二维有耗介质目标重建的Newtoin迭代方法

Newton Iterative Method to Reconstruct 2-D Lossy Dielectric Object

本文给出了一种由已知的散射场数据重建二线非均匀有耗目标的复介电常数的迭代算法。由积分方程出发，利用点匹配技术导出了依赖于未知参数的解析逆散射公式。由此可以以解析的形式计算场量对未知参数的导数（Jacobian和Hessian矩阵）。本文采用Newton优化方法迭代末解道散射问题，具有二次收敛特性。为了克服逆散射中解的不适定性，连续采用多个方向的TM波照射目标，并采集目标区域外的散射场数据，以及采用共轭梯度法（CGM）求解逆问题．数值结果表明了本文所提方法的可行性和灵活性。

A Newton iterative method to reconstruct a 2-D lossy dielectric object is presented. Based on the boundary integral equations, an inverse scattering formulation related explicitly to the unknowns is derived by point matching technique. Hence, the derivatives of the fields with respect to these unknowns (the Jacobian and Hessian matrices)can be computed in an explicit form. Furthermore, an conjugate gradient algorithm is employed to overcome the illpossness. Numerical results show the feasibility of the presented scheme.