中文摘要：

生物组织、土壤、水等媒质的电特性是频率相关的（称为色散媒质）,常利用单极德拜（Debye）模型描述.为重建这一类媒质的色散特性,基于泛函分析和变分法,提出一种三维（3-D）时域电磁（EM）逆散射技术,主要流程为：1根据最小二乘准则,转化逆散射问题为约束最小化问题;2应用罚函数法,转化约束最小化问题为无约束最小化问题;3通过变分计算,解析导出梯度（Fréchet导数）表达式;4利用梯度法求解.此外,引入一阶吉洪诺夫（Tikhonov）正则化以应对逆问题的病态特性和噪声影响.数值应用中,将提出的方法应用到一个简单的三维癌变乳房模型,借助PRP共轭梯度（CG）算法和时域有限差分（FDTD）法,仿真结果初步证实本文方法的可行性、有效性和鲁棒性.

英文摘要：

Dielectric properties of a variety of media,such as biological tissues,soil,and water,are frequency-dependent,which are depicted frequently by a single-pole Debye model. A three-dimensional（ 3-D） time-domain electromagnetic inverse scattering technique,based on functional analysis and variation method,is developed to reconstruct dispersive properties of media. Main procedures of the technique are： 1 Inverse scattering problem is turned into a constrained minimization problem,according to the least squares criterion; 2 Resulting problem is translated into an unconstrained minimization one,using a penalty function method;3 Closed Fréchet derivatives of Lagrange function with respect to properties are derived,based on calculus of variations; 4 Resulting problem is solved with any gradient-based algorithm. Furthermore,a first-order Tikhonov＇s regularization is adopted to cope with noise and ill-posedness of the problem. In numerical experiment,the technique is applied to a simple 3-D cancerous breast model,with Polak-Ribière-Polyak conjugate gradient algorithm and finite-difference time-domain method. Simulated results demonstrate preliminarily feasibility,effectiveness and robustness of the method.