A Study of a Two-Directional Vector Multivariate Wavelet Wraps and Applications in Engineering Materials

2014 ◽  
Vol 889-890 ◽  
pp. 1270-1274
Author(s):  
Jin Shun Feng ◽  
Qing Jiang Chen
Keyword(s):  
Multiresolution Analysis ◽  
Riesz Bases ◽  
Scaling Functions ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Compactly Supported ◽  
Dilation Matrix ◽  
Engineering Materials ◽  
Vector Valued

The existence of compactly supported orthogonal two-directional vector-valued wavelets associated with a pair of orthogonal shortly supported vector-valued scaling functions is researched. We introduce a class of two-directional vector-valued four-dimensional wavelet wraps according to a dilation matrix, which are generalizations of univariate wavelet wraps. Three orthogonality formulas regarding the wavelet wraps are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet wraps. The sufficient condition for the existence of four-dimensional wavelet wraps is established based on the multiresolution analysis method.

The Research of a Two-Directional Vector-Valued Quarternary Wavelet Packets and Applications in Material Engineering

2013 ◽  
Vol 712-715 ◽  
pp. 2487-2492
Author(s):  
Jian Feng Zhou
Keyword(s):  
Functional Analysis ◽  
Frequency Analysis ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Sufficient Condition ◽  
Subdivision Scheme ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Vector Valued

In this paper, we introduce a class of vector-valued four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets. The defini -tion of biorthogonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method. Three biorthogonality formulas regarding the wavelet packets are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

Properties and Constructing of a Kind of Four-Dimensional Vector Wavelet Packets According to a Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 920-925
Author(s):  
Yu Min Yu ◽  
Yu Qing Zhu
Keyword(s):  
Functional Analysis ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Sufficient Condition ◽  
Subdivision Scheme ◽  
Dimensional Vector ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Definition Of

In this paper, we introduce a sort of vector four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets. The definition of biortho- gonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method. Three biorthogonality formulas regarding the wavelet packets are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

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

Existence and Designment of Filter Banks of Biorthogonal Vector-Valued Wavelets with Three-Scale Constant Factor

2010 ◽  
Vol 439-440 ◽  
pp. 938-943
Author(s):  
Hong Wei Gao ◽  
Li Ping Ding
Keyword(s):  
Multiresolution Analysis ◽  
Filter Banks ◽  
Matrix Theory ◽  
Constant Factor ◽  
New Method ◽  
Scaling Functions ◽  
Compactly Supported ◽  
Vector Valued

In this work, the notion of vector-valued multiresolution analysis and biort- ogonal vector–valued wavelets is introduced. The existence of compactly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for constructing a class of biorthogonal compactly supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory.

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.

Study of High Dimensional Orthogonal Vector-Valued Wavelet with Scale 4

2013 ◽  
Vol 790 ◽  
pp. 665-668
Author(s):  
Wei Qing Yang
Keyword(s):  
Multiresolution Analysis ◽  
High Dimensional ◽  
Orthogonal Vector ◽  
Compactly Supported ◽  
Definition Of ◽  
Vector Valued

In this paper, we introduce the definition of vector-valued multiresolution analysis with scale 4 and orthogonal vector-valued wavelet with scale 4 is gived. The properties of compactly supported orthogonal vector-valued wavelets with scale 4 are proved.

ORTHONORMAL MRA WAVELETS: SPECTRAL FORMULAS AND ALGORITHMS

2012 ◽  
Vol 10 (01) ◽  
pp. 1250008 ◽  
Author(s):  
F. GÓMEZ-CUBILLO ◽  
Z. SUCHANECKI ◽  
S. VILLULLAS
Keyword(s):  
Multiresolution Analysis ◽  
Matrix Representation ◽  
Infinite Product ◽  
Scaling Functions ◽  
Compactly Supported ◽  
Orthonormal Bases ◽  
Spectral Decompositions ◽  
Product Matrix ◽  
Orthonormal Wavelets

Spectral decompositions of translation and dilation operators are built in terms of suitable orthonormal bases of L2(ℝ), leading to spectral formulas for scaling functions and orthonormal wavelets associated with multiresolution analysis (MRA). The spectral formulas are useful to compute compactly supported scaling functions and wavelets. It is illustrated with a particular choice of the orthonormal bases, the so-called Haar bases, which yield a new algorithm related to the infinite product matrix representation of Daubechies and Lagarias.

A Feasible Algorithm for Designing Biorthogonal Binary Finitely Supported Multiwavelet Functions

2011 ◽  
Vol 225-226 ◽  
pp. 1092-1095
Author(s):  
Bao Min Yu
Keyword(s):  
Wavelet Analysis ◽  
Multiresolution Analysis ◽  
Natural Science ◽  
Matrix Theory ◽  
Scaling Functions ◽  
Science And Engineering ◽  
Engineering Computation ◽  
Feasible Algorithm ◽  
Definition Of ◽  
Vector Valued

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this paper, the notion of vector-valued multiresolution analysis is introduced and the definition of the biorthogonal vector-valued bivariate wavelet functions is given. The existence of biorthogonal vector-valued binary wavelet functions associated with a pair of biorthogonal vector-valued finitely supported binary scaling functions is investigated. An algorithm for constructing a class of biorthogonal vector-valued finitely supported binary wavelet functions is presented by virtue of multiresolution analysis and matrix theory.

Vector-valued nonuniform multiresolution analysis on local fields

2015 ◽  
Vol 13 (04) ◽  
pp. 1550029 ◽  
Author(s):  
Firdous Ahmad Shah ◽  
M. Younus Bhat
Keyword(s):  
Multiresolution Analysis ◽  
Orthonormal Basis ◽  
Positive Characteristic ◽  
Local Fields ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Vilenkin Groups ◽  
Refinement Mask ◽  
Necessary And Sufficient ◽  
Vector Valued

A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V0 of L2(K, ℂM) has an orthonormal basis of the form {Φ (x - λ)}λ∈Λ where Λ = {0, r/N} + 𝒵, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime and 𝒵 = {u(n) : n ∈ ℕ0}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(ξ) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups.

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.

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