電磁逆散射成像問題數值求解中，非線性逆散射方程及其對應的離散方程組具有明顯的不適定性，針對求解通常所用Tikhonov 正則化方法的參數選擇在先驗選取時缺乏有效的誤差信息，而后驗選取時需要更多計算量求解有關參數的方程的困難，本文中將小參數Tikhonov 正則化方法與共軛梯度法結合，提出了不適定方程組的混合正則化方法。數據仿真表明，該方法既可保證正則化效果，也減少了計算量。
關鍵詞: 電磁逆散射 共軛梯度法 正則化

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