volume | PIER Journals

Abstract

In recent years, deep learning (DL) is becoming an increasingly important tool for solving inverse scattering problems (ISPs). This paper reviews methods, promises, and pitfalls of deep learning as applied to ISPs. More specifically, we review several state-of-the-art methods of solving ISPs with DL, and we also offer some insights on how to combine neural networks with the knowledge of the underlying physics as well as traditional non-learning techniques. Despite the successes, DL also has its own challenges and limitations in solving ISPs. These fundamental questions are discussed, and possible suitable future research directions and countermeasures will be suggested.

1. Le Cun, Y., Y. Bengio, and G. Hinton, "Deep learning," Nature, Vol. 521, No. 7553, 436-444, 2015. Google Scholar

2. Li, H., Y. Yang, D. Chen, and Z. Lin, "Optimization algorithm inspired deep neural network structure design," Proceedings of the 10th Asian Conference on Machine Learning, Proceedings of Machine Learning Research, PMLR, Vol. 95, 614-629, J. Zhu and I. Takeuchi, eds., Nov. 14–16, 2018. Google Scholar

3. Yang, Y., J. Sun, H. Li, and Z. Xu, "Deep ADMM-Net for compressive sensing MRI," Advances in Neural Information Processing Systems, Vol. 29, 10-18, Curran Associates, Inc., 2016. Google Scholar

4. Lu, Y., A. Zhong, Q. Li, and B. Dong, "Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations," International Conference on Machine Learning, 3276-3285, 2018. Google Scholar

5. E, W., "A proposal on machine learning via dynamical systems," Communications in Mathematics and Statistics, Vol. 5, No. 1, 1-11, 2017. Google Scholar

6. E, W., J. Han, and Q. Li, "A mean-field optimal control formulation of deep learning," Research in the Mathematical Sciences, Vol. 6, No. 1, 10, 2019. Google Scholar

7. Goodfellow, I., Y. Bengio, and A. Courville, Deep Learning, MIT Press, 2016.

8. Chen, X., Computational Methods for Electromagnetic Inverse Scattering, Wiley, 2018.

9. McCann, M. T., K. H. Jin, and M. Unser, "Convolutional neural networks for inverse problems in imaging: A review," IEEE Signal Processing Magazine, Vol. 34, No. 6, 85-95, 2017. Google Scholar

10. Lucas, A., M. Iliadis, R. Molina, and A. K. Katsaggelos, "Using deep neural networks for inverse problems in imaging: Beyond analytical methods," IEEE Signal Processing Magazine, Vol. 35, No. 1, 20-36, 2018. Google Scholar

11. Massa, A., D. Marcantonio, X. Chen, M. Li, and M. Salucci, "DNNs as applied to electromagnetics, antennas, and propagation — A Review," IEEE Antennas and Wireless Propagation Letters, Vol. 18, No. 11, 2225-2229, 2019. Google Scholar

12. Caorsi, S. and P. Gamba, "Electromagnetic detection of dielectric cylinders by a neural network approach," IEEE Transactions on Geoscience and Remote Sensing, Vol. 37, No. 2, 820-827, 1999. Google Scholar

13. Rekanos, I. T., "Neural-network-based inverse-scattering technique for online microwave medical imaging," IEEE Transactions on Magnetics, Vol. 38, 1061-1064, Mar. 2002. Google Scholar

14. Bermani, E., A. Boni, S. Caorsi, and A. Massa, "An innovative real-time technique for buried object detection," IEEE Transactions on Geoscience and Remote Sensing, Vol. 41, 927-931, Apr. 2003. Google Scholar

15. Salucci, M., N. Anselmi, G. Oliveri, P. Calmon, R. Miorelli, C. Reboud, and A. Massa, "Real-time NDT-NDE through an innovative adaptive partial least squares SVR inversion approach," IEEE Transactions on Geoscience and Remote Sensing, Vol. 54, No. 11, 6818-6832, 2016. Google Scholar

16. Ran, P., Y. Qin, and D. Lesselier, "Electromagnetic imaging of a dielectric micro-structure via convolutional neural networks," 2019 27th European Signal Processing Conference (EUSIPCO), 1-5, IEEE, 2019. Google Scholar

17. Fajardo, J., J. Galvn, F. Vericat, M. Carlevaro, and R. Irastorza, "Phaseless microwave imaging of dielectric cylinders: An artificial neural networks-based approach," Progress In Electromagnetics Research, Vol. 166, 95-105, Dec. 2019. Google Scholar

18. Wei, Z. and X. Chen, "Deep-learning schemes for full-wave nonlinear inverse scattering problems," IEEE Transactions on Geoscience and Remote Sensing, Vol. 57, No. 4, 1849-1860, 2019. Google Scholar

19. Yao, H. M., W. E. I. Sha, and L. Jiang, "Two-step enhanced deep learning approach for electromagnetic inverse scattering problems," IEEE Antennas and Wireless Propagation Letters, Vol. 18, No. 11, 2254-2258, 2019. Google Scholar

20. Guo, R., X. Song, M. Li, F. Yang, S. Xu, and A. Abubakar, "Supervised descent learning technique for 2-D microwave imaging," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 5, 3550-3554, 2019. Google Scholar

