computations of the anomalous field," Progress In Electromagnetic Research, Vol. 5, 351-389, 1991.

18. 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

19. 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

20. 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

21. 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

22. 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

23. Park, W.-K. and D. Lesselier, "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

24. 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

25. Park, W.-K. and D. Lesselier, "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

26. Park, W.-K. and D. Lesselier, "Reconstruction of thin electromagnetic inclusions by a level set method," Inverse Problems, Vol. 25, 085010, 2009.
doi:10.1088/0266-5611/25/8/085010

27. Rosenheinrich, W., Tables of some indefinite integrals of bessel functions, Available at http://www.fh-jena.de/ rsh/Forschung/Stoer/besint.pdf.

28. 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.

29. Solimene, R., A. Buonanno, and R. Pierri, "Imaging small PEC spheres by a linear delta-approach," IEEE Trans. on Eosci. Remote, Vol. 46, 3010-3018, 2008.
doi:10.1109/TGRS.2008.919273

30. Solimene, R., A. Buonanno, F. Soldovieri, and R. Pierri, "Physical optics imaging of 3D PEC objects: Vector and multipolarized approaches," IEEE Trans. on Eosci. Remote, Vol. 48, 1799-1808, 2010.
doi:10.1109/TGRS.2009.2035053

31. Tsang, L., J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations, Wiley, New York, 2001.

32. Zhu, G. K. and M. Popovic, "Comparison of radar and thermoacoustic technique in microwave breast imaging," Progress In Electromagnetics Research B, Vol. 35, 1-14, 2011.
doi:10.2528/PIERB11080204


© Copyright 2014 EMW Publishing. All Rights Reserved