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

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

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

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 ◽

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.

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

10.4028/www.scientific.net/amr.171-172.113 ◽

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 ◽

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.

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.938 ◽

2010 ◽

Vol 439-440 ◽

pp. 938-943

Author(s):

Hong Wei Gao ◽

Li Ping Ding

Keyword(s):

Filter Banks ◽

Matrix Theory ◽

Constant Factor ◽

New Method ◽

Scaling Functions ◽

Compactly Supported ◽

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.

A Feasible Algorithm for Designing Biorthogonal Binary Finitely Supported Multiwavelet Functions

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 ◽

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

10.4028/www.scientific.net/amr.204-210.1759 ◽

2011 ◽

Vol 204-210 ◽

pp. 1759-1762

Author(s):

Tong Qi Zhang

Keyword(s):

Operator Theory ◽

Matrix Theory ◽

Integral Transform ◽

Optimal Algorithm ◽

Higher Dimensions ◽

Wavelet Frames ◽

Finite Support ◽

Multi Scale ◽

In this paper, we propose the notion of vector-valued multiresolution analysis and the vector-valued mutivariate wavelet wraps with multi-scale factor of spaceL2(Rn, Cv), which are ge- neralizations of multivariate wavelet wraps. An approach for designing a sort of biorthogonal vec- tor-valued wavelet wraps in higher dimensions is presented and their biorthogonality trait is charac- -terized by virtue of integral transform, matrix theory, and operator theory. Two biorthogonality formulas regarding these wavelet wraps are established.

A New Procedure for Designing a Kind of Orthogonal Vector-Valued Multiscaled Wavelets and Wavelet Wraps

10.4028/www.scientific.net/amr.204-210.1733 ◽

2011 ◽

Vol 204-210 ◽

pp. 1733-1736

Author(s):

Hong Wei Gao

Keyword(s):

Filter Bank ◽

Matrix Theory ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Orthogonal Vector ◽

Novel Method ◽

Necessary And Sufficient ◽

In this paper, notion of vector-valued multiresolution analysis is introduced. So does the notion of orthogonal vector-valued wavelets A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is presented by using paraunitary vector filter bank theory and matrix theory. A novel method for constructing a kind of orthogonal shortly supported vector -valued wavelets is presented.

An Optimization Algorithm for Orthogonal Trivariate Wavelets with Short Support

10.4028/www.scientific.net/amr.461.835 ◽

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 ◽

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.

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

10.4028/www.scientific.net/amr.889-890.1270 ◽

2014 ◽

Vol 889-890 ◽

pp. 1270-1274

Author(s):

Jin Shun Feng ◽

Qing Jiang Chen

Keyword(s):

Riesz Bases ◽

Scaling Functions ◽

Sufficient Condition ◽

Analysis Method ◽

Compactly Supported ◽

Dilation Matrix ◽

Engineering Materials ◽

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.

Vector-valued nonuniform multiresolution analysis on local fields

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691315500290 ◽

2015 ◽

Vol 13 (04) ◽

pp. 1550029 ◽

Cited By ~ 3

Author(s):

Firdous Ahmad Shah ◽

M. Younus Bhat

Keyword(s):

Orthonormal Basis ◽

Positive Characteristic ◽

Local Fields ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Vilenkin Groups ◽

Refinement Mask ◽

Necessary And Sufficient ◽

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.

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.1093 ◽

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 ◽

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.