Inverse scattering problems are inherently challenging, given the fact they are ill-posed and nonlinear. This paper presents a powerful deep learning-based approach that relies on generative adversarial networks to accurately and efficiently reconstruct randomly-shaped two-dimensional dielectric objects from amplitudes of multi-frequency scattered electric fields. An adversarial autoencoder (AAE) is trained to learn to generate the scatterer's geometry from a lower-dimensional latent representation constrained to adhere to the Gaussian distribution. A cohesive inverse neural network (INN) framework is set up comprising a sequence of appropriately designed dense layers, the already-trained generator as well as a separately trained forward neural network. The images reconstructed at the output of the inverse network are validated through comparison with outputs from the forward neural network, addressing the non-uniqueness challenge inherent to electromagnetic (EM) imaging problems. The trained INN demonstrates an enhanced robustness, evidenced by a mean binary cross-entropy (BCE) loss of $0.13$ and a structure similarity index (SSI) of $0.90$. The study not only demonstrates a significant reduction in computational load, but also marks a substantial improvement over traditional objective-function-based methods. It contributes both to the fields of machine learning and EM imaging by offering a real-time quantitative imaging approach. The results obtained with the simulated data, for both training and testing, yield promising results and may open new avenues for radio-frequency inverse imaging.

翻译：逆散射问题因其固有的病态性和非线性而极具挑战性。本文提出了一种基于生成对抗网络的强效深度学习方法，能够从多频散射电场幅度中准确高效地重建任意形状的二维介质目标。通过训练对抗自编码器（AAE），使其在服从高斯分布的约束下，从低维潜在表示中学习生成散射体几何形状。我们构建了统一的逆神经网络（INN）框架，包含精心设计的稠密层序列、预训练生成器以及独立训练的前向神经网络。逆网络输出重建图像通过与前向神经网络输出对比验证，解决了电磁（EM）成像问题中固有的非唯一性挑战。训练后的INN展现出增强的鲁棒性，平均二元交叉熵（BCE）损失为0.13，结构相似性指数（SSI）达0.90。本研究不仅显著降低了计算负荷，更在传统基于目标函数的方法基础上实现了重大改进。通过提供实时定量成像方案，本研究对机器学习和电磁成像领域均有贡献。基于仿真数据的训练与测试结果令人鼓舞，可能为射频逆成像开辟新路径。