利用分形插值函数构造多小波尺度函数的一个新方法  

A New Method for Constructing Scale Functions of Multiwavelets with Fractal Interpolation Functions

作　　者：张彬[1] 王卫卫[1] 宋国乡[1] 

机构地区：[1]西安电子科技大学理学院,西安710071

出　　处：《工程数学学报》2002年第1期55-60,共6页Chinese Journal of Engineering Mathematics

摘　　要：S .Geronimo等利用分形插值函数构造出了L2 (R)上的平移和伸缩不变函数空间 ,但未给出构造多小波尺度函数和尺度系数矩阵的具体算法。本文给出利用分形插值函数计算尺度系数矩阵的新算法 ,并对尺度函数作二尺度相似变换 ,使其具有更高的逼近阶。Utilizing fractal interpolation functions, Geronimo et al. constructed translation and dilation invariant function spaces. However, the detail algorithm for scale functions is not available. In this paper, we propose a new scheme for calculating the multiscale function, then the scaling coefficient matrix with fractal interpolation functions and obtained a different result. It is proved that the multiscale function forms a MRA. Finally, the approximation order of the multiscale function is increased by using the TST and a smoother scale function resulted.

关 键 词：分形插值函数 多小波 二尺度相似变换 

分 类 号：O174.2[理学—数学]