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收稿考滤了一类多带正交对称小波滤波器对应多相矩阵分解结构,系统地构造了一类具有自由参数多带小波滤波器簇,以4带小波为例得到了用参数角表示的一类正交对称滤波器序列. 相似文献
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本文得到两个结果:首先证明尺度因子m与重数r的乘积为奇数时,具有相同对称/反对称中心1/2(1+μ+μ/m-1)(μ∈N)的正交向量小波系统的不存在性;其次证明尺度因子m=3,重数r为偶数时,具有相同对称/反对称中心1/2(1+μ+μ/m-1)的正交平衡向量小波系统的不存在性,这里N是正整数集合. 相似文献
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高维小波分析是分析和处理多维数字信号的有力工具.基于任意的三维正交尺度函数及相应的正交小波,提出一种构造三维插值对称尺度函数和对称小波的方法,并建立了多维信号采样定理,这一点在信号处理中具有很好的应用价值.最后给出了数值算例. 相似文献
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不同尺度下多项式滤波器的优化算法 总被引:1,自引:0,他引:1
1 引 言 在小波分析的应用中,紧支撑正交对称的小波是非常可贵的.尤其是对称性,它在实际应用中具有非常重要的意义.但Daubechies的具有紧支撑正交小波无任何对称性和反对称性(除Haar小波外).为了克服这一不足,崔锦泰和王建忠[1]提出了样条小波,样条小波用失去正交性换来了小波的对称性.A.Cohen[2]等引入了双正交小波似乎解决了这一问题,但它需要两个对偶的小波.匡正[3]等采用了小波的分式滤波器构造出了既正交又对称的小波,但却没有有限的支撑区间.本文欲采用优化的方法给出了一种构造具有任意正则性的多项式… 相似文献
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对称反对称多重尺度函数的构造 总被引:3,自引:0,他引:3
1 多重小波的定义和双尺度相似变换 作为一种分析工具,小波已经运用在各种领域,并取得了显著的成果.近年来,多重小波成为小波研究的热点.I.Daubechies[1]已经证明,对单重小波,除Harr基外不存在对称和反对称的有紧支集的小波正交基.而多重小波则不受这一限制. 利用分形插值的方法,Geronimo、Hardin和 Massopust[2]等构造出了GHM多重小波,相应的多重尺度函数和多重小波函数如图1和图2所示.GHM多重小波的两个尺度函数都是对称的,相应的小波函数则一个对称另一个反对称;… 相似文献
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Petukhov 《Constructive Approximation》2008,19(2):309-328
We study tight wavelet frames associated with symmetric compactly supported refinable functions, which are obtained with the unitary extension principle . We give a criterion for the existence of two symmetric or antisymmetric compactly supported framelets.
All refinable masks of length up to 6 satisfying this criterion are found. 相似文献
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Qingtang Jiang 《Advances in Computational Mathematics》2003,18(2-4):247-268
Parameterizations of FIR orthogonal systems are of fundamental importance to the design of filters with desired properties. By constructing paraunitary matrices, one can construct tight affine frames. In this paper we discuss parameterizations of paraunitary matrices which generate tight affine frames with two symmetric/antisymmetric generators (framelets). Based on the parameterizations, several symmetric/antisymmetric framelets are constructed. 相似文献
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Xiaoyuan Yang Yan ShiWanlu Zhou 《Journal of Computational and Applied Mathematics》2011,235(8):2112-2136
In this paper, we present a general construction framework of parameterizations of masks for tight wavelet frames with two symmetric/antisymmetric generators which are of arbitrary lengths and centers. Based on this idea, we establish the explicit formulas of masks of tight wavelet frames. Additionally, we explore the transform applicability of tight wavelet frames in image compression and denoising. We bring forward an optimal model of masks of tight wavelet frames aiming at image compression with more efficiency, which can be obtained through SQP (Sequential Quadratic Programming) and a GA (Genetic Algorithm). Meanwhile, we present a new model called Cross-Local Contextual Hidden Markov Model (CLCHMM), which can effectively characterize the intrascale and cross-orientation correlations of the coefficients in the wavelet frame domain, and do research into the corresponding algorithm. Using the presented CLCHMM, we propose a new image denoising algorithm which has better performance as proved by the experiments. 相似文献
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In this paper, we introduce complex pseudo splines that are derived from pseudo splines of type I. First, we show that the
shifts of every complex pseudo spline are linearly independent. Therefore we can construct a biorthogonal wavelet system.
