Electromagnetic Inverse Scattering Problems (EISP) seek to reconstruct relative permittivity from scattered fields and are fundamental to applications like medical imaging. This inverse process is inherently ill-posed and highly nonlinear, making it particularly challenging, especially under sparse transmitter setups, e.g., with only one transmitter. While recent machine learning-based approaches have shown promising results, they often rely on time-consuming, case-specific optimization and perform poorly under sparse transmitter setups. To address these limitations, we revisit EISP from a data-driven perspective. The scarcity of transmitters leads to an insufficient amount of measured data, which fails to capture adequate physical information for stable inversion. Accordingly, we propose a fully end-to-end and data-driven framework that predicts the relative permittivity of scatterers from measured fields, leveraging data distribution priors to compensate for the incomplete information from sparse measurements. This design enables data-driven training and feed-forward prediction of relative permittivity while maintaining strong robustness to transmitter sparsity. Extensive experiments show that our method outperforms state-of-the-art approaches in reconstruction accuracy and robustness. Notably, we demonstrate, for the first time, high-quality reconstruction from a single transmitter. This work advances practical electromagnetic imaging by providing a new, cost-effective paradigm to inverse scattering. Code and models are released at https://gomenei.github.io/SingleTX-EISP/.

翻译：电磁逆散射问题（EISP）旨在从散射场中重建相对介电常数，是医学成像等应用的核心基础。该逆过程本质上是病态且高度非线性的，尤其在稀疏发射源配置（如仅使用单个发射器）下极具挑战性。尽管近期基于机器学习的方法取得了显著成效，但它们通常依赖耗时且针对特定案例的优化，且在稀疏发射源配置下表现不佳。为突破这些局限，我们从数据驱动视角重新审视EISP问题。发射源稀缺导致测量数据量不足，难以捕获足够物理信息以实现稳定反演。为此，我们提出一种全端到端的数据驱动框架，通过利用数据分布先验来补偿稀疏测量信息缺失，从而从测量场中预测散射体的相对介电常数。该设计支持数据驱动训练和相对介电常数的前馈预测，同时对发射源稀疏性保持强大鲁棒性。大量实验表明，本方法在重建精度和鲁棒性方面均优于现有最优方法。值得注意的是，我们首次实现了单发射器条件下的高质量重建。本研究通过提供一种低成本、高效的新型逆散射范式，推动了实用电磁成像技术的发展。相关代码与模型已发布于https://gomenei.github.io/SingleTX-EISP/。