Abstract
This work studies the localization of finite planar point scatterers from sparsely sampled single-incidence, single-frequency acoustic far-field data over a limited receiver aperture. Under the first Born approximation, the measurements admit low-rank Hankel representations, while different aperture-admissible Hankel pencils may lead to different completion and localization properties. We develop a unified framework covering the mathematical modeling, reconstruction algorithms, recovery theory, and numerical experiments for this problem. For general aperture-admissible Hankel pencils, we establish exact and stable recovery guarantees together with localization bounds, and derive verifiable conditions that quantify the effects of aperture geometry and source configuration. These results provide criteria for the construction and selection of Hankel pencils under a prescribed aperture. Numerical experiments on connected and disconnected apertures support the theoretical findings.