SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1372-1393, June 2024.
Abstract. 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 [math]-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.

中文翻译：

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亥姆霍兹方程的反波数相关源问题


《SIAM 数值分析杂志》，第 62 卷，第 3 期，第 1372-1393 页，2024 年 6 月。

抽象的。本文涉及对波数相关源函数的支持进行成像的多频分解方法。假设源函数是由具有先验给定辐射周期的某些时间相关源的傅里叶逆变换给出的。使用固定观察方向的多频远场数据，我们提供了一个计算标准来表征包含支撑并垂直于观察方向的最小条带。来自稀疏观察方向的远场数据可用于恢复支撑件的凸多边形。即使对于三维多频近场数据，反演算法也被证明是有效的。在近场情况下讨论了与时间相关的逆源问题的联系。通过二维和三维数值试验验证了该方法的有效性和可行性。本文提供了频域方法的数值分析，以恢复对一类可接受的时间相关源的支持。