volume | PIER Journals

Abstract

The linear sampling method (LSM) is a qualitative inverse scattering technique for reconstructing the shape of a target. It has several beneficial qualities, including the avoidance of nonlinear optimization and simplified scattering approximations. However, it often struggles when sensors can only be placed on one side of the target. In this paper, we investigate two alternative LSM formulations for overcoming the limited-aspect challenge. The first, the phase-delay frequency variation LSM (PDFV-LSM), incorporates coherent processing across frequency to improve discrimination in the range direction. The second, the phase-encoded LSM (PE-LSM), enhances the PDFV-LSM approach with a receive-beamforming operation to decrease the complexity of the inverse problem. We apply both techniques to simulated data from three-dimensional targets and three-dimensional limited-aspect arrays. We generate three-dimensional reconstructions and compare them to reconstructions from both the conventional LSM and conventional backprojection-based processing. The results demonstrate superior reconstruction fidelity for either the PDFV-LSM, the PE-LSM, or both, across a wide variety of imaging scenarios due to finer range resolution. They also demonstrate trade-offs between the two enhanced LSM techniques, with the PE-LSM achieving better range resolution and robustness to noise and the PDFV-LSM achieving better lateral resolution.

1. Chew, W. C. and Y. M. Wang, "Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method," IEEE Trans. Med. Imag., Vol. 9, No. 2, 218-225, 1990.
doi:10.1109/42.56334

2. Wang, Y. M. and W. C. Chew, "An iterative solution of the two-dimensional electromagnetic inverse scattering problem," Int. J. Imag. Syst. Technol., Vol. 1, No. 1, 100-108, 1989.
doi:10.1002/ima.1850010111

3. Cui, T. J. and W. C. Chew, "Inverse scattering of two-dimensional dielectric objects buried in a lossy Earth using the distorted Born iterative method," IEEE Trans. Geosci. Remote Sens., Vol. 39, No. 2, 339-346, 2001.
doi:10.1109/36.905242

4. Van den Berg, P. M. and A. Abubakar, "A contrast source inversion method," Inverse Problems, Vol. 13, 1607-1620, 1997.
doi:10.1088/0266-5611/13/6/013

5. Gilmore, C., P. Mojabi, and J. LoVetri, "Comparison of an enhanced distorted born iterative method and the multiplicative-regularized contrast source inversion method," IEEE Trans. Ant. Prop., Vol. 57, No. 8, 2341-2351, 2009.
doi:10.1109/TAP.2009.2024478

6. Poli, L., G. Oliveri, and A. Massa, "Imaging sparse metallic cylinders through a local shape function Bayesian compressive sensing approach," Journal of the Optical Society of America, Vol. 30, No. 6, 1261-1272, 2013.
doi:10.1364/JOSAA.30.001261

7. Takenaka, T., Z. Q. Meng, T. Tanaka, and W. C. Chew, "Local shape function combined with genetic algorithm applied to inverse scattering for strips," Microw. Opt. Technol. Lett., Vol. 16, 337-341, 1997.
doi:10.1002/(SICI)1098-2760(19971220)16:6<337::AID-MOP5>3.0.CO;2-L

8. Otto, G. P. and W. C. Chew, "Microwave inverse scattering --- local shape function imaging for improved resolution of strong scatterers," IEEE Trans. Microw. Theory Technol., Vol. 42, No. 1, 137-141, 1994.
doi:10.1109/22.265541

9. Ye, X., "Electromagnetic imaging of wave impenetrable objects," Proc. 11th Eur. Conf. Antennas Propag., 1421-1428, Paris, France, 2017.

10. Ye, X., Y. Zhong, and X. Chen, "Reconstructing perfectly electric conductors by the subspace-based optimization method with continuous variables," Inverse Problems, Vol. 27, No. 55011, 2011.

11. Shen, J., Y. Zhong, X. Chen, and L. Ran, "Inverse scattering problems of reconstructing perfectly electric conductors with TE illumination," IEEE Trans. Antennas Propag., Vol. 61, No. 9, 4713-4721, Sep. 2013.
doi:10.1109/TAP.2013.2271891

12. Bevacqua, M. and T. Isernia, "Shape reconstruction via equivalence principles, constrained inverse source problems and sparsity promotion," Progress In Electromagnetic Research, Vol. 158, 37-48, 2017.
doi:10.2528/PIER16111404

13. Bevacqua, M. and R. Palmeri, "Qualitative methods for the inverse obstacle problem: A comparison on experimental data," Journal of Imaging, Vol. 5, No. 4, 47, 2019.
doi:10.3390/jimaging5040047

