德拜色散媒质的三维时域电磁逆散射技术（英文）  

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

作　　者：刘广东[1] 余广群 范士民[1] 

机构地区：[1]阜阳师范学院物理与电子工程学院,阜阳236037 [2]阜阳肿瘤医院乳腺外科,阜阳236018

出　　处：《计算物理》2015年第4期455-468,共14页Chinese Journal of Computational Physics

基　　金：Supported by National Natural Science Foundation of China(61071022);Key Program of Natural Science Foundation of Anhui Higher Education Institutions of China(KJ2014A193);Science and Technology Program of Anhui Province,China(12010302080,1501031114);Natural Science Foundation of Fuyang Teachers College,China(2014FSKJ14)

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.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.

关 键 词：乳腺癌检测 电磁逆散射 单极德拜色散模型 吉洪诺夫正则化 时域有限差分法 

分 类 号：TN95[电子电信—信号与信息处理] O441[电子电信—信息与通信工程]