Optimized Landweber iterative fast image reconstruction algorithm for electromagnetic tomography
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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。
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关键词:
- 电磁层析成像(EMT) /
- 人群搜索算法(SOA) /
- 图像重建 /
- 降维 /
- 灵敏度矩阵优化
Abstract:Due to the pathological property and ill-posedness of sensitivity matrix in Electromagnetic Tomography (EMT), the quality of the reconstructed image is relatively low. To improve the imaging quality and imaging speed, this paper proposes an optimized Landweber iterative fast iteration image reconstruction algorithm. Firstly, dimension reduction algorithm is used to decrease the sensitivity matrix dimension to eliminate the redundant information of sensitivity matrix and reduce the calculation load of each iteration. Secondly, Seeker Optimization Algorithm (SOA) is used to optimize the dimension-reduced sensitivity matrix. This optimization operation can reduce the condition number and improve the morbidity degree of sensitivity matrix. Finally, Landweber iteration algorithm and preprocessed sensitivity matrix are used to reconstruct image. Simulation experimental results show that, under the same experimental conditions, compared with Landweber iteration algorithm, the proposed algorithm increase the quality of reconstructed image and decrease the calculation load of image reconstruction.
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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 
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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
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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
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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
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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
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