电磁逆散射成像的一种混合正则化方法

电磁逆散射成像问题数值求解中，非线性逆散射方程及其对应的离散方程组具有明显的不适定性，针对求解通常所用Tikhonov 正则化方法的参数选择在先验选取时缺乏有效的误差信息，而后验选取时需要更多计算量求解有关参数的方程的困难，本文中将小参数Tikhonov 正则化方法与共轭梯度法结合，提出了不适定方程组的混合正则化方法。数据仿真表明，该方法既可保证正则化效果，也减少了计算量。
关键词: 电磁逆散射 共轭梯度法 正则化

A Hybrid Regularized Method of Electromagnetic Inverse Scattering . ZHOU Ding-fa
(School of Communication and Control Engineering ,Southern Yangtze University,Wuxi 214122 China) Abstract: In numerically solving electromagnetic inverse scattering problem, there are ill-posedness of the nonlinear inverse scattering equation and its discrete form. In the conventional Tikhonov regularization for the solution, both the prior and the posterior determinations of the regularization parameter are difficult because of lack of effective error information and more computations for solving the equations for the parameter, respectively.
In this paper, a hybrid regularization technique is presented by combination of the Tikhonov regularization method with little parameter and the conjugate gradient method. The simulation results show that the proposed method can not only make the effective regularization but also need less the arithmetic operations.
Key words:Electromagnetic inverse scattering; Conjugate gradient method; Regularization