Recently, studies have shown the potential of integrating field-type iterative methods with deep learning (DL) techniques in solving inverse scattering problems (ISPs). In this article, we propose a novel Variational Born Iterative Network, namely, VBIM-Net, to solve the full-wave ISPs with significantly improved flexibility and inversion quality. The proposed VBIM-Net emulates the alternating updates of the total electric field and the contrast in the variational Born iterative method (VBIM) by multiple layers of subnetworks. We embed the calculation of the contrast variation into each of the subnetworks, converting the scattered field residual into an approximate contrast variation and then enhancing it by a U-Net, thus avoiding the requirement of matched measurement dimension and grid resolution as in existing approaches. The total field and contrast of each layer's output is supervised in the loss function of VBIM-Net, which guarantees the physical interpretability of variables of the subnetworks. In addition, we design a training scheme with extra noise to enhance the model's stability. Extensive numerical results on synthetic and experimental data both verify the inversion quality, generalization ability, and robustness of the proposed VBIM-Net. This work may provide some new inspiration for the design of efficient field-type DL schemes.

提出了一种新颖的变分Born迭代网络（VBIM-Net）来解决全波散射问题，具有显著改进的灵活性和反演质量，通过多层子网络来模拟总电场和对比度在变分Born迭代方法（VBIM）中的交替更新，并将对比度变化的计算嵌入到每个子网络中，通过U-Net增强，从而避免了现有方法中所需的匹配测量维度和网格分辨率要求。VBIM-Net的损失函数中监督每层输出的总场和对比度，保证了子网络变量的物理可解释性，此外，设计了带有额外噪声的训练方案来增强模型的稳定性，大量的数值结果在合成和实验数据上都验证了所提出的VBIM-Net的反演质量、泛化能力和鲁棒性，这项工作可能为有效的场类型深度学习方案的设计提供了一些新的灵感。

VBIM-Net：反散射问题的变分Born迭代网络