用于非均匀介质重建的选代算法收敛性的研究

研究轴对称二维非均匀介质重建迭代算法的收敛性问题。首先借助于玻恩近似将非线性积分方程线性化，然后，利用玻恩迭代法和变形玻恩迭代法，由散射场数据对轴对称二维非均匀介质进行重建。通过几个例子研究了影响迭代算法收敛性的几种因素，如送代算法本身、积分离散化后的网格划分、正则化方法中的正则化参数选取等。

Researches on the Convergence of the Iterative Algorithms in the Reconstruction of Two-dimensional Axisymmetric Inhomogeneous Media

The convergence problem of the iterative method applied to the reconstruction of twodimensional axisymmetric inhomogeneous media is studied. The nonlinear integral equation is first linearized by using Born approximation, and then the measurements are used to reconstruct the twodimensional inhomogeneous media by using the Born iterative method and the distorted Born iterative method. Several examples are given to study some factors affecting the convergence of iterative method, such as the iterative method itself, the radial grid in the process of integral equation discretization and regularization parameters in the regularization methods and so on.