We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced based on the integral over the frequency variable. A factorization of this multi-frequency near field operator is further given and analysed. Motivated by such a factorization, we introduce a multi-frequency sampling method to reconstruct the source support. Its theoretical foundation is then derived from the properties of the factorized operators and a properly chosen point spread function. Numerical examples are provided to illustrate the multi-frequency sampling method with sparse near field measurements. Finally we briefly discuss how to extend the near field case to the far field case.
翻译：我们考虑了近地多频率稀少测量的反源问题。与基于空间变量整体的近地操作员相比,在频率变量整体的基础上引入了近地操作员的多频率操作员。进一步给出和分析了该近地操作员多频率的因子化。受这种因子化的驱动,我们采用了多频率取样方法来重建源支持。然后,其理论基础来自参数化操作员的特性和适当选择的点扩散功能。提供了数字实例,以说明多频率取样方法,而近地测量则稀少。最后,我们简要讨论了如何将近地取样扩大到远地案例。
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