Contrast-Source-Based Physics-Driven Neural Network for Inverse Scattering Problems

TL;DR

The paper tackles the ill-posed, nonlinear inverse scattering problem (ISP) with limited data by introducing CSPDNN, a contrast-source based physics-driven neural network that predicts the induced current distribution $J$ rather than directly estimating $ε_r$. It integrates a state-consistency and data-fidelity loss with a bound constraint and an adaptive total-variation regularization to adapt to varying contrast and noise levels, thereby achieving fast and robust reconstructions. CSPDNN demonstrates about 3×–4× speedups over competing solvers and maintains high reconstruction quality across complex, lossy, and noisy scenarios, with successful experimental validation on FoamDielExt data. The approach offers practical potential for non-destructive testing, security screening, and subsurface imaging by delivering accurate, stable ISP solutions without requiring large training datasets.

Abstract

Deep neural networks (DNNs) have recently been applied to inverse scattering problems (ISPs) due to their strong nonlinear mapping capabilities. However, supervised DNN solvers require large-scale datasets, which limits their generalization in practical applications. Untrained neural networks (UNNs) address this issue by updating weights from measured electric fields and prior physical knowledge, but existing UNN solvers suffer from long inference time. To overcome these limitations, this paper proposes a contrast-source-based physics-driven neural network (CSPDNN), which predicts the induced current distribution to improve efficiency and incorporates an adaptive total variation loss for robust reconstruction under varying contrast and noise conditions. The improved imaging performance is validated through comprehensive numerical simulations and experimental data.

Figures (6)

• Figure 1: The configuration of 2-D inverse scattering problems.
• Figure 2: The network architecture of the proposed CSPDNN solver.
• Figure 3: Comparison of imaging results for complex scatterers obtained by SOM, uSOM, PDNN, and CSPDNN solver.
• Figure 4: Reconstruction results of lossy scatterers using SOM, uSOM, PDNN, and CSPDNN solver.
• Figure 5: Tests of noise robustness of the ISP solver SOM, uSOM, PDNN and CSPDNN.