一族GHM型多尺度函数的构造

Construction of a family of GHM-based multi-scaling functions

从具有2阶逼近的GHM多尺度函数出发,鉴于其逼近阶数相对较低的缺点,利用两尺度相似变换(TST)的方法,构造变换矩阵Mr(ω),将它的逼近阶提高到了任意大于2的整数,并保持了紧支性和对称性,提高了GHM多小波逼近光滑函数的能力。

This paper is based on the GHM multi-scaling functions with approximation order 2. With the help of two-scale similarity transform (TST), after constructing suitable transform matrix Mr(w) we are able to increase the approximation order to an arbitrary integer which is bigger than 2, and preserve the symmetry and compact support of the new multi-scaling functions. After doing that, we will get a family of new multi-wavelets based on GHM multi-wavelets, whose ability of approximating smooth functions is improved.