PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 106 > pp. 225-241

NON-ITERATIVE IMAGING OF THIN ELECTROMAGNETIC INCLUSIONS FROM MULTI-FREQUENCY RESPONSE MATRIX

By W.-K. Park

Full Article PDF (322 KB)

Abstract:
Although MUSIC (MUltiple SIgnal Classification)-type algorithm has shown feasibilities as a non-iterative imaging technique of thin penetrable electromagnetic inclusion from its far-field multi-static response (MSR) matrix, it induces a poor result whenever one tries to obtain such inclusion of both dielectric and magnetic contrast with respect to the embedding homogeneous space R2 case. In this paper, we develop an improved non-iterative imaging algorithm based on the modeling of multi-frequency MSR matrix according to a rigorous asymptotic expansion of the scattering amplitude. Numerical examples exhibit that presented algorithm performs satisfactorily for single and multiple thin inclusions, even with a fair amount of random noise.

Citation:
W.-K. Park, "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
http://www.jpier.org/PIER/pier.php?paper=10052506

References:
1. Alvarez, 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., An Introduction to Mathematics of Emerging Biomedical Imaging, Vol. 62, Mathematics and Applications Series, Springer-Verlag, Berlin, 2008.

3. Ammari, H., J. Garnier, H. Kang, W. K. Park, and K. Solna, "Imaging schemes for perfectly conducting cracks,", submitted.

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

6. Beretta, E. and E. Francini, "Asymptotic formulas for perturbations of the electromagnetic fields in the presence of thin imperfections," Contemp. Math., Vol. 333, 49-63, 2003.

7. Capdeboscq, Y. and M. Vogelius, "Imagerie electromagnetique de petites inhomogeneites," ESAIM: Proc., Vol. 22, 40-51, 2008.
doi:10.1051/proc:072204

8. Chen, X.-D., "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

9. 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

10. Cheng, X., B.-I.Wu, H. Chen, and J. A. Kong, "Imaging of objects through lossy layer with defects," Progress In Electromagnetics Research, Vol. 84, 11-26, 2008.
doi:10.2528/PIER08052302

11. Chien, W., "Inverse scattering of an un-uniform conductivity scatterer buried in a three-layer structure," Progress In Electromagnetics Research, Vol. 82, 1-18, 2008.
doi:10.2528/PIER08012902

12. Conceicao, R. C., M. O'Halloran, M. Glavin, and E. Jones, "Comparison of planar and circular antenna configurations for breast cancer detection using microwave imaging," Progress In Electromagnetics Research, Vol. 99, 1-20, 2009.
doi:10.2528/PIER09100204

13. Davy, M., J.-G. Minonzio, J. de Rosny, C. Prada, and M. Fink, "Influence of noise on subwavelength imaging of two close scatterers using time reversal method: Theory and experiments," Progress In Electromagnetics Research, Vol. 98, 333-358, 2009.
doi:10.2528/PIER09071004

14. 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

15. 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

16. Fannjiang, A. and K. Solna, "Broadband resolution analysis for imaging with measurement noise," J. Opt. Soc. Am. A, Vol. 24, 1623-1632, 2007.
doi:10.1364/JOSAA.24.001623

17. Hou, S., K. Huang, K. Solna, and H. Zhao, "A phase and space coherent direct imaging method," J. Acoust. Soc. Am., Vol. 125, No. 1, 227-238, 2009.
doi:10.1121/1.3035835

18. Hou, S., K. Solna, and H. Zhao, "A direct imaging algorithm for extended targets," Inverse Problems, Vol. 22, 1151-1178, 2006.
doi:10.1088/0266-5611/22/4/003

19. Kay, S. M., Fundamentals of Statistical Signal Processing, Detection Theory, Prentice Hall, 1998.

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

21. Li, F., X. Chen, and K. Huang, "Microwave imaging a buried object by the GA and using the S11 parameter," Progress In Electromagnetics Research, Vol. 85, 289-302, 2008.
doi:10.2528/PIER08081401

22. Nazarchuk, Z. T. and K. Kobayashi, "Mathematical modelling of electromagnetic scattering from a thin penetrable target," Progress In Electromagnetics Research, Vol. 55, 95-116, 2005.
doi:10.2528/PIER05022003

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. 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

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. Raza, M. I. and R. E. DuBroff, "Detecting dissimilarities in EM constitutive parameters using differential imaging operator on reconstructed wavefield," Progress In Electromagnetics Research, Vol. 98, 267-282, 2009.
doi:10.2528/PIER09092403

28. Semnani, A. and M. Kamyab, "Truncated cosine Fourier series expansion method for solving 2-D inverse scattering problems," Progress In Electromagnetics Research, Vol. 81, 73-97, 2008.
doi:10.2528/PIER07122404

29. Solimene, R., A. Brancaccio, R. Pierri, and F. Soldovieri, "TWI experimental results by a linear inverse scattering approach," Progress In Electromagnetics Research, Vol. 91, 259-272, 2009.
doi:10.2528/PIER09021609

30. Zhou, H., T. Takenaka, J. Johnson, and T. Tanaka, "A breast imaging model using microwaves and a time domain three dimensional reconstruction method," Progress In Electromagnetics Research, Vol. 93, 57-70, 2009.
doi:10.2528/PIER09033001


© Copyright 2014 EMW Publishing. All Rights Reserved