点源激励波场下的逆障碍物散射问题

Inverse Obstacle Scattering Problem for Point Source Excited Wave Fields

研究了从点源激励散射场的近场信息来再现三维障碍物形状的反问题 ,提出了一种非线性最优化求解方法 .该算法只需求解一个不适定的线性系和一个适定的非线性最小化问题 ,而且只需要点源入射场的散射场在某个有限孔径中若干有限个入射和测量点上的近场测量信息 .数值结果表明 ,对较小的波数 ,即使当入射和观测孔径为 π/4立体角时 。

A nonlinear optimization algorithm was proposed for solving the inverse problem of reconstructing the shape of a three dimensional obstacle from the information of the near field measurements for point source fields. The algorithm only needs to solve an ill posed linear system and a well posed minimization problem and requires only the knowledge of the near field measurements of the scattered fields due to point source fields at a finite number of incidence and observation points distributed over a limited aperture. The numerical results show that a reasonable reconstruction is also possible for low wavenumbers even when the incidence and observation aperture is as small as the possible π/4 solid angle.