多尺度多重向量值双正交小波的构建算法与性质

研究多尺度多重向量值双正交小波的构建算法与性质.运用向量细分格式、矩阵理论和多重向量值多分辨分析,证明了与一对给定的多尺度多重向量值双正交尺度函数对应的多尺度多重向量值双正交小波函数的存在性.提出了紧支撑多尺度多重向量值双正交小波的构造算法.讨论了多尺度多重向量值小波包的性质,得到了多重向量值小波包的双正交公式与向量值小波包基.     

向量值正交小波包

引进对应于2尺度向量值尺度函数的多分辨分析和向量值小波的概念.给出向量值小波包的定义及其构造算法,研究了向量值正交小波包的正交性,并讨论了空间L2(R,CN)的正交分解.     

多尺度双向向量值小波的构造与性质

本文研究多尺度双向向量值正交小波的存在性、构造算法与性质.利用多分辨分析理论,时频分析方法与矩阵理论,给出紧支撑多尺度双向向量值正交小波的构造算法,得到多尺度双向向量值小波包的正交公式与向量值小波包基.推广了向量值正交小波的概念.     

多尺度紧支撑向量值正交小波的构造

引入了多尺度向量值多分辨分析．利用矩阵理论,给出多尺度紧支撑向量值正交小波存在的必要条件及其构造方法．     

一类向量值正交小波的设计与性质

引入整数因子伸缩的向量值正交小波与向量值小波包的概念.运用仿酉向量滤波器理论和矩阵理论,给出具有整数因子伸缩的向量值正交小波存在的充要条件.提供了紧支撑向量值正交的构建算法,给出了相应的构建算例.利用时频分析方法与算子理论,刻画了一类向量值正交小波包的性质,得到了整数伸缩的向量值小波包的正交公式.     

矩阵伸缩的多元多重向量值小波包的双正交性

1引言 小波分析是二十世纪八十年代中期发展起来的一个数学分枝,其应用涉及自然科学与工程技术的许多领域[1-3].向量值小波从属多小波理论范畴.文献[4]引入向量值小波的概念,讨论了多重向量值双正交小波的存在性及其构造.Bacchelli等[5]证明了多重向量值双正交小波的存在性.文献[6]运用多重向量值双正交小波变换研究海洋涡流现象.     

矩阵伸缩的高维向量值小波包

本文给出了对应于任意整数矩阵伸缩的高维向量值正交小波包的定义及其构造方法．并讨论了这种向量值正交小波包的性质,得到向量值函数空间L2(Rs,Cr)的新的正交小波基．     

一类平衡对称向量小波滤波器组参数化公式

向量小波因可以同时具有正交性、紧支性、对称性和较高的消失矩性质,使得对它的研究备受关注.本文在有限脉冲滤波器无损系统的格式结构基础上,研究一类具有对称性质的向量值滤波器组,给出其参数化公式,并由该参数化形式构造出一些具有一定平衡阶的向量小波.     

紧支撑多重向量值正交小波包的性质

给出紧支撑多重向量值正交小波包的定义及构造方法.运用矩阵理论与积分变换,研究了多重向量值正交小波包的性质,得到三个正交性公式.进而,得到空间L2(R,Cr)的一个新的规范正交基.     

多重a尺度双向双正交向量值小波的构造

基于双向向量值小波的基本理论,通过酉矩阵,给出了a尺度r重双向向量值小波双正交条件,得到了a尺度r重双向向量值构造算法,最后给出算例.     

Construction and decomposition of biorthogonal vector-valued wavelets with compact support

In this article, we introduce vector-valued multiresolution analysis and the biorthogonal vector-valued wavelets with four-scale. The existence of a class of biorthogonal vector-valued wavelets with compact support associated with a pair of biorthogonal vector-valued scaling functions with compact support is discussed. A method for designing a class of biorthogonal compactly supported vector-valued wavelets with four-scale is proposed by virtue of multiresolution analysis and matrix theory. The biorthogonality properties concerning vector-valued wavelet packets are characterized with the aid of time–frequency analysis method and operator theory. Three biorthogonality formulas regarding them are presented.     

