In this paper, we consider the imaging of thin dielectric inclusions completed embedded in the homogeneous domain. To image such inclusion from boundary measurements, topological derivation concept is adopted. For that purpose, an asymptotic expansion of the boundary perturbations that are due to the presence of a small inclusion is considered. Applying this formula, we can design only one iteration procedure for imaging of thin inclusions by means of solving adjoint problem. Various numerical experiments without and with some noise show how the proposed techniques behave
2. Ammari, H., An Introduction to Mathematics of Emerging Biomedical Imaging, Vol. 62, Mathematics and Applications Series, Springer-Verlag, Berlin, 2008.
3. 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.
4. Ammari, H. and H. Kang, Reconstruction of Small Inhomogeneities from Boundary Measurements, Vol. 1846, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2004.
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.
6. Auroux, D. and M. Masmoudi, "Image processing by topological asymptotic analysis," ESAIM: Proc., Vol. 26, 24-44, 2009.
7. 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, 2000.
8. Carpio, A. and M.-L. Rapun, "Solving inhomogeneous inverse problems by topological derivative methods," Inverse Problems, Vol. 24, 045014, 2008.
9. Chen, X., "Subspace-based optimization method in electric impedance tomography," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 11-12, 1397-1406, 2009.
10. Cheney, M., "The linear sampling method and the MUSIC algorithm," Inverse Problems, Vol. 17, 591-595, 2001.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. Dorn, O. and D. Lesselier, "Level set methods for inverse scattering," Inverse Problems, Vol. 22, R67-R131, 2006.
17. Eschenauer, H. A., V. V. Kobelev, and A. Schumacher, "Bubble method for topology and shape optimization of structures," Struct. Optim., Vol. 8, 42-51, 1994.
18. Hou, S., K. Sølna, and H. Zhao, "A direct imaging algorithm for extended targets," Inverse Problems, Vol. 22, 1151-1178, 2006.
19. Kirsch, A. and S. Ritter, "A linear sampling method for inverse scattering from an open arc," Inverse Problems, Vol. 16, 89-105, 2000.
20. Lee, H. and W. K. Park, "Location search algorithm of thin conductivity inclusions via boundary measurements," ESAIM: Proc., Vol. 26, 217-229, 2009.
21. 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.
22. 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.
23. Nazarchuk, Z. and K. Kobayashi, "Mathematical modelling of electromagnetic scattering from a thin penetrable target," Progress In Electromagnetic Research, Vol. 55, 95-116, 2005.
24. Park, W. K., "Non-iterative imaging of thin electromagnetic inclusions from multi-frequency response matrix," Progress In Electromagnetic Research, Vol. 106, 225-241, 2010.
25. Park, W. K., "On the imaging of thin dielectric inclusions buried within a half-space," Inverse Problems, Vol. 26, 074008, 2010.
26. 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.
27. 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.
28. Park, W. K. and D. Lesselier, "Reconstruction of thin electromagnetic inclusions by a level set method," Inverse Problems, Vol. 25, 085010, 2009.
29. Ramananjaona, C., M. Lambert, D. Lesselier, and J.-P. Zolé sio, "Shape reconstruction by controlled evolution of a level set: from a min-max formulation to numerical experimentation," Inverse Problems, Vol. 17, 1087-1111, 2001.
30. 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.
31. Sokolowski, J. and A. Zochowski, "On the topological derivative in shape optimization," SIAM J. Control Optim., Vol. 37, No. 4, 1251-1272, 1999.
32. Soleimani, M., "Simultaneous reconstruction of permeability and conductivity in magnetic induction tomography," Journal of Electromagnetic Waves and Applications, Vol. 23, 785-798, 2009.
33. Zhou, H., T. Takenaka, J. E. 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.