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压缩感知在电容层析成像中的应用

张立峰

张立峰. 压缩感知在电容层析成像中的应用[J]. 北京航空航天大学学报, 2017, 43(11): 2316-2321. doi: 10.13700/j.bh.1001-5965.2017.0052
引用本文: 张立峰. 压缩感知在电容层析成像中的应用[J]. 北京航空航天大学学报, 2017, 43(11): 2316-2321. doi: 10.13700/j.bh.1001-5965.2017.0052
ZHANG Lifeng. Compressed sensing application to electrical capacitance tomography[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(11): 2316-2321. doi: 10.13700/j.bh.1001-5965.2017.0052(in Chinese)
Citation: ZHANG Lifeng. Compressed sensing application to electrical capacitance tomography[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(11): 2316-2321. doi: 10.13700/j.bh.1001-5965.2017.0052(in Chinese)

压缩感知在电容层析成像中的应用

doi: 10.13700/j.bh.1001-5965.2017.0052
基金项目: 

国家自然科学基金 51306058

中央高校基本科研业务费专项资金 2017MS131

详细信息
    作者简介:

    张立峰  男, 博士, 副教授, 硕士生导师。主要研究方向:电学层析成像技术

    通讯作者:

    张立峰, E-mail: hdlfzhang@126.com

  • 中图分类号: TP391.4

Compressed sensing application to electrical capacitance tomography

Funds: 

National Natural Science Foundation of China 51306058

Fundamental Research Funds for the Central Universities 2017MS131

More Information
  • 摘要:

    压缩感知(CS)理论是在充分利用信号稀疏性或可压缩性的情况下,对信号进行少量采样即可实现信号的精确重建。本文尝试将CS理论应用于电容层析成像(ECT)图像重建中,首先,使用快速傅里叶变换(FFT)基将原始图像灰度信号进行稀疏化处理;其次,将ECT灵敏度矩阵的各行按随机顺序进行排列,得到ECT系统随机观测矩阵;最后,选取当前普遍使用的基于内点法、梯度投影(GPSR)算法以及贪婪算法的CS图像重建算法进行ECT图像重建,并与线性反投影及Landweber迭代算法进行了对比。仿真实验结果表明:基于CS图像理论的ECT图像重建算法,其重建精度有所提高。本文同时分析了3种CS图像重建算法的优缺点及适用范围。

     

  • 图 1  初始重建图像

    Figure 1.  Initial reconstructed images

    图 2  基于最优阈值处理的重建图像

    Figure 2.  Reconstructed images based on optimal threshold processing

    表  1  初始重建图像相对误差

    Table  1.   Relative error of initial reconstructed image

    流型 Er
    LBP Landweber 内点法 GPSR OMP
    流型1 1.405 3 0.793 3 0.807 8 0.590 7 0.798 8
    流型2 1.238 3 0.807 0 0.689 1 0.675 2 0.689 3
    流型3 1.570 9 0.882 6 0.718 9 0.774 0 0.863 9
    流型4 2.002 7 1.020 4 0.892 5 0.883 7 0.938 1
    流型5 2.052 8 1.114 7 0.904 1 1.091 0 0.971 5
    下载: 导出CSV

    表  2  初始重建图像相关系数

    Table  2.   Correlation coefficient of initial reconstructed image

    流型 Cc
    LBP Landweber 内点法 GPSR OMP
    流型1 0.616 9 0.769 6 0.813 8 0.874 2 0.737 5
    流型2 0.569 3 0.742 3 0.843 1 0.839 0 0.855 8
    流型3 0.445 8 0.685 0 0.730 3 0.812 9 0.575 2
    流型4 0.357 8 0.603 0 0.662 7 0.728 8 0.551 6
    流型5 0.322 8 0.536 6 0.675 2 0.632 2 0.525 6
    下载: 导出CSV

    表  3  后处理重建图像相对误差

    Table  3.   Relative error of reconstructed image after processing

    流型 Er
    后处理
    LBP
    后处理
    Landweber
    后处理内点法 后处理
    GPSR
    后处理
    OMP
    流型1 0.854 9 0.339 7 0.392 2 0.277 4 0.425 1
    流型2 0.784 5 0.392 2 0.240 2 0.219 3 0.325 2
    流型3 0.872 0 0.692 2 0.489 5 0.102 1 0.747 8
    流型4 1.258 3 0.640 3 0.517 4 0.408 2 0.822 9
    流型5 1.030 8 0.698 2 0.497 6 0.559 0 0.702 0
    下载: 导出CSV

    表  4  后处理重建图像相关系数

    Table  4.   Correlation coefficient of reconstructed image after processing

    流型 Cc
    后处理
    LBP
    后处理
    Landweber
    后处理内点法 后处理
    GPSR
    后处理
    OMP
    流型1 0.630 6 0.943 1 0.813 8 0.958 4 0.738 8
    流型2 0.696 6 0.920 4 0.966 6 0.972 2 0.938 3
    流型3 0.681 9 0.700 6 0.870 6 0.994 1 0.507 8
    流型4 0.552 2 0.846 1 0.797 4 0.915 4 0.542 7
    流型5 0.500 2 0.716 9 0.819 3 0.799 4 0.663 0
    下载: 导出CSV

    表  5  重建图像所用时间

    Table  5.   Consumed time of image reconstruction

    流型 重建图像所用时间/s
    LBP Landweber 内点法 GPSR OMP
    流型1 0.013 43 4.799 04 8.609 49 2.779 11 0.060 46
    流型2 0.014 73 4.585 68 8.791 92 2.623 62 0.043 96
    流型3 0.011 82 5.560 35 9.095 21 3.539 22 0.054 18
    流型4 0.013 81 5.262 73 9.862 51 4.610 25 0.087 01
    流型5 0.015 43 5.040 01 9.932 23 4.735 56 0.119 94
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-02-06
  • 录用日期:  2017-04-24
  • 刊出日期:  2017-11-20

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