Improved capacitance imaging biconjugate gradient image reconstruction algorithm
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摘要:
针对电容层析成像技术（ECT）逆问题中软场效应的影响，以及重建图像时使用的传统迭代类算法迭代次数多、成像速度慢等问题，将双共轭梯度（BICG）应用到电容层析成像技术中，为了得到更好的重建效果，提出了双共轭梯度与正则化思想相结合来求解逆问题的最佳解。通过COMSOL5.3软件进行建模，使用MATLAB 2014a进行图像重建与图像评估，分别使用Tikhonov、Landweber、共轭梯度（CG）、BICG、所提改进算法进行图像重建。实验表明：所提改进算法的成像效果不仅优于其他迭代类算法，而且大大缩短了图像重建需要的时间；尤其对一些复杂流型成像效果更佳，图像错误率低至约0.2，相关系数高达约0.88，成像时间缩短至2.77 s，迭代次数减少至20次。
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关键词:
- 电容层析成像技术(ECT) /
- 双共轭梯度(BICG)算法 /
- 算法改进 /
- 图像重建 /
- COMSOL
Abstract:Aimed at the influence of the soft field effect on the inverse electrical capacitance tomography (ECT) problem and to solve the problems that the traditional iterative algorithm used to reconstruct images has numerous iteration times, and that the imaging speed is slow, for the first time, biconjugate gradient (BICG) is applied to the capacitance tomography technology. In order to obtain a better reconstruction effect, a BICG and regularization idea are combined to solve the optimal solution of the inverse problem. The experiment was modeled by COMSOL5.3 software and MATLAB 2014a was used for image reconstruction and image evaluation. The images were reconstructed using Tikhonov, Landweber, conjugate gradient (CG), BICG and improved biconjugate gradient algorithm. Experiments show that the effect of the improved biconjugate gradient algorithm is not only better than other iterative algorithms, but also greatly reduces the time required for image reconstruction. The experimental results show that the biconjugate gradient algorithm has better imaging effect in some complicated flow patterns. The error is as low as 0.2, the correlation coefficient is as high as 0.88, the imaging time is reduced to 2.77 s, and the number of iterations is reduced to 20 times.
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表 1 IME计算值
Table 1. Calculated values of IME
仿真模型 Tikhonov算法 Landweber算法 CG算法 BICG算法 改进算法 核心流 0.3880 0.2537 0.2420 0.2857 0.2524 双泡流 0.4201 0.3813 0.4227 0.3512 0.3503 三泡流 0.4802 0.4254 0.5012 0.4003 0.4010 层流 0.5046 0.4213 0.9344 0.3612 0.3410 环流 0.6548 0.5826 0.5802 0.2013 0.2106 
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表 2 CORR计算值
Table 2. Calculated values of CORR
仿真模型 Tikhonov算法 Landweber算法 CG算法 BICG算法 改进算法 核心流 0.7012 0.8063 0.7901 0.7886 0.8095 双泡流 0.6325 0.6418 0.6558 0.7802 0.7795 三泡流 0.5361 0.5904 0.5418 0.6217 0.6223 层流 0.5241 0.6908 0.0130 0.7146 0.7134 环流 0.4529 0.4608 0.4621 0.8592 0.8786
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表 3 成像算法数据对比
Table 3. Comparison of imaging algorithm data
算法 迭代次数 成像时间/s Tikhonov算法 3.06 Landweber算法 120 4.47 CG算法 200 10.32 BICG算法 50 3.12 改进算法 20 2.77
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