﻿ 一种电磁层析图像快速重建算法<sup>*</sup>
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An algorithm for fast reconstruction of electromagnetic tomography images
LIU Ze, XIAO Jun, LIU Xianglong, ZHAO Pengfei, LI Yong, HUO Jiwei
School of Electronic Information Engineering, Beijing Jiaotong University, Beijing 100044, China
Received: 2017-10-23; Accepted: 2017-12-01; Published online: 2018-01-26 17:11
Foundation item: National Natural Science Foundation of China (61771041)
Corresponding author. LIU Ze, E-mail: zliu@bjtu.edu.cn
Abstract: For the inverse problem of electromagnetic tomography (EMT), the pathological and ill posed problems of the sensitivity matrix are discussed. A new electromagnetic tomography image reconstruction algorithm is proposed for this situation. Firstly, the principal component analysis (PCA) is used to reduce the dimension of the sensitivity matrix, and then the singular value decomposition (SVD) is used to calculate the generalized inverse matrix to reconstruct the image. After the covariance matrix of the sensitivity matrix is obtained, we need to compute the number of eigenvalues that the covariance matrix should retain. Then the maximization of the image correlation coefficient algorithm is proposed to solve it by using the unique multi-sample characteristics of the sensitivity matrix. It is more reasonable for sensitivity matrix to remove redundant information. And it improves the stability of the solution as far as possible without losing imaging feature information. When the actual data is used for imaging, this algorithm needs only one matrix multiplication, which provides the possibility for fast real-time imaging. In conclusion, compared with the traditional single step algorithm and iterative algorithm, the proposed algorithm has obvious advantages in both imaging quality and speed.
Keywords: electromagnetic tomography (EMT)     principal component analysis (PCA)     singular value decomposition (SVD)     image correlation coefficient maximization     dimensionality reduction

1 灵敏度矩阵降维原理

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 图 1 仿真数据和实验数据的协方差矩阵及其特征值分布 Fig. 1 Covariance matrix and eigenvalue distribution of simulation data and experimental data

2 特征值个数选取算法原理

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 图 2 多样本的图像相关系数均值分布 Fig. 2 Image correlation coefficient mean distribution with multi-sample

3 奇异值分解原理

4 仿真和实验 4.1 仿真

 样本类型 LBP法 Tikhonov正则化法 Landweber迭代算法 降维SVD 1物体 -0.010 0 0.506 4 0.787 1 0.801 5 2物体 -0.007 0 0.595 4 0.761 9 0.688 5 3物体 -0.027 4 0.538 6 0.707 9 0.652 5 4物体 -0.040 6 0.424 5 0.644 9 0.606 1 5长物体 -0.026 5 0.279 6 0.319 4 0.326 4

 样本类型 LBP法 Tikhonov正则化法 Landweber迭代算法 降维SV 1物体 1.188 7 1.046 7 0.753 2 0.751 1 2物体 1.102 8 0.726 5 0.675 2 0.795 5 3物体 1.042 9 0.729 7 0.637 6 0.668 2 4物体 1.069 5 0.788 3 0.662 2 0.684 0 5长物体 3.422 0 0.886 5 0.868 8 0.875 2

 ms 样本类型 LBP法 Tikhonov正则化法 Landweber迭代算法 降维SVD 1物体 1.1 0.4 200.1 0.2 2物体 1.2 0.4 306.4 0.2 3物体 1.1 0.4 440.4 0.2 4物体 1.2 0.3 280.8 0.2 5长物体 1.2 0.4 453.2 0.2

4.2 实验

 图 3 电动平移台及其控制器 Fig. 3 Electric moving stage and its controller
 图 4 8线圈传感器激励检测系统 Fig. 4 8-coil sensor excitation and detection system

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 样本类型 LBP法 Tikhonov正则化法 Landweber迭代算法 降维SVD 1物体 0.531 6 0.612 2 0.652 3 0.647 5 2物体 0.453 4 0.543 3 0.608 4 0.599 0 3物体 0.467 1 0.519 1 0.587 9 0.590 4

 样本类型 LBP法 Tikhonov正则化法 Landweber迭代算法 降维SVD 1物体 0.960 3 0.787 0 0.674 1 0.685 0 2物体 0.959 7 0.696 6 0.667 2 0.671 1 3物体 0.953 7 0.778 3 0.693 0 0.687 6

5 结论

1) 相较于传统的LBP法、Tikhonov正则化法，本文算法在成像质量上具有优势。

2) 相较于传统的Landweber迭代算法、LBP法、Tikhonov正则化法，本文算法在成像时间上具有优势。

3) 灵敏度矩阵中多样本的利用，对电磁层析成像各算法的参数选取问题具有一定借鉴意义，可一定程度上避免偶然性。

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#### 文章信息

LIU Ze, XIAO Jun, LIU Xianglong, ZHAO Pengfei, LI Yong, HUO Jiwei

An algorithm for fast reconstruction of electromagnetic tomography images

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(8): 1569-1576
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0651