Tikhonov正则化在Zernike多项式拟合中的应用  

Application of Tikhonov Regularization Method in Zernike Polynomials Fitting

作　　者：汉语[1,2] 伍凡[1] 万勇建[1] 房凯[1] 

机构地区：[1]中国科学院光电技术研究所,成都610209 [2]中国科学院研究生院,北京100039

出　　处：《光电工程》2010年第7期60-63,共4页Opto-Electronic Engineering

基　　金：国家自然科学基金资助项目(60808017)

摘　　要：Zernike多项式系数的求解问题是一个典型的离散不适定问题,最小二乘法、格拉姆-斯密特正交化法和Householder变换法均无法求得稳定的数值解。本文对导致该问题解的不稳定性的原因进行了分析,并采用Tikhonov正则化法对Zernike多项式系数进行求解,利用L曲线准则确定了正则参数。数值仿真结果表明,Tikhonov正则化法有效的保证了解的稳定性,利用该方法得到的拟合面形很好的反映了面形的真实情况。To acquire coefficients of Zernike polynomials is a discrete ill-posedness problem.Common methods,such as Least Squares Error method,Cram-Schmidt orthogonalization method and Householder transformation method,can not obtain a stable numerical solution.The instability of ill-posedness problem is analyzed and a Tikhonov regularization method is introduced to solve ill-posed problem.The L curve criterion is used to determine regularization parameter.Simulation result shows that Tikhonov regularization method is stable and effective for solving ill-posedness problem.

关 键 词：Zernike多项式拟合 不适定问题 Tikhonov正则化法 L曲线准则 

分 类 号：TQ171.6[化学工程—玻璃工业]