Learning-Assisted Inversion for Solving Nonlinear Inverse Scattering Problem

Abstract

Solving inverse scattering problems (ISPs) is challenging because of its intrinsic ill-posedness and the nonlinearity. When dealing with highly nonlinear ISPs, i.e., those scatterers with high contrast and/or electrically large size, the traditional iterative nonlinear inversion methods converge slowly and take lots of computation time, even maybe trapped into local wrong solution. To alleviate the above challenges, a learning-assisted (LA) inversion approach termed as the LA inversion method (LAIM) with advanced generative adversarial network (GAN) in virtue of a new recently established contraction integral equation for inversion (CIE-I) is proposed to achieve a good balance between the computational efficiency and the accuracy of solving highly nonlinear ISPs. The preliminary profiles composed of only small amount of low-frequency components can be got efficiently by the Fourier bases expansion of CIE-I inversion (FBE-CIE-I). The physically exacted information can be taken as the input of the neural network to recover super-resolution image with more high-frequency components. A weighted loss function composed of the adversarial loss, mean absolute percentage error (MAPE), and structural similarity (SSIM) is used under the pix2pix GAN framework. In addition, the self-attention module is used at the end of the generator network to capture the physical distance information between two pixels and enhance the inversion accuracy of the feature scatterers. To further improve the inversion efficiency, the data-driven method (DDM) is used to achieve real-time imaging by cascading U-net and pix2pix GAN, where U-net is used to replace FBE-CIE-I in the LAIM. Compared with other LA inversion, both the synthetic and experimental examples have validated the merits of the proposed LAIM and DDM.