改进的共轭梯度算法的图像重建算法  

An Improved Conjugate Gradient Algorithm for Image Reconstruction Algorithm

作　　者：马敏[1] 张彩霞[1] 姬晶晶[1] 王化祥[2] 

机构地区：[1]中国民航大学,天津300300 [2]天津大学电气与自动化工程学院,天津300072

出　　处：《计量学报》2013年第1期27-30,共4页Acta Metrologica Sinica

基　　金：国家自然科学基金青年基金（61102096）;天津市自然科学基金（11JCYBJC06900）;中国民航大学中央高校基金（ZXH2010C005）

摘　　要：针对电容层析成像图像重建问题的病态性，在Tikhonov正则化的基础上，以正则化解决方案的规模和给定数据的质量为理论依据，引入一个数学变换，提出了一种新的正则化方法，该方法克服了常规正则化方法扰乱原系统的缺陷。同时，将ECT物理模型进行规范化，并对共轭梯度算法进行改进。仿真实验表明，改进的共轭梯度算法的成像质量高于LBP算法、Tikhonov正则化算法和共轭梯度算法，并利用相关系数进行了验证。Considering the image reconstruction of electrical capacitance tomography is an ill-conditioned problem, a new regularization method is proposed based on the size of the regularized solution and the quality to fitting the given data in Tikhonov regularization method. This method introduces a mathematical transformation, which overcomes the shortcomings of the disruption of conventional regularization. Meanwhile, the ECT physical model is normalized, and the conjugate gradient algorithm is improved. The simulation results show that the improved algorithm is better than LBP algorithm, conventional Tikhonov regularization algorithm as well as conjugate gradient algorithm in image quality, which is validated by the correlation coefficient.

关 键 词：计量学 电容层析成像 敏感阵列电极 图像重建 共轭梯度算法 相关系数 

分 类 号：TB937[一般工业技术—计量学]