双向多尺度双正交向量值小波和小波包的构造

摘要

In this paper,based on the basic theory and the concept of vector-valued wavelet, the r multiplicity multi-scale vector-valued multi-resolution analysis and subspace of vector valued concepts are introduced.The pa⁃per also shows the condition of a series of Riesz basic of sub-space Vj that can be composed by vector-valued func⁃tions. In addition, it gives some properties and conclusions related to the construction method of two-direction multi-scale bi-orthogonal vector-valued wavelets and wavelet packet.%文章以双向向量值小波的基本理论和概念为基础，给出了r重双向多尺度向量值多分辨分析和双向向量值子空间的概念，以及向量值函数系列可构成子空间Vj 的一组Riesz基的条件，并给出了双向多尺度双正交向量值小波和小波包的构造方法相关的一些性质和结论。