Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016, Article ID 7872548, 12 pages
http://dx.doi.org/10.1155/2016/7872548
Research Article

Interpretation of MUSIC for Location Detecting of Small Inhomogeneities Surrounded by Random Scatterers

Department of Mathematics, Kookmin University, Seoul 02707, Republic of Korea

Received 27 October 2015; Revised 5 January 2016; Accepted 6 January 2016

Academic Editor: Eric Florentin

Copyright © 2016 Won-Kwang Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems, vol. 15, no. 2, pp. R41–R93, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. H. Ammari, G. Bao, and J. L. Fleming, “An inverse source problem for Maxwell's equations in magnetoencephalography,” SIAM Journal on Applied Mathematics, vol. 62, no. 4, pp. 1369–1382, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. A. S. Fokas, Y. Kurylev, and V. Marinakis, “The unique determination of neuronal currents in the brain via magnetoencephalography,” Inverse Problems, vol. 20, no. 4, pp. 1067–1082, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. Y. T. Kim, I. Doh, B. Ahn, and K.-Y. Kim, “Construction of static 3D ultrasonography image by radiation beam tracking method from 1D array probe,” Journal of the Korean Society for Nondestructive Testing, vol. 35, no. 2, pp. 128–133, 2015. View at Publisher · View at Google Scholar
  5. S.-H. Son, H.-J. Kim, K.-J. Lee et al., “Experimental measurement system for 3–6 GHz microwave breast tomography,” Journal of Electromagnetic Engineering and Science, vol. 15, no. 4, pp. 250–257, 2015. View at Google Scholar
  6. H. Ammari, E. Iakovleva, and D. Lesselier, “Two numerical methods for recovering small inclusions from the scattering amplitude at a fixed frequency,” SIAM Journal on Scientific Computing, vol. 27, no. 1, pp. 130–158, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM Journal on Scientific Computing, vol. 29, no. 2, pp. 674–709, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-D inclusion in half space and MUSIC imaging,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 9, pp. 2598–2609, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 12, pp. 3542–3549, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. H. Ammari, 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,” Multiscale Modeling & Simulation, vol. 3, no. 3, pp. 597–628, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. R. Griesmaier, “Reciprocity gap MUSIC imaging for an inverse scattering problem in two layered media,” Inverse Problems and Imaging, vol. 3, no. 3, pp. 389–403, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  12. R. Song, R. Chen, and X. Chen, “Imaging three-dimensional anisotropic scatterers in multilayered medium by multiple signal classification method with enhanced resolution,” Journal of the Optical Society of America A, vol. 29, no. 9, pp. 1900–1905, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. H. Ammari, J. Garnier, H. Kang, W.-K. Park, and K. Sølna, “Imaging schemes for perfectly conducting cracks,” SIAM Journal on Applied Mathematics, vol. 71, no. 1, pp. 68–91, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. H. Ammari, H. Kang, H. Lee, and W.-K. Park, “Asymptotic imaging of perfectly conducting cracks,” SIAM Journal on Scientific Computing, vol. 32, no. 2, pp. 894–922, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. H. Ammari, H. Kang, E. Kim, M. Lim, and K. Louati, “A direct algorithm for ultrasound imaging of internal corrosion,” SIAM Journal on Numerical Analysis, vol. 49, no. 3, pp. 1177–1193, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. C. Y. Ahn, K. Jeon, and W.-K. Park, “Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem,” Journal of Computational Physics, vol. 291, pp. 198–217, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  17. W.-K. Park, “Asymptotic properties of MUSIC-type imaging in two-dimensional inverse scattering from thin electromagnetic inclusions,” SIAM Journal on Applied Mathematics, vol. 75, no. 1, pp. 209–228, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  18. W.-K. Park and D. Lesselier, “MUSIC-type imaging of a thin penetrable inclusion from its multi-static response matrix,” Inverse Problems, vol. 25, no. 7, Article ID 075002, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. H. Ammari, J. Garnier, H. Kang, M. Lim, and K. Sølna, “Multistatic imaging of extended targets,” SIAM Journal on Imaging Sciences, vol. 5, no. 2, pp. 564–600, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. S. Hou, K. Sølna, and H. Zhao, “A direct imaging algorithm for extended targets,” Inverse Problems, vol. 22, no. 4, pp. 1151–1178, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. S. Hou, K. Sølna, and H. Zhao, “A direct imaging method using far-field data,” Inverse Problems, vol. 23, no. 4, pp. 1533–1546, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. B. Scholz, “Towards virtual electrical breast biopsy: space-frequency MUSIC for trans-admittance data,” IEEE Transactions on Medical Imaging, vol. 21, no. 6, pp. 588–595, 2002. View at Publisher · View at Google Scholar · View at Scopus
