Generalizable Neural Electromagnetic Inverse Scattering

TL;DR:

We propose the first generalizable, physics-driven inverse scattering framework, which works in an end-to-end manner and achieves more accurate reconstructions on unseen cases. It remains robust even with a single transmitter and achieves real-time inference with over $300{,}000 \times$ speed-up.

Solving Electromagnetic Inverse Scattering Problems (EISP) is fundamental in applications such as medical imaging, where the goal is to reconstruct the relative permittivity from scattered electromagnetic field. This inverse process is inherently ill-posed and highly nonlinear, making it particularly challenging. A recent machine learning-based approach shows promising results by leveraging continuous implicit functions. However, it requires case-specific optimization, lacks generalization to unseen data, and fails under sparse transmitter setups (e.g., with only one transmitter). To address these limitations, we revisit EISP from a physics-informed perspective, reformulating it as a two-stage transmission–scattering process. This formulation reveals the induced current as a generalizable intermediate representation, effectively decoupling the nonlinear scattering process from the ill-posed inverse problem. Built on this insight, we propose the first generalizable physics-driven framework for EISP, comprising a current estimator and a permittivity solver, working in an end-to-end manner. The current estimator explicitly learns the induced current as a physical bridge between the incident and scattered field, while the permittivity solver computes the relative permittivity directly from the estimated induced current. Extensive experiments show that our method outperforms state-of-the-art approaches in reconstruction accuracy, generalization, and robustness. Notably, it achieves high-quality results even with a single transmitter—a setting where prior methods consistently fail. This work offers a fundamentally new perspective on electromagnetic inverse scattering and represents a major step toward cost-effective practical solutions for electromagnetic imaging.

Overview of our method. We decouple EISP into two physical stages: inverse scattering and inverse transmission, identifying the induced current field $\mathbf{J}$ as bridging the relative permittivity and scattered field. Our framework consists of (1) a current estimator that predicts $\hat{\mathbf{J}}({\bf{x}})$ from the scattered field $\mathbf{E}^\text{s}$ (using positional encoding $\gamma({\bf{x}})$ for spatial expressiveness) and (2) a permittivity solver that computes $\hat{\boldsymbol{\epsilon}_r}$ from $\hat{\mathbf{J}}$ and incident field $\mathbf{E}^\text{i}$. The current estimator learns the mapping $\mathbf{E}^\text{s} \rightarrow \mathbf{J}$ to solve inverse scattering, while the permittivity solver addresses inverse transmission by directly calculating $\boldsymbol{\epsilon}_r$ from $\mathbf{E}^\text{i}$ and $\hat{\mathbf{J}}$. Final $\hat{\boldsymbol{\epsilon}_r}$ is obtained by aggregating estimates $\{\hat{\boldsymbol{\epsilon}_r}^\text{(1)}, \dots, \hat{\boldsymbol{\epsilon}_r}^{(N)}\}$ across all $N$ transmitters.

Qualitative comparison under the single-transmitter setting:

Qualitative comparison under the multiple-transmitter setting:

Qualitative comparison under the single-transmitter setting for 3D reconstruction: