电磁逆散射问题中的泛函方法

用于电磁逆散射问题中关于未知介质分布的非线性积分方程经离散化后，其相应的矩阵方程通常是病态方程。对于病态的矩阵方程，其解或是不存在或是不唯一。这取决于该矩阵方程是超定的还是欠定的。对于这样的不适定问题，可用一些泛函方法使其转化为适定问题。文中介绍了用于电磁逆散射问题中的最小二乘方法、奇异值分解方法、正则化方法和最大熵方法，并对各种方法的优缺点给出评价。

Functional Methods of Inverse Problems in Electromagnetics

The nonlinear integral equation for unknown media distribution applied to inverse scatteringproblem in electromagnetics is discretized,then its corresponding matrix equation is ill-condititoned. Thesolution of the ill-conditioned matrix equation generally is nonexistent or nonunique,depending on that thematrix equation is overdetermined or underdetermined. Some functional methods can transform the ill-posedproblem into well-posed problem. This paper introduces the least square method, the singulat value decomposition method. the regularization method and the maximum entropy method, and gives theevaluation to advantages and disadvantages for the various methods.