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优化Landweber迭代快速电磁层析成像图像重建算法

霍继伟 刘泽 王亚东 袁伟 王成飞

霍继伟, 刘泽, 王亚东, 等 . 优化Landweber迭代快速电磁层析成像图像重建算法[J]. 北京航空航天大学学报, 2021, 47(8): 1571-1579. doi: 10.13700/j.bh.1001-5965.2020.0284
引用本文: 霍继伟, 刘泽, 王亚东, 等 . 优化Landweber迭代快速电磁层析成像图像重建算法[J]. 北京航空航天大学学报, 2021, 47(8): 1571-1579. doi: 10.13700/j.bh.1001-5965.2020.0284
HUO Jiwei, LIU Ze, WANG Yadong, et al. Optimized Landweber iterative fast image reconstruction algorithm for electromagnetic tomography[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(8): 1571-1579. doi: 10.13700/j.bh.1001-5965.2020.0284(in Chinese)
Citation: HUO Jiwei, LIU Ze, WANG Yadong, et al. Optimized Landweber iterative fast image reconstruction algorithm for electromagnetic tomography[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(8): 1571-1579. doi: 10.13700/j.bh.1001-5965.2020.0284(in Chinese)

优化Landweber迭代快速电磁层析成像图像重建算法

doi: 10.13700/j.bh.1001-5965.2020.0284
基金项目: 

国家自然科学基金 61771041

北京市自然科学基金 4192045

详细信息
    通讯作者:

    刘泽, E-mail: zliu@bjtu.edu.cn

  • 中图分类号: TP23;TP212

Optimized Landweber iterative fast image reconstruction algorithm for electromagnetic tomography

Funds: 

National Natural Science Foundation of China 61771041

Beijing Municipal Natural Science Foundation 4192045

More Information
  • 摘要:

    电磁层析成像(EMT)中灵敏度矩阵的病态性、不适定性导致重建图像质量较差。为了提高重建图像的质量与速度,提出了一种优化Landweber迭代快速图像重建算法。首先,对灵敏度矩阵作降维映射,去除灵敏度矩阵中的冗余信息,减少每次迭代的计算量。然后,利用人群搜索算法(SOA)优化降维后的灵敏度矩阵,降低灵敏度矩阵的条件数,改善其病态程度。最后,通过Landweber迭代算法和预处理后的灵敏度矩阵进行图像重建。仿真实验结果表明:相同实验条件下,相比于Landweber迭代算法,所提算法有效提高了成像质量,降低了成像运算量。

     

  • 图 1  典型灵敏度矩阵分布

    Figure 1.  Typical sensitivity matrix distribution

    图 2  原始协方差矩阵特征值

    Figure 2.  Eigenvalues of original covariance matrix

    图 3  灵敏度矩阵条件数收敛曲线

    Figure 3.  Convergence curve of condition number of sensitivity matrix

    表  1  无噪声情况下图像重建结果

    Table  1.   Results of image reconstruction without noise

    表  2  无噪声情况下不同成像算法相关系数比较

    Table  2.   Comparison of correlation coefficients among different imaging algorithms without noise

    模型序号 相关系数
    LBP算法 Tikhonov算法 Landweber迭代算法 本文算法
    1 0.166 5 0.394 5 0.719 1 0.810 9
    2 0.066 1 0.354 5 0.732 8 0.868 9
    3 0.112 6 0.385 8 0.719 2 0.754 9
    4 0.114 7 0.354 4 0.690 2 0.720 1
    5 0.153 1 0.433 1 0.693 2 0.750 7
    6 0.075 7 0.146 3 0.435 6 0.794 8
    7 0.112 1 0.289 8 0.575 3 0.788 8
    8 0.148 2 0.178 1 0.568 1 0.701 8
    9 0.239 3 0.279 3 0.539 6 0.642 8
    10 0.378 2 0.569 7 0.687 1 0.730 7
    下载: 导出CSV

    表  3  无噪声情况下不同成像算法图像误差比较

    Table  3.   Comparison of image error among different imaging algorithms without noise

    模型序号 图像误差
    LBP算法 Tikhonov算法 Landweber迭代算法 本文算法
    1 1.200 2 1.025 6 0.718 6 0.652 2
    2 1.172 5 0.961 8 0.676 1 0.535 1
    3 1.195 8 1.034 2 0.792 3 0.756 4
    4 1.205 9 1.001 6 0.782 9 0.765 7
    5 1.340 6 1.157 3 0.949 7 0.792 5
    6 1.071 8 0.974 7 0.894 1 0.608 7
    7 1.399 6 0.901 1 0.872 4 0.858 9
    8 1.279 4 0.956 3 0.810 4 0.725 2
    9 1.589 4 0.907 4 0.850 9 0.862 4
    10 0.964 2 0.911 1 0.936 6 0.788 0
    下载: 导出CSV

    表  4  噪声情况下图像重建结果

    Table  4.   Results of image reconstruction with noise

    表  5  噪声情况下不同成像算法相关系数比较

    Table  5.   Comparison of correlation coefficients among different imaging algorithms with noise

    模型序号 相关系数
    LBP算法 Tikhonov算法 Landweber迭代算法 本文算法
    1 0.166 8 0.394 2 0.714 3 0.803 1
    2 0.066 4 0.351 5 0.728 1 0.862 5
    3 0.112 2 0.387 1 0.716 7 0.757 1
    4 0.114 1 0.354 7 0.687 2 0.757 1
    5 0.152 7 0.433 6 0.695 4 0.756 9
    6 0.017 8 0.154 91 0.451 3 0.689 2
    7 0.125 9 0.289 2 0.574 3 0.783 3
    8 0.141 9 0.176 1 0.565 4 0.691 3
    9 0.240 4 0.277 1 0.536 8 0.637 7
    10 0.378 0 0.571 3 0.685 1 0.729 4
    下载: 导出CSV

    表  6  噪声情况下不同成像算法图像误差比较

    Table  6.   Comparison of image error among different imaging algorithms with noise

    模型序号 图像误差
    LBP算法 Tikhonov算法 Landweber迭代算法 本文算法
    1 1.200 7 1.021 9 0.725 6 0.684 5
    2 1.180 3 0.961 9 0.680 8 0.543 2
    3 1.191 0 1.033 7 0.763 0 0.804 4
    4 1.208 4 0.999 2 0.784 8 0.749 5
    5 1.337 8 1.149 5 0.937 7 0.810 4
    6 1.006 8 0.974 1 0.886 6 0.712 0
    7 1.381 5 0.901 3 0.874 5 0.883 8
    8 1.265 1 0.956 8 0.816 5 0.739 9
    9 1.597 5 0.908 1 0.850 8 0.874 9
    10 0.963 7 0.909 6 0.941 2 0.782 7
    下载: 导出CSV

    表  7  两种成像算法运算量比较

    Table  7.   Comparison of calculation load between two imaging algorithms

    算法 加法运算量 减法运算量 乘法运算量
    本文算法 12 538 644 19 320
    Landweber迭代算法 17 682 644 27 048
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-06-20
  • 录用日期:  2020-08-14
  • 刊出日期:  2021-08-20

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