volume | PIER Journals

Abstract

The linear sampling method (LSM) is a very popular method for determining the boundary of an object from the scattered field. However, there are instances where LSM provides the convex hull of the boundary rather than the true boundary. There are two common generalizations to LSM: the Generalized Linear Sampling Method (GLSM) and the Multipoles-based Linear Sampling Method (MLSM). In this paper, the ability of GLSM and MLSM to overcome some of the deficiencies of LSM are investigated. It is found that GLSM may be ideal for imaging thin features of scatterers and that MLSM can provide an improvement over LSM in a more general sense. GLSM may also require user input to adjust the indicator function whereas MLSM does not appear to rely as much on indicator function adjustments for adequate results.

1. Pastorino, M. and A. Randazzo, Microwave Imaging: Methods and Applications, Artech House, Boston, MA, 2018.

2. Tobon Vasquez, J. A., R. Scapaticci, G. Turvani, M. Ricci, L. Farina, A. Litman, M. R. Casu, L. Crocco, and F. Vipiana, "Noninvasive inline food inspection via microwave imaging technology: An application example in the food industry," IEEE Antennas and Propagation Magazine, Vol. 62, No. 5, 18-32, 2020, doi: 10.1109/MAP.2020.3012898.
doi:10.1109/MAP.2020.3012898 Google Scholar

3. Neira, L. M., B. D. Van Veen, and S. C. Hagness, "High-resolution microwave breast imaging using a 3-D inverse scattering algorithm with a variable-strength spatial prior constraint," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 11, 6002-6014, 22017, doi: 10.1109/TAP.2017.2751668.
doi:10.1109/TAP.2017.2751668 Google Scholar

4. Hopfer, M., R. Planas, A. Hamidipour, T. Henriksson, and S. Semenov, "Electromagnetic tomography for detection, differentiation, and monitoring of brain stroke: A virtual data and human head phantom study," IEEE Antennas and Propagation Magazine, Vol. 59, No. 5, 86-97, 2017, doi: 10.1109/MAP.2017.2732225.
doi:10.1109/MAP.2017.2732225 Google Scholar

5. Salucci, M., G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, "Electromagnetic subsurface prospecting by a multifocusing inexact Newton method within the second-order Born approximation," J. Opt. Soc. Am. A, Vol. 31, No. 6, 1167-1179, Jun. 2014, doi: 10.1364/JOSAA.31.001167.
doi:10.1364/JOSAA.31.001167 Google Scholar

6. Palmeri, R., M. T. Bevacqua, A. F. Morabito, and T. Isernia, "Design of artifiial-material-based antennas using inverse scattering techniques," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 12, 7076-7090, 2018, doi: 10.1109/TAP.2018.2871707.
doi:10.1109/TAP.2018.2871707 Google Scholar

7. Bozza, G., M. Brignone, and M. Pastorino, "Aplication of the no-sampling linear sampling method to breast cancer detection," IEEE Transactions on Biomedical Engineering, Vol. 57, No. 10, 2525-2534, 2010, doi: 10.1109/TBME.2010.2055059.
doi:10.1109/TBME.2010.2055059 Google Scholar

8. 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 Google Scholar

9. Colton, D., H. Haddar, and M. Piana, "The linear sampling method in inverse electromagnetic scattering theory," Inverse Problems, Vol. 19, 105-137, 2003.
doi:10.1088/0266-5611/19/6/057 Google Scholar

10. Agarwal, K. and Y. Zhong, "A multipole-expansion based linear sampling method for solving inverse scattering problems," Optics Express, Vol. 12, No. 6, 6366-6381, Mar. 2010.
doi:10.1364/OE.18.006366 Google Scholar

11. Crocco, L., L. Di Donato, I. Catapano, and T. Isernia, "An improved simple method for imaging the shape of complex targets," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 2, 843-851, Feb. 2013.
doi:10.1109/TAP.2012.2220329 Google Scholar

12. Potthast, R., "A study on orthogonality sampling," Inverse Problems, Vol. 26, No. 7, 074 015, 2010.
doi:10.1088/0266-5611/26/7/074015 Google Scholar

13. Akıncı, M. N., M. Çayören, and I. Akduman, "Near-field orthogonality sampling method for microwave imaging: Theory and experimental verifiation," IEEE Trans. Microwave Theory Tech., Vol. 64, No. 8, 2489-2501, Aug. 2016.
doi:10.1109/TMTT.2016.2585488 Google Scholar

14. Chen, X., Computational Methods for Electromagnetic Inverse Scattering, John Wiley & Sons, Hoboken, NJ, 2018.
doi:10.1002/9781119311997

15. Bevacqua, M. T. and R. Palmeri, "Qualitative methods for the inverse obstacle problem: A comparison on experimental data," Journal of Imaging, Vol. 5, No. 4, 2019, ISSN: 2313-433X, doi: 10.3390/jimaging5040047, [Online]. Available: https://www.mdpi.com/2313-433X/5/4/47.
doi:10.3390/jimaging5040047 Google Scholar

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

17. Richmond, J., "Scattering by a dielectric cylinder of arbitrary crossectional shape," IEEE Transactions on Antennas and Propagation, Vol. 13, No. 3, 334-341, May 1965.
doi:10.1109/TAP.1965.1138427 Google Scholar

18. Oskooi, A. F., D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, "MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method," Computer Physics Communications, Vol. 181, 687-702, Jan. 2010, doi: doi:10.1016/j.cpc.2009.11.008.
doi:10.1016/j.cpc.2009.11.008 Google Scholar

19. Cakoni, F., D. Colton, and P. Monk, "Qualitative methods in inverse electromagnetic scattering theory," IEEE AP Magazine, Vol. 59, No. 5, 24-33, Oct. 2017. Google Scholar

20. 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, May 2007.
doi:10.1109/TAP.2007.895563 Google Scholar

21. 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, Apr. 2012.
doi:10.1109/TAP.2012.2186250 Google Scholar

Dr. Yeasmin Sultana

Professor James Richie