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 inverse 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. 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相关源函数支撑的多频因子分解方法。假设源函数由具有先验已知辐射周期的某个时间相关源的傅里叶逆变换给出。利用固定观测方向下的多频远场数据，我们提出了表征与观测方向垂直且包含支撑的最小带状区域的数值判据。来自稀疏观测方向的远场数据可用于恢复支撑的Θ-凸多边形。该反演算法在三维多频近场数据情形下同样被证明有效。针对近场情形，本文讨论了与时间相关逆源问题的关联。二维与三维数值实验验证了该方法的有效性与可行性。本文为恢复某类可容许时间相关源支撑的频域方法提供了数值分析。