二维非均匀介质目标重建中选择阻尼因子修正的Feltcher算法

二维介质目标的重构是通过在目标外获得的散射场实现的。为克服问题的病态性，本文采用多方向的横磁波(TM)照射目标，用矩量法(MOM)将散射的积分方程离散为矩阵方程，对方程组的求解采用阻尼最小二乘法，其中对阻尼因子的选取采用修正的Feltcher算法。数值结果表明：该方法的收敛性较好，能获得好的重构结果。

A Modified Feltcher Algorithm of Selecting Damping Factor in the Reconstruction of Two-Dimensional Inhomogeneous Media

In the reconstruction of two-dimensional inhomogeneous media, existing methods for selecting damping factor either require iterative selection by experience or face trouble in the selection of initial value within a narrow range. We propose a new method that can compute the damping factor directly and still, with due care, select a suitable initial value easily within a fairly large range. We use the method of moment (MOM) with pulse-basis function and point matching to discretize the integral equation. In order to improve the ill-posedness, the object is illuminated by different-direction transverse magnetic (TM) waves. We explain in some detail how to use the well-known damping least squares method to solve the matrix equation. For determining the damping factor that appears in the matrix equation, we use a modified Feltcher algorithm to make it suitable for complex-number calculations. We explain in much detail how to use modified Feltcher algorithm to determine the damping factor. A numerical example shows the method possesses good convergence and can obtain good reconstruction results.