Journal of electromagnetic engineering and science

  • 제11권1호
  • /
  • Pages.56-61
  • /
  • 2011
  • /
  • 2671-7255(pISSN)
  • /
  • 2671-7263(eISSN)
한국전자파학회 (The Korean Institute of Electromagnetic Engineering and Science)
권호 표지
DOI QR코드

DOI QR Code

Topological Derivative for Fast Imaging of Two-Dimensional Thin Dielectric Inclusions in The Wave Propagation Environment

  • Park, Won-Kwang (Department of Mathematics, The College of Natural Sciences, Kookmin University)
  • 투고 : 2010.11.26
  • 심사 : 2011.02.15
  • 발행 : 2011.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we consider the topological derivative concept for developing a fast imaging algorithm of thin inclusions with dielectric contrast with respect to an embedding homogeneous domain with a smooth boundary. The topological derivative is evaluated by applying asymptotic expansion formulas in the presence of small, perfectly conducting cracks. Through the careful derivation, we can design a one-iteration imaging algorithm by solving an adjoint problem. Numerical experiments verify that this algorithm is fast, effective, and stable.

키워드

참고문헌

  1. D. Alvarez, O. Dorn, N. Irishina, and M. Moscoso, "Crack reconstruction using a level-set strategy," J. Comput. Phys., vol. 228, pp. 5710-5721, 2009. https://doi.org/10.1016/j.jcp.2009.04.038
  2. F. Delbary, K. Erhard, R. Kress, R. Potthast and J. Schulz, "Inverse electromagnetic scattering in a twolayered medium with an application to mine detection," Inverse Problems, vol. 24, 015002, 2008. https://doi.org/10.1088/0266-5611/24/1/015002
  3. O. Dorn, D. Lesselier, "Level set methods for inverse scattering," Inverse Problems, vol. 22, R67-R131, 2006. https://doi.org/10.1088/0266-5611/22/4/R01
  4. W.-K. Park, D. Lesselier, "Reconstruction of thin electromagnetic inclusions by a level set method," Inverse Problems, vol. 25, 085010, 2009. https://doi.org/10.1088/0266-5611/25/8/085010
  5. M. Cheney, "The linear sampling method and the MUSIC algorithm," Inverse Problems, vol. 17, pp. 591-595, 2001. https://doi.org/10.1088/0266-5611/17/4/301
  6. D. Colton, H. Haddar, and P. Monk, "The linear sampling method for solving the electromagnetic inverse scattering problem," SIAM J. Sci. Comput., vol. 24, pp. 719-731, 2002.
  7. W.-K. Park, D. Lesselier, "Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency," J. Comput. Phys., vol. 228, pp. 8093-8111, 2009. https://doi.org/10.1016/j.jcp.2009.07.026
  8. W.-K. Park, D. Lesselier, "MUSIC-type imaging of a thin penetrable inclusion from its far-field multi-static response matrix," Inverse Problems, vol. 25, 075002, 2009. https://doi.org/10.1088/0266-5611/25/7/075002
  9. W.-K. Park, "Non-iterative imaging of thin electromagnetic inclusions from multi-frequency response matrix," Progress in Electromagnetic Research, vol. 106, pp. 225-241, 2010. https://doi.org/10.2528/PIER10052506
  10. W.-K. Park, "On the imaging of thin dielectric inclusions buried within a half-space," Inverse Problems, vol. 26, 074008, 2010. https://doi.org/10.1088/0266-5611/26/7/074008
  11. H. Ammari, H. Kang, H. Lee, and W.-K. Park, "Asymptotic imaging of perfectly conducting cracks," SIAM J. Sci. Comput., vol. 32, pp. 894-922, 2010. https://doi.org/10.1137/090749013
  12. D. Auroux, M. Masmoudi, "Image processing by topological asymptotic analysis," ESAIM Proc., vol. 26, pp. 24-44, 2009. https://doi.org/10.1051/proc/2009003
  13. A. Capiro, M.-L. Rapun, "Solving inhomogeneous inverse problems by topological derivative methods," Inverse Problems, vol. 24, 045014, 2008. https://doi.org/10.1088/0266-5611/24/4/045014
  14. H. A. Eschenauer, V. V. Kobelev, and A. Schumacher, "Bubble method for topology and shape optimization of structuresn," Struct. Optim., vol. 8, pp. 42-51, 1994. https://doi.org/10.1007/BF01742933
  15. J. Sokolowski, A. Zochowski, "On the topological derivative in shape optimization," SIAM J. Control Optim., vol. 37, pp. 1251-1272, 1999. https://doi.org/10.1137/S0363012997323230
  16. W.-K. Park, "On the imaging of thin dielectric inclusions via topological derivative concept," Progress in Electromagnetic Research, vol. 110, pp. 237-252, 2010. https://doi.org/10.2528/PIER10101305

피인용 문헌

  1. Shape Reconstruction of Thin Electromagnetic Inclusions via Boundary Measurements: Level-Set Method Combined with the Topological Derivative vol.2013, 2013, https://doi.org/10.1155/2013/125909
  2. Improved subspace migration for imaging of small and arc-like perfectly conducting cracks vol.28, pp.4, 2014, https://doi.org/10.1080/09205071.2013.866526