三维障碍物形状反演问题的一种简单算法

A simple method for the shape identification problem of a three-dimensional obstacle

研究了从声散射场的远场分布的信息，再现三维物体形状的反问题．基于将在有限个测量方向上的远场数据作加权合成的思想，提出了求解这类反问题的一种简单快速算法．在这个算法中，既不需预先知道散射体的边界类型，也不需预先知道散射体个数的信息．对有限孔径远场数据的数值算例表明了这一方法是实用和有效的．

This paper deals with the inverse Problem to recovery the shape of a three-dimensional obstacle from the knowledge of the far-field pattern of the scattering wave. A simple fast method is proposed for solving the inverse problem, which is based on a weighted superposition technique of the far-field data at a finite number of observation directions. The method requires no a prior knowledge of the type of boUndary condition imposed on the objects, nor does it depend upon prior information about the nUmber of the objects. Some numerical examples are given with the fleded aperture far-field data showing Validity and practicality of this method for low wavenumbers.