发表机构
Southern University of Science and Technology; Shenzhen International Center for Mathematics; School of Mathematics and Statistics, Hubei Center for Applied Mathematics, and Hubei Key Laboratory of Computational Science, Wuhan University; School of Artificial Intelligence, Hubei Center for Applied Mathematics, and Hubei Key Laboratory of Computational Science, Wuhan University（南方科技大学; 深圳国际数学中心; 武汉大学数学与统计学院、应用数学湖北省协同创新中心、计算科学湖北省重点实验室; 武汉大学人工智能学院、应用数学湖北省协同创新中心、计算科学湖北省重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对稀疏有限孔径声学数据，提出基于Hankel补全的统一框架，实现离网格点散射体的稳定定位，并给出样本复杂度与定位误差界。
AI 中文摘要
我们研究在有限接收孔径上，从稀疏采样的单入射、单频率声学远场数据中定位$s$个不同的平面点散射体的问题。在第一Born近似下，相干数据形成二维离网格指数和，并具有低秩Hankel表示。有限孔径通常允许多个孔径容许的Hankel束，这些束具有不同的提升维度、采样重数和Vandermonde条件数。因此，Hankel束的选择影响数据补全和后续定位。在本工作中，我们引入一个基于一般孔径容许Hankel束的结构化补全和离网格定位的统一框架。我们在无噪声情况下建立精确恢复，并在有界噪声下从随机孔径样本数（与$s$成线性关系，直至由束几何、源条件和对数项决定的因子）建立稳定恢复，同时给出以补全误差表示的显式定位界。该分析将束几何的贡献与源配置引起的条件数分离，并为稳定补全和MUSIC分辨提供可验证的充分条件。这些结果为在给定物理孔径下选择样本高效的Hankel束提供定量标准。在连通和不连通孔径上的数值实验展示了束几何、采样和噪声的影响。
英文摘要
We study the localization of $s$ distinct 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 coherent data form a two-dimensional off-grid exponential sum and admit a low-rank Hankel representation. A limited aperture generally admits multiple aperture-admissible Hankel pencils with different lifted dimensions, sampling multiplicities, and Vandermonde conditioning. Hence, the choice of the Hankel pencil affects both data completion and subsequent localization. In this work, we introduce a unified framework for structured completion and off-grid localization based on general aperture admissible Hankel pencils. We establish exact recovery in the noiseless case and stable recovery under bounded noise from a number of random aperture samples that is linear in $s$, up to factors determined by the pencil geometry, source conditioning, and logarithmic terms, together with an explicit localization bound in terms of the completion error. The analysis separates the contribution of the pencil geometry from the conditioning induced by the source configuration and provides verifiable sufficient conditions for stable completion and MUSIC resolution. These results yield quantitative criteria for selecting sample efficient Hankel pencils under a prescribed physical aperture. Numerical experiments on connected and disconnected apertures demonstrate the effects of pencil geometry, sampling, and noise.
