基于最小二乘RBF的含噪声散乱数据逼近  

Approximation of Noisy Scattered Data Based on Least Square RBF

作　　者：夏磊 李水艳[1] XIA Lei;LI Shui-yan(College of science,Hohai University,Nanjing,Jiangsu 211100,China)

机构地区：[1]河海大学理学院,江苏南京211100

出　　处：《计算技术与自动化》2021年第1期96-100,共5页Computing Technology and Automation

基　　金：国家自然科学基金资助项目(11771120);中央高校基本科研业务费(B200202005)。

摘　　要：径向基函数能够有效的对散乱数据进行差值和逼近,因此在信号和图形处理等领域应用广泛,例如信号重构。针对从含有噪音的散乱数据中逼近原始数据,提出了一种基于最小二乘的变分模型,该模型由包含L 2范数的拟合项和光滑项构成,光滑项通过三角网格上的拉普拉斯平滑方法来实现对函数梯度的约束,并应用最小二乘法求解该模型。最后通过数值实验对噪音数据进行逼近和误差分析来验证此方法的有效性。Radial Basis Function(RBF)is widely used in signal and graph processing because it can effectively perform difference and approximation to scattered data,such as signal reconstruction.Aiming at approximating the original data from scattered data with noise,a variational model based on radial basis function is proposed.The model is composed of fitting terms and smooth terms containing L 2-norm,and the least square method is applied to solve the model.Finally,numerical experiments are carried out to approximate the noise data and the error between the approximate data and the original data is given to verify the effectiveness of this method.

关 键 词：散乱数据 逼近 径向基函数 最小二乘 

分 类 号：TN911.7[电子电信—通信与信息系统]