多重网格技术与波恩迭代法相结合的反演新方法

A Novel Inversion Method Combining Born Iterative Method with Multi-Grid Technique

本文将多重网格技术与波恩迭代法 (BIM)相结合 ,利用时域散射数据对二维无耗非均匀介质剖面进行了反演 .在反演迭代过程中 ,待反演目标区域的离散网格由粗逐渐变细 .由于在反演的初期 ,目标区域离散网格较粗 ,离散反演积分方程所得到的矩阵方程的维数较小、条件数较低 ,使得该方法具有稳定性好、更容易收敛到真解的特点 .通过反演实例表明 ,该方法极大地降低了反演过程的计算量 ,与传统的BIM方法相比能更精确地反演高对比度的散射目标 .更为重要的是本文方法简单可行。

A novel inversion method combining the Born iterative method (BIM) with multi grid technique is developed to solve the nonlinear inverse scattering problem for two dimensional lossless dielectric inhomogeneties using time domain scattering data.In the inversion procedure,the size of the discretization grid inside objects is reduced gradually.In the previous inversion procedure,because the condition number and dimension number of the matrix obtained by discretizing the integral equation are relatively small,this method has a good robustness and ability to converge more easily to the true profile.Several examples are given to show that this method reduces vastly computational time of the inversion procedure and can accurately reconstruct the higher contrast scattering object than that of the BIM.It is more important that this method has the simplicity and can be used to other arbitrary inverse scattering method.