基于QR分解的对称共轭梯度法成像算法  

Symmetrical Conjugate Gradient Algorithm Based on QR Decomposition for Image Reconstruction

作　　者：马世文[1] 王化祥[1] 

机构地区：[1]天津大学电气与自动化工程学院,天津300072

出　　处：《传感技术学报》2011年第8期1168-1171,共4页Chinese Journal of Sensors and Actuators

基　　金：国家自然科学基金重大国际合作项目"基于ECT/ERT双模电学成像技术多相管流测量研究"(60820106002);国家自然科学重点基金项目"多模态过程成像关键技术研究"(60532020)

摘　　要：为了快速得到高质量的重建图像,提出了对称共轭梯度法成像算法,大大缩减了迭代次数,同时,将ERT物理模型进行规范化和Tikhonov正则化处理,进而将QR分解的思想引入ERT方程的求解中,提出基于QR分解的对称共轭梯度算法,实现了单步图像重建。理论分析表明,该算法具有良好的收敛性。通过典型流型的仿真实验,证明了该算法可以获得高质量的重建图像。Electrical Resistance Tomography（ERT）is a popular process tomography technique and has been widely used in many industrial areas.However,the inverse problem of the ERT system is ill-conditioned.Therefore,a symmetric conjugate gradient algorithm based on QR decomposition（RQSCG）was proposed.It is theoretically proven that this algorithm can converge only by one step.In addition,simulation results also show that this algorithm gives a better imaging quality and reduces computational time obviously,compared with conjugate gradient（CG）algorithm.

关 键 词：电阻层析成像 QR分解 共轭梯度法 对称共轭梯度法 

分 类 号：TN911.73[电子电信—通信与信息系统]