Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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APPLICATION OF THE BIFOCUSING METHOD IN MICROWAVE IMAGING WITHOUT BACKGROUND INFORMATION

  • SEONG-HO SON (DEPARTMENT OF MECHANICAL ENGINEERING, SOONCHUNHYANG UNIVERSITY) ;
  • WON-KWANG PARK (DEPARTMENT OF INFORMATION SECURITY, CRYPTOLOGY, AND MATHEMATICS, KOOKMIN UNIVERSITY)
  • Received : 2023.05.08
  • Accepted : 2023.06.20
  • Published : 2023.06.25
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Abstract

In this study, we consider the application of the bifocusing method (BFM) for identifying the locations and shapes of small anomalies from scattering parameter data when the exact values of background permittivity and conductivity are unknown. To this end, an imaging function using numerical focusing operator is introduced and its mathematical structure is revealed by establishing a relationship with an infinite series of Bessel functions, antenna arrangements, and anomaly properties. On the basis of the revealed structure, we demonstrate why inaccurate location and size of anomalies were retrieved via the BFM. Some simulation results are illustrated using synthetic data polluted by random noise to support the theoretical result.

Keywords

Acknowledgement

This research was supported by the Soonchunhyang University Research Fund and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2020R1A2C1A01005221).

References

  1. K. Ito, B. Jin, and J. Zou, A direct sampling method to an inverse medium scattering problem, Inverse Problems, 28 (2012), Article No. 025003.
  2. S. Kang, M. Lambert, and W.-K. Park, Direct sampling method for imaging small dielectric inhomogeneities: analysis and improvement, Inverse Problems, 34 (2018), Article No. 095005.
  3. S.-H. Son, K.-J. Lee, and W.-K. Park, Application and analysis of direct sampling method in real-world microwave imaging, Applied Mathematics Letters, 96 (2019), 47-53. https://doi.org/10.1016/j.aml.2019.04.016
  4. S. Cosgun, E. Bilgin, and M. Cayoren, Microwave imaging of breast cancer with factorization method: SPI-ONs as contrast agent, Medical Physics, 47 (2020), 3113-3122. https://doi.org/10.1002/mp.14156
  5. J. Guo, G. Yan, J. Jin, and J. Hu, The factorization method for cracks in inhomogeneous media, Applications of Mathematics, 62 (2017), 509-533. https://doi.org/10.21136/AM.2017.0194-16
  6. K. H. Leem, J. Liu, and G. Pelekanos, An extended direct factorization method for inverse scattering with limited aperture data, Inverse Problems in Science and Engineering, 28 (2020), 754-776. https://doi.org/10.1080/17415977.2019.1647195
  7. H. Ammari, J. Garnier, H. Kang, W.-K. Park, and K. Solna, Imaging schemes for perfectly conducting cracks, SIAM Journal on Applied Mathematics, 71 (2011), 68-91. https://doi.org/10.1137/100800130
  8. H. Ammari, J. Garnier, H. Kang, M. Lim, and K. Solna, Multistatic imaging of extended targets, SIAM Journal on Imaging Sciences, 5 (2012), 564-600. https://doi.org/10.1137/10080631X
  9. W.-K. Park, Real-time microwave imaging of unknown anomalies via scattering matrix, Mechanical Systems and Signal Processing, 118 (2019), 658-674. https://doi.org/10.1016/j.ymssp.2018.09.012
  10. H. F Alqadah, A compressive multi-frequency linear sampling method for underwater acoustic imaging, IEEE Transactions on Image Processing, 25 (2016), 2444-2455. https://doi.org/10.1109/TIP.2016.2548243
  11. L. Audibert and H. Haddar, The generalized linear sampling method for limited aperture measurements, SIAM Journal on Imaging Sciences, 10 (2017), 845-870. https://doi.org/10.1137/16M110112X
  12. M. G. Aram, M. Haghparast, M. S. Abrishamian, and A. Mirtaheri, Comparison of imaging quality between linear sampling method and time reversal in microwave imaging problems, Inverse Problems in Science and Engineering, 24 (2016), 1347-1363. https://doi.org/10.1080/17415977.2015.1104308
  13. Q. Bao, S. Yuan, and F. Guo, A new synthesis aperture-MUSIC algorithm for damage diagnosis on complex aircraft structures, Mechanical Systems and Signal Processing, 136 (2010), Article No. 106491.
  14. W.-K. Park, Asymptotic properties of MUSIC-type imaging in two-dimensional inverse scattering from thin electromagnetic inclusions, SIAM Journal on Applied Mathematics, 75 (2015), 209-228. https://doi.org/10.1137/140975176
  15. W.-K. Park, Application of MUSIC algorithm in real-world microwave imaging of unknown anomalies from scattering matrix, Mechanical Systems and Signal Processing, 153 (2021), Article No. 107501.
