多个生成元的对称紧小波框架

Symmetric Tight Wavelet Frames with Many Generators

在构造出3个面具函数,进而得到具有消失矩的对称的紧小波框架的基础上,首先证明了多个生成元的对称紧小波框架的存在性,同时具体构造了5个面具函数d1(η),d2(η),d3(η),d4(η),d5(η),使得小波函数f1(t),…,f5(t)生成L2(R)的紧小波框架,并且它们是对称的或者是反对称的。

By constructing three mask functions, the symmetric tight wavelet frame with vanishing moments are obtained, the existence of the symmetric tight wavelet frame with many generators is proved and the algorithm of constructing five mask functions is given such that a tight wavelet frame can be generated with the square integral.