论文标题
从一个在一个稀疏观察方向上测得的多频数据成像移动点源（第I部分）：远场情况
Imaging a moving point source from multi-frequency data measured at one and sparse observation directions (part I): far-field case
论文作者
论文摘要
我们提出了一种多频算法，用于从一个频率域中的一个和稀疏的远场观察方向成像移动点源的轨迹。移动源的起点和终端时间点都应该是已知的。我们在远场区域介绍了可观察方向（角度）的概念，并为直动和圆形运动提供了所有可观察的方向（角度）。在可观察到的方向上，只要轨道函数具有一定的单调特性，就可以成像包含轨迹和垂直于方向的最小行程。没有单调性，就只能期望恢复较薄的条带。在稀疏观察方向上测量的远场数据可用于恢复轨迹的$θ$ -CONVEX域。二维数值示例均已实施，以显示该方法的有效性和可行性。
We propose a multi-frequency algorithm for imaging the trajectory of a moving point source from one and sparse far-field observation directions in the frequency domain. The starting and terminal time points of the moving source are both supposed to be known. We introduce the concept of observable directions (angles) in the far-field region and derive all observable directions (angles) for straight and circular motions. At an observable direction, it is verified that the smallest trip containing the trajectory and perpendicular to the direction can be imaged, provided the orbit function possesses a certain monotonical property. Without the monotonicity one can only expect to recover a thinner strip. The far-field data measured at sparse observable directions can be used to recover the $Θ$-convex domain of the trajectory. Both two- and three-dimensional numerical examples are implemented to show effectiveness and feasibility of the approach.
