  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.