14. Stevanovic, M., L. Crocco, A. Djordjevic, and A. Nehorai, "Higher order sparse microwave imaging of PEC scatterers," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 3, 988-997, 2016.
doi:10.1109/TAP.2016.2521879

15. Vojnovic, N., M. Stevanovic, L. Crocco, and A. Djordjevic, "High-order sparse shape imaging of pec and dielectric targets using TE polarized fields," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 4, 2035-2043, 2018.
doi:10.1109/TAP.2018.2809455

16. Nikolic, M. M., A. Nehorai, and A. R. Djordjevic, "Electromagnetic imaging of hidden 2-D PEC targets using sparse-signal modeling," IEEE Trans. Geosci. Remote Sens., Vol. 51, No. 5, 2707-2721, 2013.
doi:10.1109/TGRS.2012.2215042

17. Wang, F. F. and Q. H. Liu, "A Bernoulli-Gaussian binary inversion method for high-frequency electromagnetic imaging of metallic reflectors," IEEE Trans. Antennas Propag., Vol. 68, No. 4, 3184-3193, 2020.
doi:10.1109/TAP.2019.2952005

18. Soldovieri, F., A. Brancaccio, G. Leone, and R. Pierri, "Shape reconstruction of perfectly conducting objects by multiview experimental data," IEEE Trans. Geosci. Remote Sens., Vol. 43, No. 1, 65-71, 2005.
doi:10.1109/TGRS.2004.839432

19. Solimene, R., A. Buonanno, F. Soldovieri, R. Pierri, and , "Physical optics imaging of 3-D PEC objects: Vector and multipolarized approaches," IEEE Trans. Geosci. Remote Sens., Vol. 48, No. 4, 1799-1808, 2010.
doi:10.1109/TGRS.2009.2035053

20. Cakoni, F., D. Colton, and P. Monk, The Linear Sampling Method in Inverse Scattering Theory, Society for Industrial and Applied Mathematics, 2011.

21. Colton, D., H. Haddar, and M. Piana, "The linear sampling method in inverse electromagnetic scattering theory," Inverse Problems, Vol. 19, S105-S137, 2003.
doi:10.1088/0266-5611/19/6/057

22. Cakoni, F. and D. Colton, "The linear sampling method for cracks," Inverse Problems, Vol. 19, 279-295, 2003.
doi:10.1088/0266-5611/19/2/303

23. Cakoni, F., D. Colton, and H. Haddar, "The linear sampling method for anisotropic media," J. Comp. App. Math., Vol. 146, 285-299, 2002.
doi:10.1016/S0377-0427(02)00361-8

24. Catapano, I., L. Crocco, and T. Isernia, "On simple methods for shape reconstruction of unknown scatterers," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 5, 1431-1436, 2007.
doi:10.1109/TAP.2007.895563

25. Guzina, B., F. Cakoni, and C. Bellis, "On the multifrequency obstacle reconstruction via the linear sampling method," Inverse Problems, Vol. 29, 125005, 2010.
doi:10.1088/0266-5611/26/12/125005

26. Catapano, I., F. Soldovieri, and L. Crocco, "On the feasibility of the linear sampling method for 3D GPR surveys," Progress In Electromagnetics Research, Vol. 118, 185-203, 2011.
doi:10.2528/PIER11042704

27. Ambrosanio, M., M. Bevacqua, T. Isernia, and V. Pascazio, "Performance analysis of tomographic methods against experimental contactless multistatic ground penetrating radar," IEEE Journal of Selected Topics in Applied Earth Observation and Remote Sensing, Vol. 14, 1171-1183, 2021.
doi:10.1109/JSTARS.2020.3034996

28. Catapano, I., L. Crocco, and T. Isernia, "Improved sampling methods for shape reconstruction of 3-D buried targets," IEEE Transactions on Geoscience and Remote Sensing, Vol. 46, No. 10, 3265-3273, 2008.
doi:10.1109/TGRS.2008.921745

29. Cheney, M., "The linear sampling method and the MUSIC algorithm," Inverse Problems, Vol. 17, No. 4, 591-595, 2000.
doi:10.1088/0266-5611/17/4/301

30. Guo, Y., P. Monk, and D. Colton, "The linear sampling method for sparse small aperture data," Applicable Analysis, Vol. 95, No. 8, 1599-1615, 2016.
doi:10.1080/00036811.2015.1065317

