Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Direct Sampling Method). We present a modular framework that significantly improves multi-source localization from extremely sparse single-frequency measurements. First, we extend a uniqueness theorem for the inverse source problem, proving that a unique solution is guaranteed under limited viewing apertures. Second, we employ a Deep Operator Network (DeepONet) with a branch-trunk architecture to interpolate the sparse measurements, lifting six to ten samples within the narrow aperture to a sufficiently dense synthetic aperture. Third, the super-resolved field is fed into the Direct Sampling Method (DSM). For a single source, we derive an error estimate showing that sparse data alone can achieve grid-level precision. In two- and three-source trials, localization from raw sparse measurements is unreliable, whereas DeepONet-reconstructed data reduce localization error by about an order of magnitude and remain effective with apertures as small as $\pi/4$. By decoupling interpolation from inversion, the framework allows the interpolation and inversion modules to be swapped with neural operators and classical algorithms, respectively, providing a practical and flexible design that improves localization accuracy compared with standard baselines.

翻译：从窄孔径收集的Helmholtz边界数据进行逆源定位是高度不适定且严重欠采样的，这削弱了经典求解器（例如直接采样方法）的性能。我们提出了一种模块化框架，显著提升了从极稀疏单频测量中进行多源定位的能力。首先，我们扩展了逆源问题的唯一性定理，证明在有限视角孔径下仍能保证唯一解的存在。其次，我们采用具有分支-主干架构的深度算子网络（DeepONet）对稀疏测量进行插值，将窄孔径内的六至十个样本提升为足够密集的合成孔径数据。第三，超分辨率重建后的场数据被输入直接采样方法（DSM）进行处理。针对单源情况，我们推导了误差估计，表明仅凭稀疏数据即可实现网格级精度。在双源和三源实验中，基于原始稀疏测量的定位结果不可靠，而经DeepONet重建的数据可将定位误差降低约一个数量级，且在孔径小至$\pi/4$时仍保持有效。该框架通过解耦插值与反演过程，允许分别用神经算子和经典算法替换插值模块与反演模块，提供了一种实用且灵活的设计方案，其定位精度较标准基线方法有明显提升。