半空间三维目标的快速声学成像

研究了从声散射场的远场分布的信息来再现半空间三维目标几何特征信息的反问题,提出了求解这种非线性不适定问题的一种简单快速算法。该方法的一个特别的性质是只需要通过一个不适定的线性方程组求解,即可简单快速地得到半空间中三维目标几何特征信息的一个清晰的像,而且目标的个数和边界条件的类型等几何与物理的先验信息在本算法中都是不需要的。数值算例保证了本算法的有效性。

Fast acoustic imaging for three dimensional objects in a half-space

An inverse problem aimed to recover the geometrical characteristics of a three dimensional object in the half-space from the knowledge of the far-field pattern of the acoustic scattering waves is investigated. A simply fast method is presented to solve the nonlinear and ill-posed inverse problem. A particular feature of the scheme is that it can reproduce a clear visualization of a three dimensional object in the half space only from the solution of a linear system even when neither the number of components nor the surface boundary condition of each component needs be known a priori.The algorithm has been verified to be considerably efficient by some numerical examples.