This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the Fourier transform of some time-dependent source with a priori given radiating period. Using the multi-frequency far-field data at a fixed observation direction, we provide a computational criterion for characterizing the smallest strip containing the support and perpendicular to the observation direction. The far-field data from sparse observation directions can be used to recover a $\Theta$-convex polygon of the support. The inversion algorithm is proven valid even with multi-frequency near-field data in three dimensions. The connections to time-dependent inverse source problems are discussed in the near-field case. We also comment on possible extensions to source functions with two disconnected supports. Numerical tests in both two and three dimensions are implemented to show effectiveness and feasibility of the approach. This paper provides numerical analysis for a frequency-domain approach to recover the support of an admissible class of time-dependent sources.

翻译：本文研究用于成像波数依赖源函数支撑的多频因子分解方法。假设源函数由具有先验给定辐射周期的时变源函数的傅里叶变换给出。利用固定观测方向的多频远场数据，我们提供了一个计算判据来刻画包含支撑且垂直于观测方向的最小条带。稀疏观测方向的远场数据可用于恢复支撑的$\Theta$-凸多边形。该反演算法甚至在使用三维多频近场数据时仍被证明有效。在近场情形下讨论了与时间依赖反源问题的关联。我们还评述了可能拓展至具有两个不连通支撑的源函数的情况。在二维和三维中实施的数值测试表明了该方法的有效性和可行性。本文为频率域方法恢复可容许类时变源函数的支撑提供了数值分析。