This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter. Regarding the inverse problem, in addition to a basic indicator function based on the approximate solutions, a novel indicator function is developed to construct the direct sampling method to recover both point-like and extended scatterers. Numerical experiments demonstrate that the proposed algorithms are effective in reconstructing both two-dimensional and three-dimensional scatterers with a single moving emitter.

翻译：本文研究以单个移动点源作为发射源的时域前向散射与逆散射问题。针对移动发射源的前向散射问题，本文给出了近似解。关于逆问题，除了基于近似解的基本指示函数外，本文还提出了一种新型指示函数，用于构建直接采样方法以重建点状和扩展散射体。数值实验表明，所提算法能有效利用单个移动发射源重建二维和三维散射体。