基于加权奇异值分解截断共轭梯度的电容层析图像重建  

Image reconstruction based on weighted SVD truncation conjugate gradient algorithm for electrical capacitance tomography

作　　者：陈宇[1,2] 高宝庆[1] 张立新[1] 陈德运[1] 于晓洋[1] 

机构地区：[1]哈尔滨理工大学,黑龙江哈尔滨150080 [2]东北林业大学,黑龙江哈尔滨150040

出　　处：《光学精密工程》2010年第3期701-707,共7页Optics and Precision Engineering

基　　金：国家自然科学基金资助项目(No.60572153;60972127);高等学校博士学科点专项科研基金资助项目(No.2008-2011);黑龙江省自然科学基金资助项目(No.F200609);教育部春晖计划资助项目(No.Z2007-1-15013)

摘　　要：针对电容层析成像技术(ECT)中的"软场"效应和病态问题,提出了一种基于加权奇异值分解(SVD)截断共轭梯度的电容层析(ECT)图像重建算法。阐述了电容层析成像工作原理,提出了12电极ECT系统的测量方法。在分析灵敏度矩阵的奇异值分解理论的基础上,推导出了加权SVD截断共轭梯度的数学模型,并利用Tikhonov方法进行正则化加权处理。最后,分析了算法的收敛性,并将其应用于电容层析成像系统的图像重建中。实验结果表明,对于层流,截断共轭梯度算法的平均误差能达到27.54%,全部流型平均迭代步数达到13步,与LBP、Landweber和CG算法比较,该算法具有成像效果好,成像速度快,易于实现等特点。To solve the ＂soft-field＂ effect and ill-posed problem in electrical capacitance tomography, an image reconstruction algorithm based on weighted Singular Value Decomposition（SVD） truncation conjugate gradient is presented for electrical capacitance tomography. The working principle of electrical capacitance tomography is introduced and a measurement method for ECT system with 12 electrodes is proposed. On analysis of the sensitive matrix based on the SVD theory, a weighted conjugate gradient truncated SVD mathematical model is derived,and it is weighted normally by Tikhonov regularization method. Finally, the convergence of the algorithm is analyzed and applied to the image reconstruction for electrical capacitance tomography. Experimental results and simulation data indicate that for laminar flow, the average error can reach 27.54%, and the average number of iterative stepsfor all flow regimes can achieve 13 by the proposed algorithm. Compared with LBP, Landweber and CG algorithms, the algorithm has advantages in good image quality,high image speed and is a feasible and effective method for image reconstruction.

关 键 词：电容层析成像 图像重建 奇异值分解 共轭梯度算法 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]