31. Haddar, H., A. Lechleiter, and S. Marmorat, "An improved time domain linear sampling method for Robin and Neumann obstacles," Applicable Analysis, Vol. 93, No. 2, 369-390, 2014.
doi:10.1080/00036811.2013.772583

32. Audibert, L. and H. Haddar, "The generalized linear sampling method for limited aperture measurements," SIAM J. Imag. Sci., Vol. 10, No. 2, 845-870, 2017.
doi:10.1137/16M110112X

33. Kuo, Y.-H. and J.-F. Kiang, "Deep-learning linear sampling method for shape restoration of multilayered scatterers," Progress In Electromagnetics Research C, Vol. 124, 197-209, 2022.
doi:10.2528/PIERC22081005

34. Cakoni, F., M. Fares, and H. Haddar, "Analysis of two linear sampling methods applied to electromagnetic imaging of buried objects," Inverse Problems, Vol. 22, 845-867, 2006.
doi:10.1088/0266-5611/22/3/007

35. Burfeindt, M. and H. Alqadah, "Boundary-condition-enhanced linear sampling method imaging of conducting targets from sparse receivers," IEEE Trans. Ant. Prop., Vol. 70, No. 3, 2246-2260, 2022.
doi:10.1109/TAP.2021.3118831

36. Burfeindt, M. and H. Alqadah, "Qualitative inverse scattering for sparse-aperture data collections using a phase-delay frequency variation constraint," IEEE Transactions on Antennas and Propagation, Vol. 68, No. 11, 7530-7540, 2020.
doi:10.1109/TAP.2020.2998217

37. Burfeindt, M. and H. Alqadah, "Qualitative inverse scattering from three-dimensional limited apertures using phase-delay frequency variation regularization," Proc. IEEE Int. Symp. Ant. Prop. USNC-URSI Nat. Radio Sci. Meeting, 1696-1697, 2022.

38. Burfeindt, M. and H. Alqadah, "Receive-beamforming-enhanced linear sampling method imaging," Proceedings of the IEEE Research and Applications of Photonics in Defense (RAPID) Conference, 2021.

39. Burfeindt, M. and H. Alqadah, "Phase-encoded linear sampling method imaging of conducting surfaces from full and limited synthetic apertures," IEEE Open Journal of Antennas and Propagation, Vol. 3, 1191-1205, 2022.
doi:10.1109/OJAP.2022.3214613

40. Burfeindt, M. and H. Alqadah, "Ground penetrating radar imaging via the linear sampling method under a phase-encoded formulation," Proceedings of the IEEE Research and Applications of Photonics in Defense (RAPID) Conference, 2022.

41. Balanis, C., Advanced Engineering Electromagnetics, Sec. 6.6, John Wiley and Sons, 1989.

42. Alqadah, H. and M. Burfeindt, "An adaptive monostatic inverse scattering approach using virtual multistatic geometries," Proc. IEEE Radar Conference, 2023.

43. Akinci, M. N., M. Cayoren, and I. Akduman, "Near-field orthogonality sampling method for microwave imaging: Theory and experimental verification," IEEE Trans. Microw. Theory Techn., Vol. 64, No. 8, 2489-2501, 2016.
doi:10.1109/TMTT.2016.2585488

44. Leem, K. H., J. Liu, and G. Pelekanos, "Two direct factorization methods for inverse scattering problems," Inverse Problems, Vol. 34, No. 12, 125004, 2018.
doi:10.1088/1361-6420/aae15e

45. Satopaa, V., J. Albrecht, D. Irwin, and B. Raghavan, "Finding a `Kneedle' in a Haystack: Detecting knee points in system behavior," Proc. Int. Conf. Dist. Comp. Sys. Workshops, 2011.

46. Hansen, P. C., Rank-Deficient and Discrete Ill-posed Problems, Society for Industrial and Applied Mathematics, 1998.
doi:10.1137/1.9780898719697

47. Crocco, L., I. Catapano, L. Di Donato, and T. Isernia, "The linear sampling method as a way to quantitative inverse scattering," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 4, 1844-1853, 2012.
doi:10.1109/TAP.2012.2186250

48. Palmeri, R., M. Bevacqua, L. Crocco, T. Isernia, and L. Di Donato, "Microwave imaging via distorted iterated virtual experiments," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 2, 829-838, 2017.
doi:10.1109/TAP.2016.2633070

49. Geffrin, J. and P. Sabouroux, "Continuing with the Fresnel database: experimental setup and improvements in 3D scattering measurements," Inverse Problems, Vol. 25, No. 024001, 1-18, 2009.

Dr. Matthew Burfeindt

Dr. Hatim F. Alqadah