The Research of Bivariate Minimum-Energy Wavelet Frames and Pseudoframes

2010 ◽  
Vol 159 ◽  
pp. 1-6
Author(s):  
Ping An Wang
Keyword(s):  
Explicit Formula ◽  
Multiresolution Analysis ◽  
Minimum Energy ◽  
Laurent Polynomial ◽  
Sufficient Condition ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Existence Criterion ◽  
Generalized Multiresolution Analysis ◽  
Active Research

Frames have become the focus of active research, both in theory and in applications. In the article, the notion of bivariate minimum-energy wavelet frames is introduced. A precise existence criterion for minimum-energy frames in terms of an inequality condition on the Laurent polynomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also establish- ed. The sufficient condition for the existence of a class of affine pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresol- -ution structure.

A Study of Binary Minimum-Energy Shortly Supported Wavelet Frames Associated with a Scaling Function

2011 ◽  
Vol 219-220 ◽  
pp. 500-503
Author(s):  
Qing Jiang Chen ◽  
Gai Hu
Keyword(s):  
Explicit Formula ◽  
Multiresolution Analysis ◽  
Scaling Function ◽  
Minimum Energy ◽  
Research Field ◽  
Sufficient Condition ◽  
Wavelet Frames ◽  
Existence Criterion ◽  
Generalized Multiresolution Analysis ◽  
Active Research

Frames have become the focus of active research field, both in theory and in applications. In the article, the binary minimum-energy wavelet frames and frame multiresolution resolution are introduced. A precise existence criterion for minimum-energy frames in terms of an ineqity conditi- -on on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient condition for the existence of affine pseudoframes is obtained by virtue of a generalized multiresolution analysis. The pyramid de -composition scheme is established based on such a generalized multiresolution structure.

The Bivariate Minimum-Energy Tight Wavelet Frames and Applications in Economics and Management

2014 ◽  
Vol 915-916 ◽  
pp. 1412-1417
Author(s):  
Jian Guo Shen
Keyword(s):  
Multiresolution Analysis ◽  
Material Science ◽  
Minimum Energy ◽  
Research Field ◽  
Wavelet Frames ◽  
Science And Engineering ◽  
Interdisciplinary Field ◽  
Existence Criterion ◽  
Generalized Multiresolution Analysis ◽  
Active Research

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. Frames have become the focus of active research field, both in the-ory and in applications. In the article, the binary minimum-energy wavelet frames and frame multi-resolution resolution are introduced. A precise existence criterion for minimum-energy frames in terms of an ineqity condition on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient condi tion for the existence of tight wavelet frames is obtained by virtue of a generalized multiresolution analysis.

The Research of Bivariate Minimum-Energy Frames and Frames of Subspace and Application in Particle Physics

2012 ◽  
Vol 459 ◽  
pp. 280-283
Author(s):  
Yan Hui Lv
Keyword(s):  
Particle Physics ◽  
Materials Science ◽  
Minimum Energy ◽  
Research Field ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Generalized Multiresolution Analysis ◽  
Properties Of Materials ◽  
Active Research ◽  
The Relationship

Materials science is an applied science concerned with the relationship between the struc- ture and properties of materials. Frames have become the focus of active research field, both in the- ory and in applications. In the article, the binary minimum-energy wavelet frames and frame multi- resolution are introduced. A precise exist-ence criterion for minimum-energy frames in terms of an ineqity condition on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient con-dition for the existence of affine pseudoframes is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresolution structure.

The Excellent Traits of a Class of Orthogonal Quarternary Wavelet Wraps with Short Support

2011 ◽  
Vol 219-220 ◽  
pp. 496-499
Author(s):  
Guo Xin Wang ◽  
De Lin Hua
Keyword(s):  
Functional Analysis ◽  
Multiresolution Analysis ◽  
Frame Theory ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Orthogonal Wavelet ◽  
Decomposition Scheme ◽  
Novel Approach ◽  
Generalized Multiresolution Analysis

The frame theory has been one of powerful tools for researching into wavelets. In this article, the notion of orthogonal nonseparable quarternary wavelet wraps, which is the generalizati- -on of orthogonal univariate wavelet wraps, is presented. A novel approach for constructing them is presented by iteration method and functional analysis method. A liable approach for constructing two-directional orthogonal wavelet wraps is developed. The orthogonality property of quarternary wavelet wraps is discussed. Three orthogonality formulas concerning these wavelet wraps are estabished. A constructive method for affine frames of L2(R4) is proposed. The sufficient condition for the existence of a class of affine pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresolution structure.

