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1.
一类二维不可分非正交小波包 总被引:4,自引:0,他引:4
Zuowei Shen构造了L^2(R^s)空间的二进制小泡包,与伸缩矩阵M=(1 1 1 -1)相关的小波适用于二维图像处理中的梅花状子取样,本文给出了一种构造非正交M-小滤包的方法。 相似文献
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In this paper,the notion of orthogonal vector-valued wavelet packets of space L2(Rs,Cn)is introduced.A procedure for constructing the orthogonal vector-valued wavelet packets is presented.Their properties are characterized by virtue of time-frequency analysis method,matrix theory and finite group theory,and three orthogonality formulas are obtained.Finally,new orthonormal bases of space L2(Rs,Cn)are extracted from these wavelet packets. 相似文献
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本文给出伸缩矩阵行列式为2的一类二元半正交小波包的构造算法.该小波包是以频域给出的,随着用于小波包分裂的滤波器选取的不同会得到L2(R2)中形态各异的Riesz基,这样使得L2(R2)中小波基的选择更灵活. 相似文献
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Qingjiang Chen Cuiling Wang Zhengxing Cheng School of Science Xi’an University of Architecture Technology Xi’an China. School of Science Xi’an Jiaotong University Xi’an China. 《高等学校计算数学学报(英文版)》2007,16(1):45-53
In this paper, we introduce matrix-valued multiresolution analysis and matrix- valued wavelet packets. A procedure for the construction of the orthogonal matrix-valued wavelet packets is presented. The properties of the matrix-valued wavelet packets are investigated. In particular, a new orthonormal basis of L2(R, Cs×s) is obtained from the matrix-valued wavelet packets. 相似文献
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紧支撑多重向量值正交小波包的性质 总被引:1,自引:0,他引:1
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. 相似文献
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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. 相似文献
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对具有任意伸缩矩阵A的插值加细函数,给出对应于L^2(R^s)中的小波包的一个构造方法.采样空间被直接分解来取代对加细函数的符号分解.按照这个方法构造的插值小波包能对基插值空间提供较为精细的分解,因而对自适应的插值给出较好的局部化. 相似文献
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Biswaranjan Behera 《Proceedings Mathematical Sciences》2001,111(4):439-463
The orthonormal basis generated by a wavelet ofL
2(ℝ) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets.
We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis ofL
2(ℝ
d
) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized to this setting. Further,
we show how to construct various orthonormal bases ofL
2(ℝ
d
) from the multiwavelet packets. 相似文献
10.
任意矩阵伸缩的正交小波包 总被引:17,自引:2,他引:15
1 引言 Coifman和Meyer引入L~2(R)中正交小波包,可以用张量积形式构造L~2(R~2)上的二维正交小波包;Chui和Li研究单变量非正交小波包和对偶小波包;Shen给出矩阵伸缩为2I时L~2(R~s)上非张量积小波包的构造算法;程正兴给出矩阵小波包的构 相似文献
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Lars F. Villemoes 《Comptes Rendus Mathematique》2002,335(10):793-796
We construct basic wavelet packets with uniformly bounded localization in both time and frequency. The corresponding orthonormal bases of wavelet packets are parametrized by dyadic segmentations obeying a local variation condition. To cite this article: L.F. Villemoes, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 793–796. 相似文献
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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. 相似文献
16.
In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles.We also prove how to construct various tight frames for L2(Rd) by replac-ing some mother framelets. 相似文献
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《分析论及其应用》2015,(3):221-235
The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium(1998) and Z. Y. Li, et al.(2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L~2(R~2). In this paper, we choose 2I2=(_0~2 _2~0)as the dilation matrix and consider the 2 I2-dilation orthogonal multivariate waveletΨ = {ψ_1, ψ_2, ψ_3},(which is called a dyadic bivariate wavelet) multipliers. We call the3 × 3 matrix-valued function A(s) = [ f_(i, j)(s)]_(3×3), where fi, jare measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)( ψ_1(s), ψ_2(s), ψ_3(s)) ~T=( g_1(s), g_2(s), g_3(s))~ T is a dyadic bivariate wavelet whenever(ψ_1, ψ_2, ψ_3) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L.Shi(2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising. 相似文献
18.
Guo-mao Wang 《高校应用数学学报(英文版)》2008,23(3):303-312
The purpose of this paper is to investigate the mean size formula of wavelet packets (wavelet subdivision tree) on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree. 相似文献
19.
Spherical wavelet transform and its discretization 总被引:3,自引:0,他引:3
A continuous version of spherical multiresolution is described, starting from continuous wavelet transform on the sphere. Scale discretization enables us to construct spherical counterparts to wavelet packets and scale discrete wavelets. The essential tool is the theory of singular integrals on the sphere. It is shown that singular integral operators forming a semigroup of contraction operators of class (C
0) (like Abel-Poisson or Gauß-Weierstraß operators) lead in a canonical way to (pyramidal) algorithms.Supported by the Graduiertenkolleg Technomathematik, Kaiserslautern. 相似文献
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In this paper, we introduce a class of vector-valued wavelet packets of space L2(R2,Cκ), which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time–frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space L2(R2,Cκ) from these wavelet packets. Relation to some physical theories such as the Higgs field is also discussed. 相似文献