电子学报 ›› 2015, Vol. 43 ›› Issue (12): 2518-2524.DOI: 10.3969/j.issn.0372-2112.2015.12.026

• 科研通信 • 上一篇    下一篇

多极德拜色散媒质的时域电磁逆散射改进技术

刘广东1, 葛新同2   

  1. 1. 阜阳师范学院物理与电子工程学院, 安徽阜阳 236037;
    2. 阜阳师范学院数学与统计学院, 安徽阜阳 236037
  • 收稿日期:2014-07-03 修回日期:2014-09-26 出版日期:2015-12-25 发布日期:2015-12-25
  • 通讯作者: 刘广东
  • 作者简介:葛新同 男,1966年生于安徽蒙城.现为阜阳师范学院数学与统计学院讲师、工学博士.研究方向为不确定最优控制及金融数学.E-mail:gxtong01234@163.com
  • 基金资助:

    国家自然科学基金(No.61071022);安徽高校省级自然科学研究重点项目(No.KJ2014A193);安徽省科技计划项目(No.12010302080);阜阳师范学院自然科学研究项目(No.2014FSKJ14)

An Improved Time-Domain Electromagnetic Inverse Scattering Technique for Multi-Pole Debye Dispersive Media

LIU Guang-dong1, GE Xin-tong2   

  1. 1. School of Physics and Electronic Engineering, Fuyang Normal College, Fuyang, Anhui 236037, China;
    2. School of Mathematics and Statistics, Fuyang Normal College, Fuyang, Anhui 236037, China
  • Received:2014-07-03 Revised:2014-09-26 Online:2015-12-25 Published:2015-12-25

摘要:

在已有的经验模型中,多极德拜(Debye)模型最适合高精地描述生物组织、土壤、水等媒质的色散特性.为了同时反演这类媒质的电磁参数,本文提出了一种时域逆散射改进技术:分别应用迭代法和吉洪诺夫(Tikhonov)正则化技术克服逆问题的非线性和病态性困难;解析导出了目标泛函关于目标参数的梯度;迭代重建过程中,产生的正演、反演子问题分别选用时域有限差分(FDTD)法、共轭梯度(CG)法求解.噪声环境下,通过两个一维(1-D)的数值算例,初步证实了该技术的可行性和鲁棒性.

关键词: 电磁逆散射, 多极德拜色散媒质, 吉洪诺夫正则化, 时域有限差分法

Abstract:

The Debye model with multiple relaxation times is most suitable for highly accurate description of the dispersion characteristics of many media,such as biological tissues,soil,and water,among the developed empirical models.In order to reconstruct the electromagnetic properties of these dispersive media simultaneously,a modified time-domain inverse scattering technique is presented.Firstly,in the proposed technology,the nonlinearity and ill-posedness of the inverse problem is circumvented by an iterative method and the Tikhonov's regularization,respectively.Secondly,a set of closed gradients (Fréchet derivatives) of its cost functional with respect to objective parameters are derived for the aforementioned inverse problem.Then,the finite-difference time-domain (FDTD) method and any conjugate gradient (CG) method is applied,at its each iteration,to solve the resulting forward and backward sub-problem,respectively.Lastly,the feasibility and robustness for the inversion technique are preliminarily confirmed by two one-dimensional (1-D) numerical examples where a model of the additive white Gaussian noise (AWGN) is considered.

Key words: electromagnetic inverse scattering, multi-pole Debye dispersive media, Tikhonov's regularization, finite-difference time-domain (FDTD) method

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