三维有限孔径逆声散射问题的数值解

从声散射场远场分布的信息来再现三维障碍物形状反问题的数值解,提出了求解这类非线性且不适定反问题的一种非线性最优化方法,该方法的主要特点是只需声散射场的远场分布在某个有限孔径中若干个入射和观测方向上的远场信息。数值结果表明,对较小的波数,即使只用在较小的入射和观测范围中的远场测量信息,得到三维障碍物的一个合理的重构也是可能的。

Numerical Solution of the Limited Aperture Problem in Three-Dimensional Inverse Acoustic Scattering

This work was devoted to the numerical solution of the inverse problem of reconstructing the shape of a three-dimensional obstacle from the knowledge of the far field patterns of acoustic scattered waves. A nonlinear optimization method was proposed and analyzed for numerically solving the nonlinear and ill-posed inverse problem. A main feature of this scheme is that it requires only the information of the far-field patterns of the acoustic scattered waves at a finite number of incidence and observation directions distributed over some limited ranges. The numerical results demonstrate that the proposed scheme has some capacity for obtaining a reasonable reconstruction of a three-dimensional obstacle from the far field measurements over some small ranges of directions of incidence and observation for low wave numbers.