用于电磁源重建的多频远场数据增强
Multi-frequency far-field data enrichment for electromagnetic source reconstruction
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中文总结 AI 辅助
本文针对电磁源重建中多频远场数据欠采样的问题，提出基于ALOHA方法的两阶段数据增强策略，实现了高子采样率和强噪声下的准确稳定重建，性能优于标准ℓ₁压缩感知基线。
中文摘要 AI 辅助
从远场辐射图重建未知电磁源是一个基础逆问题，广泛应用于生物医学成像、无损检测和电信领域。但实际场景中，以奈奎斯特采样率采集密集多频远场测量数据往往不可行，欠采样或稀疏数据会引入非辐射源分量，破坏解的唯一性，应用标准反演技术时会产生严重伪影。为克服这一局限，本文提出一种两阶段重建策略，利用紧支撑、几何稀疏源具有有限创新率（FRI）的物理特性：第一阶段构建关联的环绕结构汉克尔矩阵，借助未知源FRI带来的矩阵低秩特性增强子采样数据，将缺失的多频远场数据恢复转化为基于Annihilating Filter-based Low-rank Hankel Matrix Completion Approach（ALOHA，基于湮灭滤波器的低秩汉克尔矩阵补全方法）求解的约束矩阵补全任务；第二阶段采用傅里叶反演方案从增强数据集中重建电流源密度。对电磁源模型的大量数值评估表明，该增强框架可有效消除欠采样伪影、解决非唯一性挑战，在高子采样率（如仅30%至50%可用样本）和强噪声条件（10 dB信噪比）下，能提供准确稳定的重建结果，性能优于标准ℓ₁压缩感知基线方法。
英文摘要
Reconstructing unknown electromagnetic sources from far-field radiation patterns is a fundamental inverse problem with broad applications in biomedical imaging, non-destructive testing, and telecommunications. In practical settings, however, collecting dense multi-frequency far-field measurements at the Nyquist sampling rate is often infeasible. Under-sampled or sparse data introduce non-radiating source components that sever the uniqueness of the solution, creating severe artifacts when standard inversion techniques are applied. To overcome this limitation, we present a two-stage reconstruction strategy exploiting the physical property that compactly supported, geometrically sparse sources exhibit a finite rate of innovations (FRI). In the first stage, we construct an associated wrap-around structured Hankel matrix. By leveraging the low-rank property of the matrix due to FRI of the unknown sources, we enrich the sub-sampled data. To that end, we convert missing multi-frequency far-field data recovery into a constrained matrix completion task solved via Annihilating Filter-based Low-rank Hankel Matrix Completion Approach (ALOHA). In the second stage, a Fourier inversion scheme reconstructs the current source density from the enriched dataset. Extensive numerical evaluations on electromagnetic source models show that our enrichment framework effectively eliminates under-sampling artifacts and resolves non-uniqueness challenges. The method delivers accurate and stable reconstructions under high sub-sampling rates (e.g., with $30$\% to $50$\% available samples) and strong noise conditions ($10$ dB SNR), outperforming standard $\ell_1$-compressed sensing baselines.
