用迭代方法和双共轭梯度法重建二维电导率剖面分布

本文着重阐述采用积分方程的迭代方法并结合双共轭梯度（ＢＣＧ）法对低频近声非均匀背景介质中二维轴对称电导率剖面的反演，并仅用ｚ向采集的数据进行目标重建。首先，基于等反演目标区内、外的电场积分方程。建立超反演积分方程，将积分方程离散化为矩阵方程用迭代方法求解目标区电导率分布。在每次迭代过程中，格林函数不断被更新。同时用正则人垭消除解的不适定性。文中利用不完备的测量数据对复杂的电导率同进行了反演。模拟结

Reconstruction of the 2-Dimensional Inhomogeneous Conductivity Profile Using Iterative and Bi-Conjugate Gradient Method

In this paper,the inversion and reconstruction of 2-dimensional inhomogeneous conductivity profile for low-frquency near field using iterative algorithm and bi-conjugate gradient method (BCG) is decribed. Based on the internal and external electric field integration equations, the inversion equation is derived. By using the method of moments ,the integral equation can be discretized into matrix form. The Green′s function is updated in every iteration step. Then, ill-posed problem is circumvented by imposing additional constraints on the solution using the Tikhonov regularzation method. Numerical results show that this method is of faster convergence and higher inverse quality than that which introduced in reference [8].