In this work, we propose a deep learning-based imaging method for addressing the multi-frequency electromagnetic (EM) inverse scattering problem (ISP). By combining deep learning technology with EM physical laws, we have successfully developed a multi-frequency neural Born iterative method (NeuralBIM), guided by the principles of the single-frequency NeuralBIM. This method integrates multitask learning techniques with NeuralBIM's efficient iterative inversion process to construct a robust multi-frequency Born iterative inversion model. During training, the model employs a multitask learning approach guided by homoscedastic uncertainty to adaptively allocate the weights of each frequency's data. Additionally, an unsupervised learning method, constrained by the physical laws of ISP, is used to train the multi-frequency NeuralBIM model, eliminating the need for contrast and total field data. The effectiveness of the multi-frequency NeuralBIM is validated through synthetic and experimental data, demonstrating improvements in accuracy and computational efficiency for solving ISP. Moreover, this method exhibits strong generalization capabilities and noise resistance. The multi-frequency NeuralBIM method explores a novel inversion method for multi-frequency EM data and provides an effective solution for the electromagnetic ISP of multi-frequency data.

In this paper, we propose the neural Born iteration method (NeuralBIM) for solving 2D inverse scattering problems (ISPs) by drawing on the scheme of physics-informed supervised residual learning (PhiSRL) to emulate the computing process of the traditional Born iteration method (TBIM). NeuralBIM employs independent convolutional neural networks (CNNs) to learn the alternate update rules of two different candidate solutions with their corresponding residuals. Two different schemes of NeuralBIMs are presented in this paper including supervised and unsupervised learning schemes. With the data set generated by method of moments (MoM), supervised NeuralBIMs are trained with the knowledge of total fields and contrasts. Unsupervised NeuralBIM is guided by the physics-embedded loss functions founding on the governing equations of ISPs, which results in no requirements of total fields and contrasts for training. Representative numerical results further validate the effectiveness and competitiveness of both supervised and unsupervised NeuralBIMs.