volume | PIER Journals

Abstract

A deep learning linear sampling method (DLSM), composed of linear sampling method (LSM) and a convolutional neural network (CNN) of U-Net, is proposed to restore shape of multilayered scatterers with cylindrical or rectangular cross section. Simulations over random samples with different geometrical parameters are used to verify the efficacy of the proposed method.

1. 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

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

3. Shao, W. and Y. Du, "Microwave imaging by deep learning network: Feasibility and training method," IEEE Trans. Antennas Propagat., Vol. 68, No. 7, 5626-5634, Jul. 2020.
doi:10.1109/TAP.2020.2978952

4. Agarwal, K., X. Chen, and Y. Zhong, "A multipole-expansion based linear sampling method for solving inverse scattering problems," Optics Express, Vol. 18, No. 6, 6366-6381, 2010.
doi:10.1364/OE.18.006366

5. Cakoni, F., D. Colton, and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering, SIAM Press, 2011.
doi:10.1137/1.9780898719406

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

7. Burfeindt, M. J. and H. F. Alqadah, "Qualitative inverse scattering for sparse-aperture data collections using a phase-delay frequency variation constraint," IEEE Trans. Antennas Propagat., Vol. 68, No. 4, 7530-7540, Nov. 2020.

8. Potthast, R., "A study on orthogonality sampling," Inverse Problem, Vol. 26, No. 7, 074015, 2010.
doi:10.1088/0266-5611/26/7/074015

9. Bevacqua, M. T., T. Isernia, R. Palmeri, M. N. Akinci, and L. Crocco, "Physical insight unveils new imaging capabilities of orthogonality sampling method," IEEE Trans. Antennas Propagat., Vol. 68, No. 5, 4014-4021, May 2020.
doi:10.1109/TAP.2019.2963229

10. Li, J. Z., H. Y. Liu, and J. Zou, "Strengthened linear sampling method with a reference ball," SIAM J. Sci. Comput., Vol. 31, 4013-4040, 2009.
doi:10.1137/080732389

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

12. Guo, R., Z. Jia, X. Song, M. Li, F. Yang, S. Xu, and A. Abubakar, "Pixel-and model-based microwave inversion with supervised descent method for dielectric targets," IEEE Trans. Antennas Propagat., Vol. 68, No. 12, 8114-8126, Jun. 2020.
doi:10.1109/TAP.2020.2999741

13. Jun. 2020, Z. and X. D. Chen, "Deep-learning schemes for full-wave nonlinear inverse scattering problems," IEEE Trans. Geosci. Remote Sensing, Vol. 57, No. 4, 1849-1860, Apr. 2019.
doi:10.1109/TGRS.2018.2869221

14. Ronneberger, O., P. Fischer, and T. Brox, "U-net: Convolutional networks for biomedical image segmentation," Medical Image Computing and Computer-Assisted Intervention (MICCAI), 234-241, 2015.

15. Khoshdel, V., A. Ashraf, and J. LoVetri, "Enhancement of multimodal microwave-ultrasound breast imaging using a deep-learning technique," Sensors, Vol. 19, No. 18, 4050, 2019.
doi:10.3390/s19184050

16. Yao, H. M., W. E. I. Sha, and L. Jiang, "Two-step enhanced deep learning approach for electromagnetic inverse scattering problems," IEEE Antennas Wireless Propagat. Lett., Vol. 18, No. 11, 2254-2258, Jan. 2019.
doi:10.1109/LAWP.2019.2925578

17. Sanghvi, Y., Y. Kalepu, and U. K. Khankhoje, "Embedding deep learning in inverse scattering problems," IEEE Trans. Comput. Imag., Vol. 6, 46-56, Jul. 2020.

18. Yago, A., M. Cavagnaro, and L. Crocco, "Deep learning-enhanced qualitative microwave imaging: Rationale and initial assessment," EuCAP, 1-5, Dusseldorf, Germany, Mar. 2021.

19. Crocco, L., I. Catapano, L. D. Donato, and T. Isernia, "The linear sampling method as a way to quantitative inverse scattering," IEEE Trans. Antennas Propagat., Vol. 60, No. 4, 1844-1853, Apr. 2012.
doi:10.1109/TAP.2012.2186250

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

21. Alom, M. Z., M. Hasan, C. Yakopcic, T. M. Taha, and V. K. Asari, "Recurrent residual convolutional neural network based on U-Net (R2U-Net) for medical image segmentation,", arXiv 1802.06955, 2018.

22. Kim, P., MATLAB Deep Learning with Machine Learning, Neural Networks and Artificial Intelligence, APress, 2017.

23. Xu, K., L. Wu, X. Ye, and X. Chen, "Deep learning-based inversion methods for solving inverse scattering problems with phaseless data," IEEE Trans. Antennas Propagat., Vol. 68, No. 11, 7457-7470, Nov. 2020.
doi:10.1109/TAP.2020.2998171

24. Vedaldi, A., K. Lenc, and A. Gupta, "MatConvNet: Convolutional neural networks for MATLAB," ACM Int. Conf. Multimedia, 689-692, 2015.

Dr. Yu-Hsin Kuo

Prof. Jean-Fu Kiang