volume | PIER Journals

Abstract

This paper proposes a novel source reconstruction method (SRM) based on the convolutional neural network algorithm. The conventional SRM method usually requires the scattered field data oversampled compared to that of target object grids. To achieve higher accuracy, the conventional SRM numerical system is highly singular. To overcome these difficulties, we model the equivalent source reconstruction process using the machine learning. The equivalent sources of the target are constructed by a convolutional neural networks (ConvNets). It allows us to employless scattered field samples or radar cross section (RCS) data. And the ill-conditioned numerical system is effectively avoided. Numerical examples are provided to demonstrate the validity and accuracy of the proposed approach. Comparison with the traditional NN is also benchmarked. We further expand the proposed method into the direction of arrival (DOA) estimation to demonstrate the generality of the proposed procedure.

1. Araque Quijano, J. L. and G. Vecchi, "Field and source equivalence in source reconstruction on 3D surfaces," Progress In Electromagnetics Research, Vol. 103, 67-100, 2010.
doi:10.2528/PIER10030309

2. Persson, K. and M. Gustason, "Reconstruction of equivalent currents using a near-field data transformation-with radome applications," Progress In Electromagnetics Research, Vol. 54, 179-198, 2005.
doi:10.2528/PIER04111602

3. Sarkar, T. K., P. Petre, A. Taaghol, and R. F. Harrington, "An alternative spherical near field to far field transformation," Progress In Electromagnetics Research, Vol. 16, 269-284, 1997.
doi:10.2528/PIER96060600

4. Li, P. and L. J. Jiang, "The far field transformation for the antenna modeling based on spherical electric field measurements," Progress In Electromagnetics Research, Vol. 123, 243-261, 2012.
doi:10.2528/PIER11102301

5. Alvarez, Y., F. Las-Heras, and M. R. Pino, "On the comparison between the spherical wave expansion and the sources reconstruction method," IEEE Trans. Antennas Propag., Vol. 56, No. 10, 3337-3341, 2008.
doi:10.1109/TAP.2008.929519

6. Crocco, L. and M. D’Urso, "The contrast source-extended Born model for 2D subsurface scattering problems," Progress In Electromagnetics Research B, Vol. 17, 343-359, 2009.
doi:10.2528/PIERB09080502

7. 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

8. Caorsi, S., G. L. Gragnani, S. Medicina, M. Pastorino, and G. A. Pinto, "A Gibbs random field-based active electromagnetic method for noninvasive diagnostics in biomedical applications," Radio Sci., Vol. 30, 291-301, 1995.
doi:10.1029/94RS00831

9. Yu, Y. and L. Carin, "Three-dimensional Bayesian inversion with application to subsurface sensing," IEEE Trans. Geosci. Remote Sens., Vol. 45, No. 5, 1258-1270, 2007.
doi:10.1109/TGRS.2007.894932

10. Chen, M. S., F. L. Liu, H. M. Du, and X. L. Wu, "Compressive sensing for fast analysis of wide-angle monostatic scattering problems," IEEE Antennas Wireless Propag. Lett., Vol. 10, 1243-1246, 2011.
doi:10.1109/LAWP.2011.2174190

11. Kleinman, R. E. and P. M. van den Berg, "Two-dimensional location and shape reconstruction," Radio Sci., Vol. 29, 1157-1169, 1994.
doi:10.1029/93RS03445

12. Sun, S., B. J. Kooij, and A. Yarovoy, "Linearized three-dimensional electromagnetic contrast source inversion and its applications to half-space configurations," IEEE Trans. Geosci. Remote Sens., Vol. 55, No. 6, 3475-3487, 2017.
doi:10.1109/TGRS.2017.2672861

13. Shan, T., X. W. Dang, M. K. Li, F. Yang, S. H. Xu, and J. Wu, "Study on a Poisson’s equation solver based on deep learning technique,", arXiv:1712.05559, 2017.

14. Yao, H., L. Jiang, and Y. Qin, "Machine learning based method of moments (ML-MoM)," Proceedings of 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, San Diego, USA, July 2017.

15. Shan, T., X. W. Dang, M. K. Li, F. Yang, S. H. Xu, and J. Wu, "Study on a 3D Possion’s equation solver based on deep learning technique," Proceedings of IEEE Int. Conf. Computational Electromagnetics, Chengdu, China, March 2018.

