The Information Optimal Algorithm Based on Poly-Scaled Wavelet Wraps and Wavelet Frames with Finite Support

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.

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

10.4028/www.scientific.net/kem.460-461.323 ◽

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 ◽

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

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

10.4028/www.scientific.net/kem.460-461.317 ◽

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 ◽

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.

Designment Algorithm on Orthogonal Two-Directional Vector-Valued Wavelets with Three-Scale Dilation Factor

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.430-432.1203 ◽

2012 ◽

Vol 430-432 ◽

pp. 1203-1206

Author(s):

Jian Tang Zhao

Keyword(s):

Frequency Analysis ◽

Multiresolution Analysis ◽

Operator Theory ◽

Matrix Theory ◽

New Method ◽

Scaling Functions ◽

Orthogonal Wavelet ◽

Time Frequency ◽

Dilation Factor ◽

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

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.20-23.1053 ◽

2010 ◽

Vol 20-23 ◽

pp. 1053-1059

Author(s):

Xin Xian Tian ◽

Ai Lian Huo

Keyword(s):

Frequency Analysis ◽

Operator Theory ◽

Matrix Theory ◽

Higher Dimensions ◽

Wavelet Packets ◽

Riesz Bases ◽

Dimensional Vector ◽

Analysis Method ◽

Time Frequency ◽

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

10.4028/www.scientific.net/kem.439-440.932 ◽

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 ◽

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.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.461.656 ◽

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 ◽

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

10.4028/www.scientific.net/kem.439-440.1099 ◽

2010 ◽

Vol 439-440 ◽

pp. 1099-1104

Author(s):

Hong Wu Li ◽

Dong Liao

Keyword(s):

Operator Theory ◽

Matrix Theory ◽

Wavelet Packet ◽

Higher Dimensions ◽

Wavelet Packets ◽

Riesz Bases ◽

Analysis Method ◽

Time Frequency ◽

Higher Dimensional ◽

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.

A Feasible Algorithm for Designing Biorthogonal Binary Finitely Supported Multiwavelet Functions

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.225-226.1092 ◽

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 ◽

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.457-458.36 ◽

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 ◽

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.