摘要
本文给出了确定尺度函数正则指数的一个公式,证明了正交的四系数滤波中Daubechies小波正则性最优,并结合B-样条对应的双正交滤波,应用提升格式,增加对偶小波的正则性.
Abstract In this paper, a formula for the Sobolev regularity index of scaling functions is given. It is proved that among the four-coefficient orthogonal filters the regularity of D4 wavelet is optimal. For the biorthogonal filters associated with B-spline functions, we increase the regularity of dual wavelets by using the lifting scheme.Keywords Wavelet regularity; Sobolev regularity index; Four-coefficient filters; Lifting scheme
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2002年第6期1069-1078,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10071096)
广东省自然科学基金资助项目(990228)