Next, we investigate the Riesz basis property of the corresponding wavelet system generated by complex pseudo splines. The
regularity of the complex pseudo splines will be analyzed. Furthermore, by using complex pseudo splines, we will construct
symmetric or antisymmetric complex tight framelets with desired approximation order. 相似文献
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M. Skopina 《Applied and Computational Harmonic Analysis》2006,20(3):375-390
Wavelets with matrix dilation are studied. An explicit formula for masks providing vanishing moments is found. The class of interpolatory masks providing vanishing moments is also described. For an interpolatory mask, formulas for a dual mask which also provides vanishing moments of the same order and for wavelet masks are given explicitly. An example of construction of symmetric and antisymmetric wavelets for a concrete matrix dilation is presented. 相似文献
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In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C1 and supported on [−1,1]. Moreover, one wavelet is symmetric, and the other is antisymmetric. These spline wavelets are then
adapted to the interval [0,1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of
the wavelet basis is established. The wavelet basis is used to solve the Sturm–Liouville equation with the Dirichlet boundary
condition. Numerical examples are provided. The computational results demonstrate the advantage of the wavelet basis.
Dedicated to Dr. Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 42C40, 41A15, 65L60.
Research was supported in part by NSERC Canada under Grants # OGP 121336. 相似文献
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Multiwavelet Frames from Refinable Function Vectors 总被引:4,自引:0,他引:4
Starting from any two compactly supported d-refinable function vectors in (L
2(R))
r
with multiplicity r and dilation factor d, we show that it is always possible to construct 2rd wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L
2(R) and they achieve the best possible orders of vanishing moments. When all the components of the two real-valued d-refinable function vectors are either symmetric or antisymmetric with their symmetry centers differing by half integers, such 2rd wavelet functions, which generate a pair of dual d-wavelet frames, can be real-valued and be either symmetric or antisymmetric with the same symmetry center. Wavelet frames from any d-refinable function vector are also considered. This paper generalizes the work in [5,12,13] on constructing dual wavelet frames from scalar refinable functions to the multiwavelet case. Examples are provided to illustrate the construction in this paper. 相似文献
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An efficient computational procedure is presented for the free vibration analysis of structures with unsymmetric geometry. The procedure is based on approximating the unsymmetric vibrational response of the structure by a linear combination of a few symmetric and antisymmetric modes (global approximation vectors), each obtained using approximately half the degrees of freedom of the original model. The three key elements of the procedure are: (a) use of mixed finite element models having independent shape functions for the internal forces (stress resultants) and generalized displacements, with the internal forces allowed to be discontinuous at interelement boundaries, (b) operator splitting, or additive decomposition of the different arrays in the governing finite element equations to delineate the contributions to the symmetric and antisymmetric response vectors, and (c) use of a reduction method through successive application of the finite element method and the classical Bubnov-Galerkin technique. The finite element method is first used to generate a few symmetric and antisymmetric global approximation response vectors. Then, the classical Bubnov-Galerkin technique is used to substantially reduce the size of the eigenvalue problem.
An initial set of global approximation vectors is selected to be a few symmetric and antisymmetric eigenvectors, and their various-order derivatives with respect to a tracing parameter identifying all the correction terms to the symmetric (and antisymmetric) eigenvectors. A modified (improved) set of approximation vectors is obtained by using the inverse iteration procedure. The effectiveness of the proposed procedure is demonstrated by means of a numerical example. 相似文献
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Theoretical and Mathematical Physics - Dynamic systems acting on the plane and possessing the Wada property have been observed. There exist only two topological types, symmetric and antisymmetric,... 相似文献