  16. M. N. Akinci, M. Cayoren, and I. Akduman, Near-field orthogonality sampling method for microwave imaging: theory and experimental verification, IEEE Transactions on Microwave Theory and Techniques, 64 (2016), 2489-2501. https://doi.org/10.1109/TMTT.2016.2585488
  17. M. T. Bevacqua, T. Isernia, R. Palmeri, M. N. Akinci, and L. Crocco, Physical insight unveils new imaging capabilities of orthogonality sampling method, IEEE Transactions on Antennas and Propagation, 68 (2020), 4014-4021. https://doi.org/10.1109/TAP.2019.2963229
  18. W.-K. Park, On the application of orthogonality sampling method for object detection in microwave imaging, IEEE Transactions on Antennas and Propagation, 71 (2023), 934-946.
  19. M. Bonnet, Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems, Engineering Analysis with Boundary Elements, 35 (2011), 223-235. https://doi.org/10.1016/j.enganabound.2010.08.007
  20. F. Le Louer and M.-L. Rapun, Topological sensitivity for solving inverse multiple scattering problems in 3D electromagnetism. Part I: one step method, SIAM Journal on Imaging Sciences, 10 (2017), 1291-1321. https://doi.org/10.1137/17M1113850
  21. W.-K. Park, Performance analysis of multi-frequency topological derivative for reconstructing perfectly conducting cracks, Journal of Computational Physics, 335 (2017), 865-884. https://doi.org/10.1016/j.jcp.2017.02.007
  22. H. Ammari, J. Garnier, W. Jing, H. Kang, M. Lim, K. Solna, and H. Wang, Mathematical and statistical methods for multistatic imaging,Lecture Notes in Mathematics 2098, Springer, Cham, 2013.
  23. H. Ammari and H. Kang, Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics 1846, Springer-Verlag, Berlin, 2004.
  24. N. Bleistein, J. Cohen, and J. S. Stockwell Jr, Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion, Interdisciplinary Applied Mathematics 13, Springer, New York, 2001.
  25. V. S. Chernyak, Fundamentals of Multisite Radar Systems: Multistatic Radars and Multiradar Systems, CRC Press, Routledge, 1998.
  26. F. Cakoni, D. Colton, and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering,CBMS-NSF Regional Conference Series in Applied Mathematics 80, Society for Industrial and Applied Mathematics, 2011.
  27. A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford University Press, 2008.
  28. A. A. Novotny and J. Sokolowski, Topological derivatives in shape optimization, Interaction of Mechanics and Mathematics Series, Springer-Verlag, Berlin, Heidelberg, 2013.
  29. L. Jofre, A. Broquetas, J. Romeu, S. Blanch, A. P. Toda, X. Fabregas, and A. Cardama, UWB tomographic radar imaging of penetrable and impenetrable objects, Proceedings of the IEEE, 97 (2009), 451-464. https://doi.org/10.1109/JPROC.2008.2008854
  30. Y. J. Kim, L. Jofre, F. De Flaviis, and M. Q. Feng, Microwave reflection tomographic array for damage detection of civil structures, IEEE Transactions on Antennas and Propagation, 51 (2003), 3022-3032. https://doi.org/10.1109/TAP.2003.818786
  31. S. Kang, W.-K. Park, and S.-H. Son, A qualitative analysis of the bifocusing method for a real-time anomaly detection in microwave imaging, Computers and Mathematics with Applications, 137 (2023), 93-101.
  32. M. Slaney, A. C. Kak, and L. E. Larsen, Limitations of imaging with first-order diffraction tomography, IEEE Transactions on Microwave Theory and Techniques, 32 (1984), 860-874. https://doi.org/10.1109/TMTT.1984.1132783
  33. W.-K. Park, H. P. Kim, K.-J. Lee, and S.-H. Son, MUSIC algorithm for location searching of dielectric anomalies from S-parameters using microwave imaging, Journal of Computational Physics, 348 (2017), 259-270. https://doi.org/10.1016/j.jcp.2017.07.035
  34. M. Haynes, J. Stang, and M. Moghaddam, Real-time microwave imaging of differential temperature for thermal therapy monitoring, IEEE Transactions on Biomedical Engineering, 61 (2014), 1787-1797. https://doi.org/10.1109/TBME.2014.2307072
  35. J.-Y. Kim, K.-J. Lee, B.-R. Kim, S.-I. Jeon, and S.-H. Son, Numerical and experimental assessments of focused microwave thermotherapy system at 925 MHz, ETRI Journal, 41 (2019), 850-862. https://doi.org/10.4218/etrij.2018-0088
  36. S.-H. Son, N. Simonov, H.-J. Kim, J.-M. Lee, and S.-I. Jeon, Preclinical prototype development of a microwave tomography system for breast cancer detection, ETRI Journal, 32 (2010), 901-910. https://doi.org/10.4218/etrij.10.0109.0626
  37. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Problems, Mathematics and Applications Series 93, Springer, New York, 1998.