Inversion of Two-Dimensional Inhomogeneous Conductivity Distribution Using the Distorted Born Iterative Method

张业荣; 聂在平; 阮颖铮

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Inversion of Two-Dimensional Inhomogeneous Conductivity Distribution Using the Distorted Born Iterative Method

更新时间：2025-12-08

- Inversion of Two-Dimensional Inhomogeneous Conductivity Distribution Using the Distorted Born Iterative Method
- Acta Electronica Sinica Issue 12, (1997)
- 作者机构：
  
  1. 华中理工大学电信系
  2. 电子科技大学微波工程系
  3. 华中理工大学电信系电子科技大学微波工程系
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN011
- Published：1997
- 稿件说明：
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[1]张业荣,聂在平,阮颖铮.用变形玻恩迭代法反演电导率的二维非均匀分布[J].电子学报,1997(12):100-104+111.

张业荣, 聂在平, 阮颖铮. Inversion of Two-Dimensional Inhomogeneous Conductivity Distribution Using the Distorted Born Iterative Method[J]. Acta Electronica Sinica, 1997, (12).
[1]张业荣,聂在平,阮颖铮.用变形玻恩迭代法反演电导率的二维非均匀分布[J].电子学报,1997(12):100-104+111. DOI：

张业荣, 聂在平, 阮颖铮. Inversion of Two-Dimensional Inhomogeneous Conductivity Distribution Using the Distorted Born Iterative Method[J]. Acta Electronica Sinica, 1997, (12). DOI：

摘要

本文把变形玻恩迭代方法用于求解二维轴对称道散射问题．该方法提供一种迭代收敛较快的反演成像算法．利用对称轴上２０ｋＨｚ电场的测量值在二维非均匀介质中对电导率分布进行反演．首先给出对于未知电导率分布的非线性积分方法．并用玻恩近似使积分方程线性化．然后用古洪诺夫正则化方法求出电导率分布．在选代过程中，数值模式匹配法用于求解正演场．数值实例表明，用简单的对称轴上测量场能得到很好的成像结果．

Abstract

In this paper

the distorted Born iterative method is used to solve two-dimensional inverse scattering problems.This method Provides an iterative algorithm with faster convergence for inversion and imagingproblem. ’The inversion is performed for conductivity of tWo-dimensional axisymmetrically inhomogeneous medium

by using measurements on the symmetry axis at 20 kHz. The nonlinear integral equation for unknown conductivity distribution is first given

and is linearized by using Born approximahon. Then the Tikhonov regularization method is used to derive the conductivity distribution. In iteration procedure

the numerical mode matchingmethod is used to solve the forward problem. It is shown from the inversion results that the good imaging resultcan be obtained from simple field measurements at the axis points.

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