A Hybrid Electromagnetic Algorithm for Reconstructing 2-D Dielectric Objects Based on the M-Net

Abstract

The electromagnetic inverse scattering problem is highly nonlinear and ill-posed, often requiring iterative optimization with regularization terms. In this paper, we propose an enhanced U-Net called M-Net that combines multi-feature input and weighted output layers with an improved loss function calculation method to improve network performance. Given the intimate connection between inverse scattering and forward scattering, this paper devotes some space to demonstrate the effectiveness of neural networks in solving electromagnetic forward problems. The lack of rigorous theoretical derivation poses challenges in ensuring the reliability of neural network output results, thereby limiting its application in electromagnetic problems. In this paper, instead of the scattered field, we utilize diffraction tomography (DT) images that contain information about both imaging models and scattering mechanisms as the input data for the neural network. This approach provides richer a priori knowledge for the neural network and reduces learning difficulty. Numerical simulations of two-dimensional circular scatterers demonstrate that the hybrid M-Net-based electromagnetic inversion algorithm can effectively reconstruct the position, profile, and relative permittivity distribution of scatterers. Comparative experiments reveal significant improvements: the hybrid M-Net achieves an average reconstruction error of $1.17\times {10}^{-4}$%, outperforming the standard U-Net ($8.39\times {10}^{-4}$%), standard M-Net ($4.07\times {10}^{-4}$%), and hybrid U-Net ($1.69\times {10}^{-4}$%). Furthermore, the algorithm demonstrates robust generalization capabilities by successfully reconstructing non-circular shapes and multi-target configurations that were not present in the training set.