The Characterization of Two-Direction Vector-Valued Wavelets and its Applications in Material Engineering

2013 ◽  
Vol 457-458 ◽  
pp. 36-39
Author(s):  
Qing Jiang Chen ◽  
Huan Chen ◽  
Hong Wei Gao
Keyword(s):  
Matrix Theory ◽  
Direction Vector ◽  
Analysis Method ◽  
Science And Engineering ◽  
Time Frequency ◽  
Multi Scale ◽  
Interdisciplinary Field ◽  
The Matrix ◽  
Vector Valued

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, we study construction and properties of orthogonal two-direction vector-valued wavelet with poly-scale. Firstly, the concepts concerning two-direct-ional vector-valued waelets and wavelet wraps with multi-scale are provided. Secondly, we prop ose a construction algorim for compactly supported orthogonal two-directional vector-valued wave lets. Lastly, properties of a sort of orthogonal two-directional vector-valued wavelet wraps are char acterized by virtue of the matrix theory and the time-frequency analysis method.

The Feature of Symmetric Frames and Two-Directional Vector Wavelets and Applications in Material Science

2014 ◽  
Vol 977 ◽  
pp. 15-18
Author(s):  
Hong Wei Gao
Keyword(s):  
Material Science ◽  
Matrix Theory ◽  
Direction Vector ◽  
Analysis Method ◽  
Science And Engineering ◽  
Time Frequency ◽  
Multi Scale ◽  
Interdisciplinary Field ◽  
The Matrix ◽  
Vector Valued

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, we study construction and properties of orthogonal two-direction vector-valued wavelet with poly-scale. Firstly, the concepts concerning two-direct-ional vector-valued waelets and wavelet wraps with multi-scale are provided. Secondly, we prop ose a construction algorim for compactly supported orthogonal two-directional vector-valued wave lets. Lastly, properties of a sort of orthogonal two-directional vector-valued wavelet wraps are char acterized by virtue of the matrix theory and the time-frequency analysis method.

Characterization of the Quarternary Wavelet Wraps with Multi-Scale Factor and Applications in Physics

2012 ◽  
Vol 461 ◽  
pp. 656-660
Author(s):  
Hai Lin Gao
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Multi Scale ◽  
Vector Valued

In t In this article, we introduce a sort of vector-valued wavelet wraps with multi-scale dilation of space L 2(Rn, Cv) , which are generaliza-tions of multivariaale wavelet wraps. A method for designing a sort of biorthogonal vector-valued wavelet wraps is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three biorthogonality formulas regarding these wavelet packets are established. Furtherore, it is shown how to obtain new Riesz bases of space L 2(Rn, Cv) from these wavelet wraps.

The Biorthogonality Property of the Multidimensional Wavelet Packets with Multi-Scale Factor

2010 ◽  
Vol 439-440 ◽  
pp. 1093-1098
Author(s):  
Jian Feng Zhou ◽  
Ping An Wang
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Multi Scale ◽  
Vector Valued

In this article, we introduce a sort of vector-valued wavelet packets with multi-scale dilation of space , which are generalizations of multivariaale wavelet packets. A method for designing a sort of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three biorthogonality formulas regarding these wavelet packets are established. Furtherore, it is shown how to obtain new Riesz bases of space from these wavelet packets.

The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 932-937
Author(s):  
Yin Hong Xia ◽  
Hua Li
Keyword(s):  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Vector Valued

In this article, the notion of a kind of multivariate vector-valued wavelet packets with composite dilation matrix is introduced. A new method for designing a kind of biorthogonal vector- valued wavelet packets in higher dimensions is developed and their biorthogonality property is inv- -estigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Two biorthogonality formulas concerning these wavelet packets are presented. Moreover, it is shown how to gain new Riesz bases of space by constructing a series of subspace of wavelet packets.