16. Zhang, H. H. and R. S. Chen, "Coherent processing and superresolution technique of multi-band radar data based on fast sparse bayesian learning algorithm," IEEE Trans. Antennas Propag., Vol. 62, No. 12, 6217-6227, 2014.
doi:10.1109/TAP.2014.2361158

17. Ayestarn, R. G., F. L. Heras, and L. F. Herran, "High accuracy neural network-based array synthesis including element coupling," IEEE Antennas Wireless Propag. Lett., Vol. 5, No. 1, 45-48, 2006.
doi:10.1109/LAWP.2006.870366

18. Ayestarn, R. G. and F. L. Heras, "Neural networks and equivalent source reconstruction for real antenna array synthesis," Electron. Lett., Vol. 39, No. 13, 956-958, 2003.
doi:10.1049/el:20030626

19. Ayestarn, R. G. and F. L. Heras, "Near filed to far field transformation using neural networks and source reconstruction," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 15, 2201-2213, 2006.
doi:10.1163/156939306779322594

20. Krizhevsky, A., I. Sutskever, and G. Hinton, "ImageNet classification with deep convolutional neural networks," Proc. Neural Information and Processing Systems, 2012.

21. Zhang, Y., D. Zhao, J. Sun, G. Zou, and W. Li, "Adaptive convolutional neural network and its application in face recognition," Neural Processing Letters, Vol. 43, No. 2, 389-399, 2015.
doi:10.1007/s11063-015-9420-y

22. Dong, C., C. Loy, K. He, and X. Tang, "Image super-resolution using deep convolutional networks," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 38, No. 2, 295-307, 2016.
doi:10.1109/TPAMI.2015.2439281

23. Sahiner, B., H.-P. Chan, N. Petrick, D. Wei, M. Helvie, D. Adler, and M. Goodsitt, "Classification of mass and normal breast tissue: a convolution neural network classifier with spatial domain and texture images," IEEE Transactions on Medical Imaging, Vol. 15, No. 5, 598-610, 1996.
doi:10.1109/42.538937

24. Hornik, K., M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural Netw., Vol. 2, No. 5, 359-366, 1989.
doi:10.1016/0893-6080(89)90020-8

25. Hoang, N., "On node distributions for interpolation and spectral methods," Mathematics of Computation, Vol. 85, No. 298, 667-692, 2015.
doi:10.1090/mcom/3018

26. Labate, G., L. Matekovits, and S. Podilchak, "A methodology for translating non-radiating sources in design parameters of cloaking devices," Proceedings of 2016 IEEE International Symposium on Antennas and Propagation (APSURSI), Fajardo, Puerto Rico, June 2016.

27. Fiddy, M. A. and R. S. Ritter, Introduction to Imaging from Scattered Fields, CRC Press, 2014.
doi:10.1201/b17623

28. Hansen, P., Discrete Inverse Problems: Insight and Algorithms, SIAM, 2010.
doi:10.1137/1.9780898718836

29. Kim, P., MATLAB Deep Learning, Apress, 2017.
doi:10.1007/978-1-4842-2845-6

30. Ng, A. Y., "Feature Selection L1 vs. L2 Regularization and Rotational Invariance," Proceedings of 21st Int’l Conf. Machine Learning, 78-86, 2004.

31. Cong, J. and B. Xiao, "Minimizing computation in convolutional neural networks," Proceedings of Int. Conf. Artif. Neural Netw., 281-290, 2014.

32. Tan, Z., Y. C. Eldar, and A. Nehorai, "Direction of arrival estimation using co-prime arrays: A super resolution viewpoint," IEEE Trans. Signal Process., Vol. 62, No. 21, 5565-5576, 2014.
doi:10.1109/TSP.2014.2354316

33. Zhang, X., L. Y. Xu, L. Xu, and D. Xu, "Direction of departure (DOD) and direction of arrival (DOA) estimation in MIMO radar with reduced-dimension MUSIC," IEEE Commun. Lett., Vol. 14, No. 12, 1161-1163, 2010.
doi:10.1109/LCOMM.2010.102610.101581

Dr. He Ming Yao

Dr. Wei E. I. Sha

Dr. Li Jun Jiang