一种电磁层析图像快速重建算法

刘泽; 肖君; 刘向龙; 赵鹏飞; 李勇; 霍继伟

doi:10.13700/j.bh.1001-5965.2017.0651

一种电磁层析图像快速重建算法

doi: 10.13700/j.bh.1001-5965.2017.0651

北京交通大学电子信息工程学院, 北京 100044

基金项目:

国家自然科学基金 61771041

详细信息

作者简介:
刘泽男, 博士, 教授。主要研究方向:过程参数检测、电磁层析成像

肖君女,硕士研究生。主要研究方向:电磁层析成像

通讯作者:
刘泽, E-mail: zliu@bjtu.edu.cn

中图分类号: TP23;TP212
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出版历程
- 收稿日期: 2017-10-23
- 录用日期: 2017-12-01
- 网络出版日期: 2018-08-20

An algorithm for fast reconstruction of electromagnetic tomography images

School of Electronic Information Engineering, Beijing Jiaotong University, Beijing 100044, China

Funds:

National Natural Science Foundation of China 61771041

More Information

Corresponding author: LIU Ze, E-mail: zliu@bjtu.edu.cn

摘要

摘要:
针对电磁层析成像（EMT）逆问题中，灵敏度矩阵的病态性、不适定性等问题，提出了一种新的电磁层析图像快速重建算法。利用主成分分析（PCA）对灵敏度矩阵做降维映射，再利用奇异值分解（SVD）求广义逆矩阵，重建图像。在选取灵敏度矩阵的协方差矩阵的特征值个数中，利用灵敏度矩阵特有的多样本特性，提出图像相关系数最大化算法，更加合理地去除灵敏度矩阵中的冗余信息，在尽可能不丢失成像特征信息的条件下，提高了解稳定性。实际采集数据成像时，该算法只需一次矩阵乘法运算，为快速实时成像提供了可能。与传统单步算法和迭代算法相比，该算法在成像质量和速度上都有较明显优势。
- 电磁层析成像(EMT) /
- 主成分分析(PCA) /
- 奇异值分解(SVD) /
- 图像相关系数最大化 /
- 降维
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.
- electromagnetic tomography (EMT) /
- principal component analysis (PCA) /
- singular value decomposition (SVD) /
- image correlation coefficient maximization /
- dimensionality reduction

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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

Figure 1. Covariance matrix and eigenvalue distribution of simulation data and experimental data

下载: 全尺寸图片幻灯片

图 2 多样本的图像相关系数均值分布

Figure 2. Image correlation coefficient mean distribution with multi-sample

下载: 全尺寸图片幻灯片

图 3 电动平移台及其控制器

Figure 3. Electric moving stage and its controller

下载: 全尺寸图片幻灯片

图 4 8线圈传感器激励检测系统

Figure 4. 8-coil sensor excitation and detection system

下载: 全尺寸图片幻灯片

表 1 灵敏度矩阵降维前后多物体成像对比

Table 1. Multi-object imaging contrast before and after dimension reduction of sensitivity matrix

表 2 各算法多物体仿真成像对比

Table 2. Comparison of multi-algorithm and multi-object simulation imaging

表 3 仿真图像相关系数数据

Table 3. Image correlation coefficient data in simulation

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

下载: 导出CSV

表 4 仿真图像相对误差数据

Table 4. Image relative error data in simulation

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

下载: 导出CSV

表 5 各算法计算时间

Table 5. Calculation time of each algorithm

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

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表 6 各算法实验成像对比

Table 6. Comparison of multi-algorithm experimental imaging

表 7 实验图像相关系数数据

Table 7. Image correlation coefficient data in experiment

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

下载: 导出CSV

表 8 实验图像相对误差数据

Table 8. Image relative error data in experiment

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

下载: 导出CSV

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