向量值正交小波的构造与向量值小波包的特征

The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed.A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory.An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented.Their characteristics is discussed by virtue of operator theory,time-frequency method.Moreover,it is shown how to design various orthonormal bases of space L2(R,Cn) from these wavelet packets.     

Existence and construction of compactly supported biorthogonal multiple vector-valued wavelets

In this paper, we introduce biorthogonal multiple vector-valued wavelets which are wavelets for vector fields. We proved that, like in the scalar and multiwavelet case, the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the existence of a pair of biorthogonal multiple vector-valued wavelet functions. Finally, we investigate the construction of a class of compactly supported biorthogonal multiple vector-valued wavelets.     

A study on orthogonal two-direction vector-valued wavelets and two-direction wavelet packets

In this paper, the notion of two-direction vector-valued multiresolution analysis and the two-direction orthogonal vector-valued wavelets are introduced. The definition for two-direction orthogonal vector-valued wavelet packets is proposed. An algorithm for constructing a class of two-direction orthogonal vector-valued compactly supported wavelets corresponding to the two-direction orthogonal vector-valued compactly supported scaling functions is proposed by virtue of matrix theory and time-frequency analysis method. The properties of the two-direction vector-valued wavelet packets are investigated. At last, the direct decomposition relation for space L₂(R)^r is presented.     

Craya decomposition using compactly supported biorthogonal wavelets

We present a new local Craya–Herring decomposition of three-dimensional vector fields using compactly supported biorthogonal wavelets. Therewith vector-valued function spaces are split into two orthogonal components, i.e., curl-free and divergence-free spaces. The latter is further decomposed into toroidal and poloidal parts to decorrelate horizontal from vertical contributions which are of particular interest in geophysical turbulence. Applications are shown for isotropic, rotating and stratified turbulent flows. A comparison between isotropic and anisotropic orthogonal Craya–Herring wavelets, built in Fourier space and thus not compactly supported, is also given.     

A study on compactly supported orthogonal vector-valued wavelets and wavelet packets

In this paper, vector-valued multiresolution analysis and orthogonal vector-valued wavelets are introduced. The definition for orthogonal vector-valued wavelet packets is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is derived by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. The properties of the vector-valued wavelet packets are investigated by using operator theory and algebra theory. In particular, it is shown how to construct various orthonormal bases of L²(R, C^s) from the orthogonal vector-valued wavelet packets.     

Biorthogonal M-band filter construction using the lifting scheme

The lifting scheme has been proposed as a new idea for the construction of 2-band compactly supported wavelets with compactly-supported duals. The basic idea behind the lifting scheme is that it provides a simple relationship between all multiresolution analyses sharing the same scaling function. It is therefore possible to obtain custom-designed compactly supported wavelets with required regularity, vanishing moments, shape, etc. In this work, we generalize the lifting scheme for the construction of compactly-supported biorthogonal M-band filters. As in the previous case, we used the flexibility of the scheme to exploit the degree of freedom left after satisfying the perfect-reconstruction conditions in order to obtain finite filters with some interesting properties, such as vanishing moments, symmetry, shape, etc., or that satisfy certain optimality requests required for particular applications. Moreover, for these lifted biorthogonal M-band filters, we give an analysis-synthesis algorithm which is more efficient than the standard algorithm realized with filters with similar compression capabilities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Compactly supported (bi)orthogonal wavelets generated by interpolatory refinable functions

This paper provides several constructions of compactly supported wavelets generated by interpolatory refinable functions. It was shown in [7] that there is no real compactly supported orthonormal symmetric dyadic refinable function, except the trivial case; and also shown in [10,18] that there is no compactly supported interpolatory orthonormal dyadic refinable function. Hence, for the dyadic dilation case, compactly supported wavelets generated by interpolatory refinable functions have to be biorthogonal wavelets. The key step to construct the biorthogonal wavelets is to construct a compactly supported dual function for a given interpolatory refinable function. We provide two explicit iterative constructions of such dual functions with desired regularity. When the dilation factors are larger than 3, we provide several examples of compactly supported interpolatory orthonormal symmetric refinable functions from a general method. This leads to several examples of orthogonal symmetric (anti‐symmetric) wavelets generated by interpolatory refinable functions. This revised version was published online in June 2006 with corrections to the Cover Date.