VBIM-Net: Variational Born Iterative Network for Inverse Scattering Problems

TL;DR

VBIM-Net introduces a physics-informed, multi-layer unrolled network that emulates the variational Born iterative method for full-wave inverse scattering. By transforming scattered-field residuals into approximate contrast variations and applying layer-wise soft physical constraints, it achieves reliable, high-quality reconstructions with robust generalization across synthetic and experimental data. The approach blends analytical VBIM steps with U-Net refinements, includes a noise-robust training scheme, and demonstrates superior performance against BIM, VBIM, SOM, and NeuralBIM, across varying noise levels, contrasts, and measurement configurations. This work advances field-type DL design for inverse problems, offering improved interpretability and practical effectiveness in ISPs while suggesting paths toward semi-supervised and resolution-flexible extensions.

Abstract

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 structural rationality 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 analytical calculation of the contrast variation into each subnetwork, 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, imposing soft physical constraints on the variables in the subnetworks, which benefits the model's performance. 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.

Figures (23)

• Figure 1: The schematic of a 2-D ISP under TM illuminations, where targets are inside the DOI $D$, and transmitting and receiving antennas are located on the circumference.
• Figure 2: The framework of the proposed VBIM-Net. VBIM-Net is composed of $K$-layer subnetworks with the same structure but independent parameters. The input of VBIM-Net is the incident field of $N_i$ incidence and the rough contrast image obtained by BPS. The output of each VBIM-Net layer includes the predicted total field $\mathbf{E}^t_{(k)}$ and contrast $\boldsymbol{\chi}_{(k)}$, $k = 1, \cdots, K$. The loss function calculation is depicted under the network framework.
• Figure 3: The structure of each layer of VBIM-Net, in which the analytical update steps are indicated by blue arrows. The networks $\mathcal{F}^{\delta\mathbf{E}^t}_{k}$ and $\mathcal{F}^{\delta\boldsymbol{\chi}}_{k}$ adopt U-Net with the same structure, as shown on the right side of the figure.
• Figure 4: Module executing the mapping $\delta\mathbf{E}^s \rightarrow \mathbf{F}^{\delta\mathbf{E}^s}$ for dimension transformation in each layer of the modified NeuralBIM.
• Figure 5: Examples of scatterers in the synthetic dataset for lossy scatterers. The first row also represents the examples from the lossless dataset.