21. Adler, J. and O. Oktem, "Solving ill-posed inverse problems using iterative deep neural networks," Inverse Problems, Vol. 33, No. 12, 124007, 2017. Google Scholar

22. Chen, G., P. Shah, J. Stang, and M. Moghaddam, "Learning-assisted multi-modality dielectric imaging," IEEE Transactions on Antennas and Propagation, 1-14, 2019. Google Scholar

23. Sanghvi, Y., Y. Kalepu, and U. K. Khankhoje, "Embedding deep learning in inverse scattering problems," IEEE Transactions on Computational Imaging, Vol. 6, 46-56, 2020. Google Scholar

24. Chen, X., "Subspace-based optimization method for solving inverse scattering problems," IEEE Trans. Geosci. Remote Sens., Vol. 48, 42-49, 2010. Google Scholar

25. Sun, Y., Z. Xia, and U. S. Kamilov, "Efficient and accurate inversion of multiple scattering with deep learning," Optics Express, Vol. 26, No. 11, 14678-14688, 2018. Google Scholar

26. Li, L., L. G. Wang, F. L. Teixeira, C. Liu, A. Nehorai, and T. J. Cui, "DeepNIS: Deep neural network for nonlinear electromagnetic inverse scattering," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 3, 1819-1825, 2019. Google Scholar

27. Li, L., L. G. Wang, and F. L. Teixeira, "Performance analysis and dynamic evolution of deep convolutional neural network for electromagnetic inverse scattering," IEEE Antennas and Wireless Propagation Letters, Vol. 18, No. 11, 2259-2263, 2019. Google Scholar

28. Xiao, J., J. Li, Y. Chen, F. Han, and Q. H. Liu, "Fast electromagnetic inversion of inhomogeneous scatterers embedded in layered media by born approximation and 3-D U-Net," IEEE Geoscience and Remote Sensing Letters, 1-5, 2019. Google Scholar

29. 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. Google Scholar

30. Van den Berg, P. M. and R. E. Kleinman, "A contrast source inversion method," Inverse Probl., Vol. 13, 1607-1620, 1997. Google Scholar

31. Khoo, Y. and L. Ying, "SwitchNet: a neural network model for forward and inverse scattering problems," SIAM Journal on Scientific Computing, Vol. 41, No. 5, A3182-A3201, 2019. Google Scholar

32. Wei, Z. and X. Chen, "Physics-inspired convolutional neural network for solving full-wave inverse scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 9, 6138-6148, 2019. Google Scholar

33. Sun, J., Z. Niu, K. A. Innanen, J. Li, and D. O. Trad, "A theory-guided deep-learning formulation and optimization of seismic waveform inversion," Geophysics, Vol. 85, No. 2, R87-R99, 2020. Google Scholar

34. Unser, M., "A representer theorem for deep neural networks," Journal of Machine Learning Research, Vol. 20, No. 110, 1-30, 2019. Google Scholar

35. Belthangady, C. and L. A. Royer, "Applications, promises, and pitfalls of deep learning for fluorescence image reconstruction," Nature Methods, 1-11, 2019. Google Scholar

36. Zhong, Y., M. Lambert, D. Lesselier, and X. Chen, "A new integral equation method to solve highly nonlinear inverse scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 5, 1788-1799, 2016. Google Scholar

37. Zhong, Y., M. Salucci, K. Xu, A. Polo, and A. Massa, "A multiresolution contraction integral equation method for solving highly nonlinear inverse scattering problems," IEEE Transactions on Microwave Theory and Techniques, 1-14, 2019. Google Scholar

38. Hamilton, S. J. and A. Hauptmann, "Deep D-Bar: Real-time electrical impedance tomography imaging with deep neural networks," IEEE Transactions on Medical Imaging, Vol. 37, 2367-2377, Oct. 2018. Google Scholar

39. Wei, Z., D. Liu, and X. Chen, "Dominant-current deep learning scheme for electrical impedance tomography," IEEE Transactions on Biomedical Engineering, Vol. 66, No. 9, 2546-2555, 2019. Google Scholar

40. Wei, Z. and X. Chen, "Induced-current learning method for nonlinear reconstructions in electrical impedance tomography," IEEE Transactions on Medical Imaging, 1-9, 2019. Google Scholar

41. Duan, X., S. Taurand, and M. Soleimani, "Artificial skin through super-sensing method and electrical impedance data from conductive fabric with aid of deep learning," Scientific Reports, Vol. 9, No. 1, 8831, 2019. Google Scholar

42. Hauptmann, A., F. Lucka, M. Betcke, N. Huynh, J. Adler, B. Cox, P. Beard, S. Ourselin, and S. Arridge, "Model-based learning for accelerated, limited-view 3-D photoacoustic tomography," IEEE Transactions on Medical Imaging, Vol. 37, 1382-1393, Jun. 2018. Google Scholar

43. Tang, W., T. Shan, X. Dang, M. Li, F. Yang, S. Xu, and J. Wu, "Study on a Poisson’s equation solver based on deep learning technique," 2017 IEEE Electrical Design of Advanced Packaging and Systems Symposium (EDAPS), 1-3, Dec. 2017. Google Scholar

Professor Xudong Chen

Prof. Zhun Wei

Professor Maokun Li

Dr. Paolo Rocca