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.
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.
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.
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.
5. E, W., "A proposal on machine learning via dynamical systems," Communications in Mathematics and Statistics, Vol. 5, No. 1, 1-11, 2017.
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.
7. Goodfellow, I., Y. Bengio, and A. Courville, Deep Learning, MIT Press, 2016.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
21. Adler, J. and O. Oktem, "Solving ill-posed inverse problems using iterative deep neural networks," Inverse Problems, Vol. 33, No. 12, 124007, 2017.
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.
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.
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.
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.
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.
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.
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.
30. Van den Berg, P. M. and R. E. Kleinman, "A contrast source inversion method," Inverse Probl., Vol. 13, 1607-1620, 1997.
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.
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.
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.
34. Unser, M., "A representer theorem for deep neural networks," Journal of Machine Learning Research, Vol. 20, No. 110, 1-30, 2019.
35. Belthangady, C. and L. A. Royer, "Applications, promises, and pitfalls of deep learning for fluorescence image reconstruction," Nature Methods, 1-11, 2019.
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.
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.
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.
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.
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.
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.
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.
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.