3尺度紧支撑双正交多小波及小波包的构造和算法  

Constructions and algorithms of compactly supported biorthogonal multiwavelets and wavelet packets with scale 3

作　　者：李万社[1] 罗立娑[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2011年第2期1-7,共7页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10571113)

摘　　要：研究了3尺度紧支撑双正交多小波及小波包的构造与算法,给出了双正交多小波的多分辨分析理论.若r重尺度函数的支撑区间较大,则可将其转化成3r重短支撑的情形,再利用矩阵理论,对两尺度符号进行矩阵化,通过对矩阵进行正交扩充,得到关于两尺度符号的方程组,求解方程组便得到双正交3尺度多小波的两尺度矩阵序列.该方法适用于任意紧支撑双正交3尺度多小波的构造.利用多分辨分析和矩阵理论,通过将2r维向量函数分组截断为两个r维向量,构造3尺度r重双正交小波包,得出其系数矩阵应满足的方程组,并给出相应的分解关系.研究了3尺度r重双正交小波包的双正交性质,这为构造空间L2(R)的小波基奠定了基础.Constructions and algorithms of compactly supported biorthogonal multiwavelets and wavelet packets with scale 3 are discussed.The notion of multiresolution analysis（MRA） and the concept of biorthogonal multiwavelets are introduced.The scaling functions with a long support and r multiplicity can be transfered as the ones with a short support and r multiplicity.Two-scale matrix symbols are written as the forms of matrices through using the matrix theory,then the matrices are extended as the orthogonal ones and the equations about the two-scale matrix symbols are obtained.Two-scale matrix sequence of biorthogonal multiwavelets with scale 3 are given by solving the equations.The method can be used for any biorthogonal wavelets with compact support and with scale 3.The biorthogonal wavelet packets with multiplicity r and scale 3 are constructed by truncating a 2r-dimensionalvector-valued function to two r-dimensional vector-valued functions,baced on the theory of matrix and MRA.The equations about the coefficient matrices are obtained and the corresponding decomposition relations of coefficient matrices are presented.At last,biorthogonal properties of biorthogonal wavelet packets with scale 3 are investigated,which are the basis for constructing the wavelet basis for L2（R）.

关 键 词：多尺度函数 双正交多小波 矩阵序列 矩阵正交扩充 小波包 

分 类 号：O174.2[理学—数学]