The Biorthogonality Traits of Vector-Valued Multivariant Small-Wave Wraps with Poly-Scale Dilation Factor

2011 ◽  
pp. 67-72
Author(s):  
Yongmei Niu ◽  
Xuejian Sun
Keyword(s):  
Small Wave ◽  
Dilation Factor ◽  
Vector Valued

The Optimality Characters of Vector-Valued Binary Small-Wave Wraps with a Constant Dilation Factor

2011 ◽  
Vol 58-60 ◽  
pp. 1460-1465
Author(s):  
Ming Pu Guo
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Analysis Method ◽  
Time Frequency ◽  
Decomposition Scheme ◽  
Finite Group Theory ◽  
Small Wave ◽  
Dilation Factor ◽  
Active Research ◽  
Vector Valued

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of orthogonal vector-valued binary small-wave wraps, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their orthogonality traits are investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas concerning these binary small-wave wraps are established. Orthonormal wavelet packet bases are obtained. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided.

The Characteristics of Trivariate Vector-Valued Super-Wave Wraps and Applications in Materials Engineering

2014 ◽  
Vol 915-916 ◽  
pp. 1062-1065
Author(s):  
Yong Yi Huang
Keyword(s):  
Dimensional Space ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Riesz Bases ◽  
Time Frequency ◽  
Decomposition Scheme ◽  
Materials Engineering ◽  
Multi Scale ◽  
Dilation Factor ◽  
Vector Valued

The rise of wavelet analysis in applied mathematics is due to its applications and the flex- ibility. We introduce vector-valued wave wraps with multi-scale dilation factor for space , which is the generalization of univariate wavelet packets. A method for constructing a sort of orthogo-nal vector-valued wavelet wraps in three-dimensional space is presented and their orthogonality traits are characterized by virtue of iteration method and time-frequency analysis method. The orthog-onality formulas concerning these wave packets are established. Moreover, it is shown how to obtain new Riesz bases of space from these wave wraps. The notion of multiple pseudo fames for subspaces with integer translation is proposed. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

An Optimization Algorithm for Orthogonal Trivariate Wavelets with Short Support

2012 ◽  
Vol 461 ◽  
pp. 835-839
Author(s):  
Ke Zhong Han
Keyword(s):  
Filter Bank ◽  
Scaling Function ◽  
Wavelet Packets ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Orthogonal Vector ◽  
Multi Scale ◽  
Dilation Factor ◽  
Necessary And Sufficient ◽  
Vector Valued

Wavelet analysis is nowadays a widely used tool in applied mathe-matics. The advantages of wavelet packets and their promising features in various application have attracted a lot of interest and effort in recent years.. The notion of vector-valued binary wavelets with two-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with multi-scale is discussed. A necessary and sufficient condition is presented by means of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal vector-valued wave-lets with compact support is proposed, and their properties are investigated.

Constructional Approaches on Vector-Valued Wavelets with Multi-Scale Dilation Factor

2011 ◽  
Vol 460-461 ◽  
pp. 323-328
Author(s):  
Qing Jiang Chen ◽  
Jian Tang Zhao
Keyword(s):  
Multiresolution Analysis ◽  
Matrix Theory ◽  
New Method ◽  
Scaling Functions ◽  
Sufficient Condition ◽  
Multi Scale ◽  
Dilation Factor ◽  
Vector Valued

In this work, the notion of vector-valued multiresolution analysis and biort- ogonal vector–valued wavelets is introduced. The existence of finitely supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is investigated. A new method for construc- -ting a class of biorthogonal finitely supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory. A sufficient condition for the existence of multiple pseudoframes for subspaces is derived

Constructive Algorithm to Two-Directional Biorthogonal Shortly Supported Wavelets with Poly-Scale Dilation Factor

2010 ◽  
Vol 171-172 ◽  
pp. 113-116
Author(s):  
Yu Min Yu ◽  
Zong Sheng Sheng
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
New Method ◽  
Wavelet Packets ◽  
Scaling Functions ◽  
Biorthogonal Wavelet ◽  
Time Frequency ◽  
Dilation Factor ◽  
Vector Valued

In this work, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelet packets is proposed and their properties is investigated by means of time-frequency analysis methodand, operator theory. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for designing a class of biorthogonal shortly supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory.

Generation and Characteristics of a Class of Four-Dimensional Multiwavelet Packets with Six-Scale Dilation Factor

2011 ◽  
Vol 460-461 ◽  
pp. 317-322
Author(s):  
Qing Jiang Chen ◽  
Zong Tian Wei
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Factor ◽  
Vector Valued

In this paper, we introduce a class of vector-valued wavelet packets of space , 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 from these wavelet packets.

Sign in / Sign up

Export Citation Format

Share Document