scholarly journals A Short Note on Wavelet Frames Based on FMRA on Local Fields

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
M. Younus Bhat
Keyword(s):  
Multiresolution Analysis ◽  
Positive Characteristic ◽  
Minimum Energy ◽  
Short Note ◽  
Explicit Construction ◽  
Local Fields ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Frame Multiresolution Analysis ◽  
Field Of Positive Characteristic

The concept of frame multiresolution analysis (FMRA) on local fields of positive characteristic was given by Shah in his paper, Frame Multiresolution Analysis on Local Fields published by Journal of Operators. The author has studied the concept of minimum-energy wavelet frames on these prime characteristic fields. We continued the studies based on frame multiresolution analysis and minimum-energy wavelet frames on local fields of positive characteristic. In this paper, we introduce the notion of the construction of minimum-energy wavelet frames based on FMRA on local fields of positive characteristic. We provide a constructive algorithm for the existence of the minimum-energy wavelet frame on the local field of positive characteristic. An explicit construction of the frames and bases is given. In the end, we exhibit an example to illustrate our algorithm.

Study of Matrix Multipliers for Normalized Frame Multi-Wavelets and Applications in Engineering Material Technology

2013 ◽  
Vol 753-755 ◽  
pp. 2321-2324
Author(s):  
Yong Fan Xu
Keyword(s):  
Fourier Multipliers ◽  
Frame Theory ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Engineering Material ◽  
Material Technology ◽  
Decomposition Scheme ◽  
Affine Frames ◽  
Active Research

Frame theory has been the focus of active research for twenty years, both in theory and applications. Matrix Fourier multipliers send every orthonoamal wavelet to an orthonoamal wavelet. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

The Fine Characters of a Sort of Biorthogonal Four-Dimensional Nonseparable Wavelet Packs

2010 ◽  
Vol 159 ◽  
pp. 7-12
Author(s):  
Hong Lin Guo ◽  
Yu Min Yu
Keyword(s):  
Iteration Method ◽  
Wavelet Packets ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Wavelet Frames ◽  
New Approach ◽  
Decomposition Scheme ◽  
Necessary And Sufficient

In this article, the notion of orthogonal nonseparable four-dimensional wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is introduced. A new approach for constructing them is presented by iteration method and wavelets as well wavelet frames. The biorthogonality properties of four-dimensi- -onal wavelet packets are discussed. Three biorthogonality formulas concerning these wavelet packs are estabished. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented.

The Characteristics of Affine Bivariate Pseudoframes of Subspace Associated with a Bivariate Filter Functions

2010 ◽  
Vol 439-440 ◽  
pp. 926-931
Author(s):  
Yu Min Yu
Keyword(s):  
Frame Theory ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Decomposition Scheme ◽  
Affine Frames ◽  
Active Research

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

The Nice Feature of a Sort of Orthogonal Finitely Supported Five-Variant Wavelet Packages

2012 ◽  
Vol 459 ◽  
pp. 289-292
Author(s):  
Hong Wei Gao ◽  
Lan Ran Fang
Keyword(s):  
Iteration Method ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Wavelet Frames ◽  
New Approach ◽  
Decomposition Scheme ◽  
Necessary And Sufficient

In this article, the notion of orthogonal nonseparable five-variant wavelet packages, whi- ch is the generalization of orthogonal univariate wavelet packages, is introduced. A new approach for constructing the wavelet packages is presented by iteration method as well wavelet frames. The orthogonality properties for five-dimensional wavelet packages are discussed. Three orthogonality formulas concerning these wavelet packages are estabished. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented.

The Character of Multiple Affine Pseudoframes with Filter Banks Based on a Pyramid Decomposition Scheme

2010 ◽  
Vol 439-440 ◽  
pp. 1111-1116
Author(s):  
Tong Qi Zhang
Keyword(s):  
Filter Banks ◽  
Sufficient Condition ◽  
Decomposition Scheme ◽  
Active Research

In recent years, frames have been the focus of active research, both in theory and applications. In this paper, the notion of multiple affine pseudoframes for subspaces of space is introduced. The concept of a generalized multiresolution structure(GMRS) is proposed. The sufficient condition for the existence of a class of multiple pseudoframes with filter banks is obtained by virtue of a generalized multiresolution structure. An approach for constructing one GMRS of Paley-Wiener subspaces of is presented based on the pyramid decomposition scheme The characteristics of affine pseudoframes for subspaces of space is provided.

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