Based on the physics-informed neural network (PINN) method, a two-step inverse scattering method is proposed to improve the efficiency and accuracy of the inversion in this work. The first step is to calculate the total fields and the initial solution of permittivity distribution in the domain of interest by a traditional inversion algorithm, the distorted finite-difference frequency-domain-based iterative method, asa prioriinformation for the cascaded PINNs. The second step is to use the calculateda priorinformation as additional parts of the data loss term in the proposed PINN framework for network training. Several typical numerical examples and one experimental example are considered to validate the proposed method. Inversion results show that the proposed method has good accuracy, efficiency, and robustness to noise. Compared with the data-driven deep learning methods in electromagnetic inversion, the proposed method belongs to an unsupervised learning framework and can handle more general problems. Compared with the traditional inverse algorithms, it is more efficient and accurate. In general, the proposed two-step method inherits the advantages of both traditional deep learning methods and inverse scattering methods. Importantly, it also establishes the bridge between traditional inverse scattering algorithms and deep learning methods.

Based on the computational framework of physics-informed neural networks (PINNs), an unsupervised deep learning method is developed for inverse problems, which features good accuracy, high efficiency, and good generality,etc. When considering the case of multi-frequency inversion, a frequency scale factor is introduced to address the scale difference problem brought by the different frequency terms and the occurrence of gradient explosion during the network training. In addition, to improve the efficiency and accuracy, a dynamic sampling strategy is proposed. Four numerical examples and one experimental example are considered to validate the effectiveness of the proposed method. The inversion results show that the proposed PINN method achieves good accuracy, efficiency, and generality, especially for electrically large and high-contrast scatterers. Moreover, the method shows good robustness against noise. Compared with traditional data-driven deep learning methods, the proposed method is efficient because it operates in an unsupervised manner and exhibits good generalization across different inversion tasks. Compared with traditional quantitative inverse scattering algorithms, the proposed method can overcome their limitations in dealing with extremely high-contrast or electrically large targets. In general, the proposed PINN not only inherits high inversion quality when compared with traditional deep learning methods, but also has better generality than traditional inverse scattering methods.

In order to improve the efficiency and accuracy of the inversion of perfectly electric conductors (PECs), an iterative method based on linear approximation (IMLA) is proposed in this work. In the iteration, the computational complexity of the proposed IMLA is well reduced by the implementation of a linear approximation, which makes the inversion highly efficient. Although the linear approximation is employed to solve the inverse scattering problem, full-wave effect is still considered to improve the inversion accuracy in the iteration. In addition, to effectively solve the ill-posed inverse scattering problem and improve the inversion quality, Tikhonov regularization method is introduced, and the corresponding regularization parameter is determined by a self-adaptive L-curve method. To verify the effects of scatterer size and noise on the reconstruction, typical two-dimensional experiments are given, and the results show that the proposed IMLA could efficiently and accurately retrieve complex PEC scatterer shapes, even in the presence of noise.

The distorted FDFD-based iterative method (DFIM) and subspace theory are combined to improve the efficiency of electromagnetic scattering inversion in this letter. With the help of singular value decomposition (SVD), the proposed subspace-based DFIM (S-DFIM) updates the total electric field with an increment produced by the deterministic subspace of the equivalent source. In the iterations, this increment can make the total electric field more accurate than that by the DFIM, which leads to faster convergence. In addition, a self-adapting scheme for getting the parameter of Tikhonov regularization is also proposed to improve the imaging quality. Numerical results show that the efficiency of the proposed method is greatly improved while maintaining good accuracy.

Two accurate finite-difference frequency-domain (FDFD)-based iterative inverse methods, referred to as FDFD-based iterative method (FIM) and distorted FDFD-based iterative method (DFIM), are proposed for electromagnetic inverse scattering. They can be considered as FDFD-based versions of BIM and DBIM and inherit the advantage of the traditional direct FDFD inversion method, i.e., there is no need for Green’s function of complex background, especially for the inhomogeneous medium. The difference is that full-wave consideration is implemented in the proposed methods to build an iterative framework. Then, the scattered field and object parameter profile are updated in each iteration. Using the high-order components in iteration formulation, both the methods are able to reconstruct high-contrast objects and provide accurate reconstruction results. Compared with other full-wave methods based on differential equation, the two methods also have a distinct characteristic that the inversion accuracy is not limited by extra constraints. The difference between the two proposed methods is whether the background coefficient matrix is updated. Generally, DFIM has faster convergence than FIM due to the updated background coefficient matrix in the iterations. To demonstrate the effectiveness of both the methods, several typical 2-D experiments are conducted. The results show that the proposed methods could achieve good accuracy and high imaging quality.