  23. H. Ammari and H. Kang, Reconstruction of Small Inhomogeneities from Boundary Measurements, vol. 1846 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  24. M. Cheney, “The linear sampling method and the MUSIC algorithm,” Inverse Problems, vol. 17, no. 4, pp. 591–595, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. B. Chen, J. J. Stamnes, A. J. Devaney, H. M. Pedersen, and K. Stamnes, “Two-dimensional optical diffraction tomography for objects embedded in a random medium,” Pure and Applied Optics: Journal of the European Optical Society Part A, vol. 7, no. 5, pp. 1181–1199, 1998. View at Publisher · View at Google Scholar · View at Scopus
  26. L. Borcea, G. Papanicolaou, C. Tsogka, and J. Berryman, “Imaging and time reversal in random media,” Inverse Problems, vol. 18, no. 5, pp. 1247–1279, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. A. Kirsch, “The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media,” Inverse Problems, vol. 18, no. 4, pp. 1025–1040, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. B. M. Shevtsov, “Backscattering and inverse problem in random media,” Journal of Mathematical Physics, vol. 40, no. 9, pp. 4359–4373, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. X. Chen, “Multiple signal classification method for detecting point-like scatterers embedded in an inhomogeneous background medium,” Journal of the Acoustical Society of America, vol. 127, no. 4, pp. 2392–2397, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. T. Rao and X. Chen, “Analysis of the time-reversal operator for a single cylinder under two-dimensional settings,” Journal of Electromagnetic Waves and Applications, vol. 20, no. 15, pp. 2153–2165, 2006. View at Publisher · View at Google Scholar · View at Scopus
  31. E. Beretta and E. Francini, “Asymptotic formulas for perturbations of the electromagnetic fields in the presence of thin imperfections,” Contemporary Mathematics, vol. 333, pp. 49–63, 2003. View at Google Scholar
  32. W.-K. Park, “Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems,” Journal of Computational Physics, vol. 283, pp. 52–80, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. W.-K. Park, “Analysis of a multi-frequency electromagnetic imaging functional for thin, crack-like electromagnetic inclusions,” Applied Numerical Mathematics, vol. 77, pp. 31–42, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. Y.-D. Joh and W.-K. Park, “Structural behavior of the MUSIC-type algorithm for imaging perfectly conducting cracks,” Progress in Electromagnetics Research, vol. 138, pp. 211–226, 2013. View at Publisher · View at Google Scholar · View at Scopus
  35. D. Colton, H. Haddar, and P. Monk, “The linear sampling method for solving the electromagnetic inverse scattering problem,” SIAM Journal on Scientific Computing, vol. 24, no. 3, pp. 719–731, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. H. Haddar and P. Monk, “The linear sampling method for solving the electromagnetic inverse medium problem,” Inverse Problems, vol. 18, no. 3, pp. 891–906, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. A. Kirsch and S. Ritter, “A linear sampling method for inverse scattering from an open arc,” Inverse Problems, vol. 16, no. 1, pp. 89–105, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. Y.-D. Joh and W.-K. Park, “Analysis of multi-frequency subspace migration weighted by natural logarithmic function for fast imaging of two-dimensional thin, arc-like electromagnetic inhomogeneities,” Computers & Mathematics with Applications, vol. 68, no. 12, pp. 1892–1904, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. J. Li, H. Liu, and J. Zou, “Locating multiple multiscale acoustic scatterers,” Multiscale Modeling & Simulation, vol. 12, no. 3, pp. 927–952, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. K. Ito, B. Jin, and J. Zou, “A direct sampling method for inverse electromagnetic medium scattering,” Inverse Problems, vol. 29, no. 9, Article ID 095018, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. K. Ito, B. Jin, and J. Zou, “A direct sampling method to an inverse medium scattering problem,” Inverse Problems, vol. 28, no. 2, Article ID 025003, 2012. View at Publisher · View at Google Scholar