This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way. Furthermore, the method can also compute the intensity of point sources provided that the sources are well separated. A simple justification of the method is done using the Green representation formula and an asymptotic expansion of the radiated field for small volume sources. The implementation of the method is non-iterative, computationally cheap, fast, and very simple. Numerical examples are presented to illustrate the performance of the method.

翻译：本文简要探讨了从固定频率的边界柯西数据中数值重建小型源的问题。我们研究了一种采样方法，能够快速且稳健地确定小型源的位置。此外，当源之间分离良好时，该方法还可计算点源的强度。通过格林表示公式和小体积源辐射场的渐近展开，我们对方法进行了简单验证。该方法实现过程无需迭代，计算成本低、速度快且操作简便。数值算例展示了该方法的性能。