A study of orthonormal multi-wavelets

被引：524

作者：

Chui, CK ^{[1
]}

Lian, JA ^{[1
]}

机构：

[1] PRAIRIE VIEW A&M UNIV,DEPT MATH,PRAIRIE VIEW,TX 77446

来源：

APPLIED NUMERICAL MATHEMATICS | 1996年 / 20卷 / 03期

基金：

美国国家科学基金会;

关键词：

compactly supported functions; multi-scaling functions; multi-wavelets; symmetric and antisymmetric functions; two-scale symbols;

D O I：

10.1016/0168-9274(95)00111-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

A general scheme for constructing symmetric and/or antisymmetric compactly supported orthonormal multiscaling functions and multi-wavelets is introduced. The main emphasis is on maximum order of polynomial-reproduction by the scaling functions, or equivalently maximum number of vanishing moments for the corresponding wavelets; particularly for those that have small supports and those that satisfy certain Hermite interpolating conditions. As an application, we recover the Geronimo-Hardin-Massopust multi-scaling function without using fractal interpolation, and consequently the corresponding Strang-Strela multi-wavelet. Explicit formulations of the two-scale relations and polynomial-reproduction identities for the scaling functions with supports [0,2] and [0,3] and multiplicity 2 as well as their corresponding multi-wavelet are also derived by following our general constructive scheme.

引用

页码：273 / 298

页数：26

共 14 条

[1]

Chui C.K., 1992, An introduction to wavelets, V1, DOI DOI 10.1109/99.388960

[2]

ON COMPACTLY SUPPORTED SPLINE WAVELETS AND A DUALITY PRINCIPLE [J].