The Presentation of Biorthogonal Non-Tensor Trivariate Wavelet Wraps in Besov Space

2012 ◽  
Vol 461 ◽  
pp. 738-742
Author(s):  
De Lin Hua
Keyword(s):  
Besov Space ◽  
Frequency Analysis ◽  
Iteration Method ◽  
Filter Bank ◽  
Matrix Theory ◽  
Analysis Method ◽  
Analogy Method ◽  
Time Frequency ◽  
Orthonormal Bases ◽  
Vector Valued

In this paper, the concept of orthogonal non-tensor bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is pro -posed by virtue of analogy method and iteration method. Their orthogonality property is investigated by using time-frequency analysis method and variable se-paration approach. Three orthogonality formulas regarding these wavelet wraps are established. Moreover, it is shown how to draw new orthonormal bases of space from these wavelet wraps. A procedure for designing a class of orthogonal vector-valued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory.

Specific Properties of a King of Trivariable Wavelet Packets with Respect to an Integer-Valued Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 1141-1146
Author(s):  
Jin Cang Han ◽  
Yang Li
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Frequency Analysis ◽  
Matrix Theory ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Finite Group Theory ◽  
Dilation Matrix ◽  
Vector Valued

In the work, the concept of orthogonal vector-valued trivariate wavelet packets, which is a generalization of uniwavelet packets, is introduced. A new method for constructing them is developed, and their characteristics is discussed by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established.

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.

Construction and Characteristics of Orthogonal Trivariate Multiwavelets with Finite Support

2012 ◽  
Vol 461 ◽  
pp. 860-863
Author(s):  
De Lin Hua ◽  
Ruo Hui Liu
Keyword(s):  
Filter Bank ◽  
Materials Science ◽  
Matrix Theory ◽  
New Method ◽  
Analysis Method ◽  
Time Frequency ◽  
Orthogonal Vector ◽  
Fundamental Properties ◽  
Necessary And Sufficient ◽  
Vector Valued

Materials science also deals with fundamental properties and characteristics of materi- als.In this paper, the notion of orthogonal vector-valued wavelets is introduced. A new method for constructing associated multiwavelets from multi-scaling functions is presented which is simple for computation. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is presented by using paraunitary vector filter bank theory, time-frequency analysis method and matrix theory. A new method for constructing a class of orthogonal finitectly supported vector-valued wavelets is presented.

The Orthogonality Characters of Multiple Vector-Valued Ternary Wavelets and Applications in Theoretical Physics

2011 ◽  
Vol 58-60 ◽  
pp. 1454-1459
Author(s):  
Hai Lin Gao
Keyword(s):  
Matrix Theory ◽  
Theoretical Physics ◽  
Operator Technique ◽  
Analysis Method ◽  
Orthonormal Wavelet ◽  
Time Frequency ◽  
Decomposition Scheme ◽  
Dilation Matrix ◽  
Active Research ◽  
Vector Valued

Wavelet analysis has been the focus of active research for twenty years, both in theory and applications. In this work, we develop the concept of a class of multiple vector-valued trivariate wavelet wraps with a dilation matrix. A new method for constructing multiple vector-valued trivariate wavelet wraps is proposed. Their characters are investigated by means of operator technique, time-frequency analysis method and matrix theory. There orthogonality formulas regarding the wavelet wraps are provided. Orthogonality decomposition relation formulas of the space L2(R3, Cr×r)are obtained by constructing a series of subspaces of the multiple vector-valued wavelet wraps. Furthermore, several orthonormal wavelet wrap bases of space L2(R3, Cr×r) are constructed from the wavelet wraps. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. Relation to theoretical physics is also discussed.

The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets

2010 ◽  
Vol 439-440 ◽  
pp. 896-901
Author(s):  
Qing Jiang Chen ◽  
Yu Ying Wang
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Novel Method ◽  
Popular Subject ◽  
Vector Valued ◽  
Orthogonal Frame

Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an integer-valued dilation matrix. A novel method for constructing multi-dimen- -sional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are established. Orthogonality decomposition relation formulas of the space are derived by constructing a series of subspaces of wavelet packets. Finally, one new orthonormal wavelet packet bases of are constructed from these wavelet packets.

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