scholarly journals TIME-SHIFTS GENERALIZED MULTIRESOLUTION ANALYSIS OVER DYADIC-SCALING REDUCING SUBSPACES

2004 ◽  
Vol 02 (03) ◽  
pp. 237-248 ◽  
Author(s):  
NHAN LEVAN ◽  
CARLOS S. KUBRUSLY
Keyword(s):  
Function Space ◽  
Multiresolution Analysis ◽  
Time Shift ◽  
Orthonormal Wavelet ◽  
Reducing Subspaces ◽  
Wandering Subspace ◽  
Generalized Multiresolution Analysis

A Generalized Multiresolution Analysis (GMRA) associated with a wavelet is a sequence of nested subspaces of the function space ℒ2(ℝ), with specific properties, and arranged in such a way that each of the subspaces corresponds to a scale 2m over all time-shifts n. These subspaces can be expressed in terms of a generating-wandering subspace — of the dyadic-scaling operator — spanned by orthonormal wavelet-functions — generated from the wavelet. In this paper we show that a GMRA can also be expressed in terms of subspaces for each time-shift n over all scales 2m. This is achieved by means of "elementary" reducing subspaces of the dyadic-scaling operator. Consequently, Time-Shifts GMRA associated with wavelets, as well as "sub-GMRA" associated with "sub-wavelets" will then be introduced.

scholarly journals Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 994 ◽  
Author(s):  
Adrian Holhoş ◽  
Daniela Roşca
Keyword(s):  
Unit Ball ◽  
Multiresolution Analysis ◽  
Uniform Grid ◽  
Orthonormal Wavelet ◽  
Wavelet Bases ◽  
Piecewise Constant ◽  
Regular Octahedron ◽  
Piecewise Constant Functions ◽  
Local Support ◽  
Volume Preserving

We construct a new volume preserving map from the unit ball B 3 to the regular 3D octahedron, both centered at the origin, and its inverse. This map will help us to construct refinable grids of the 3D ball, consisting in diameter bounded cells having the same volume. On this 3D uniform grid, we construct a multiresolution analysis and orthonormal wavelet bases of L 2 ( B 3 ) , consisting in piecewise constant functions with small local support.

Generalized multiresolution analysis on unstructured grids

2000 ◽  
Vol 86 (4) ◽  
pp. 685-715 ◽  
Author(s):  
Friederike Schröder-Pander ◽  
Thomas Sonar ◽  
Oliver Friedrich
Keyword(s):  
Multiresolution Analysis ◽  
Unstructured Grids ◽  
Generalized Multiresolution Analysis

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.

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 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.

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.

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