Vector-valued Wavelet Packets Research Articles

Vector-Valued Nonuniform Wavelet Packets

ABSTRACTWe have introduced vector-valued nonuniform multiresolution analysis(VNUMRA) in [12] where the associated subspace V0 of has, an orthonormal basis, a collection of translates of a vector valued function ϕ of the form {ϕ(x−λ)}λ∈Λ where Λ = {0,r∕N}+2ℤ, N≥1 is an integer and r is an odd integer with 1≤r≤2N−1 such that r and N are relatively prime and ℤ is the set of all integers and the corresponding dilation factor is 2N. The notion of vector-valued nonuniform wavelet packets is introduced in this paper and their various properties are investigated. The orthonormal basis of is constructed from these wavelet packets and the orthonormal decomposition relation is also given.

Construction of vector valued wavelet packets on ℝ+ using Walsh-Fourier transform

In this paper, the concept of vector-valued wavelet packets in space L 2(ℝ+, ℂ N ) is introduced. Some properties of vector-valued wavelets packets are studied and orthogonality formulas of these wavelets packets are obtained. New orthonormal basis of L 2(ℝ+, ℂ N ) is obtained by constructing a series of subspaces of vector-valued wavelet packets.

The Study of Compactly Supported Orthogonal Two-Direction Vector-Valued Wavelet Packet

The concept of two-direction vector-valued wavelet packets is proposed. An approach for constructing orthogonal two-direction vector-valued wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, algebra theory and functional analysis method. Orthogonality formulas concerning these two-direction vector-valued wavelet packets are established.

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

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.

The Traits of Two-Directional Orthogonal Multivariate Small-Wave Packages with Finite Support

In this paper, we introduce the notion of vector-valued multiresolution analysis and two-directional vector-valued multivariate wavelet packages associated with an integer-valued dilation matrix. A novel method for constructing multi-dimensional 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 establ- lished. Orthogonality decomposition relation formulas of the space are derived by constru- cting a series of subspaces of wavelet packets.

A study on orthogonal two-direction vector-valued wavelets and two-direction wavelet packets

Abstract 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 L 2 ( R ) r is presented.

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

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.

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

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

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 Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets

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.

The Nice Feature of Orthogonal Vector-Valued Bivariate Wavelet Packets with Arbitrary Integer Dilation Factor

In this paper, the notion of orthogonal vector-valued bivariate wavelet packets, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their characteristics is investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established. Orthonormal wavelet packet bases are obtained.

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

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 Properties of a Class of Higher-Dimensional Composite Wavelet Packet Bases

In this paper, we introduce a class of vector-valuedwavelet 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. obtained.

The Properties of a Sort of Multidimensional Wavelet Packets According to an Integer-Valued Dilation Matrix

Wavelet analysis has become a popular subject in scientific research in the past twenty years. In this work, we develop the concept of a class of vector-valued multivarition matrix. A new method for constructing multidimensional vector-valued wavelet packets is formulated. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. There orthogonality formulas regarding the wavelet packets are provided. Orthogonality decomposition relation formulas of the space L2(Rs)r are obtained by constructing a series of subspaces of the vector-valued wavelet packet. Furthermore, several orthonormal wavelet packet bases of space L2(Rs)r are constructed from the wavelet packets.

Construction and Characteristics of a Kind of Four-Dimensional Vector Wavelet Packets with Four-Scale Dilation

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.

Construction and decomposition of biorthogonal vector-valued wavelets with compact support

In this article, we introduce vector-valued multiresolution analysis and the biorthogonal vector-valued wavelets with four-scale. The existence of a class of biorthogonal vector-valued wavelets with compact support associated with a pair of biorthogonal vector-valued scaling functions with compact support is discussed. A method for designing a class of biorthogonal compactly supported vector-valued wavelets with four-scale is proposed by virtue of multiresolution analysis and matrix theory. The biorthogonality properties concerning vector-valued wavelet packets are characterized with the aid of time–frequency analysis method and operator theory. Three biorthogonality formulas regarding them are presented.

The characterization of vector-valued multivariate wavelet packets associated with a dilation matrix

In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an arbitrary integer-valued dilation matrix. A novel method for constructing higher-dimensional 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 regarding the wavelet packets are provided. Orthogonality decomposition relation formulas of the space L 2( R s ) r are obtained by constructing a series of subspaces of the vector-valued wavelet packets. Finally, several orthonormal wavelet packet bases of L 2( R s ) r are constructed from these wavelet packets. Relation to some physical theories such as fractal theory and E-infinity theory is also discussed.

Existence and characterization of orthogonal multiple vector-valued wavelets with three-scale

In this article, we introduce orthogonal multiple vector-valued wavelets with three-scale, which are wavelets for vector fields, based on the notion of full rank subdivision operators. It is demonstrated that, like in the scalar and multiwavelet case, the existence of an orthogonal multiple vector-valued scaling function guarantees the existence of orthogonal multiple vector-valued wavelet functions. In this context, however, scaling functions as well as wavelet functions turn out to be multiple vector-valued functions. A method for constructing a class of orthogonal multiple vector-valued compactly supported wavelets is presented by means of matrix theory. The properties of the multiple vector-valued wavelet packets are characterized by virtue of operator theory and time–frequency analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Relation to some physical theories such as E-infinity Cantorian spacetime theory and fractal theory is also discussed.

The properties of a class of biorthogonal vector-valued nonseparable bivariate wavelet packets

In this paper, we introduce a class of vector-valued wavelet packets of space L 2 ( R 2 , C κ ) , 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 L 2 ( R 2 , C κ ) from these wavelet packets. Relation to some physical theories such as the Higgs field is also discussed.

Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases

In this paper, we introduce vector-valued non-separable higher-dimensional wavelet packets with an arbitrary integer dilation factor. An approach for constructing vector-valued higher-dimensional wavelet packet bases is proposed. Their characteristics are investigated by means of harmonic analysis method, matrix theory and operator theory, and three orthogonality formulas concerning the wavelet packets are presented. Orthogonal decomposition relation formulas of the space L 2 ( R n ) p are derived by designing a series of subspaces of the vector-valued wavelet packets. Moreover, several orthonormal wavelet packet bases of L 2 ( R n ) p are constructed from the wavelet packets. Relation to some physical theories such as E-infinity theory and multifractal theory is also discussed.