德拜色散媒质的三维时域电磁逆散射技术

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,将提出的目的 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目的 的可行性、有效性和鲁棒性.

Three-Dimensional Time-Domain Electromagnetic Inverse Scattering Technique for Debye Dispersive Media

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.