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 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.

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.

scholarly journals Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fengjuan Zhu ◽  
Qiufu Li ◽  
Yongdong Huang
Keyword(s):  
Scaling Function ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Reconstruction Algorithm ◽  
Wavelet Function ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Numerical Examples ◽  
Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed.

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.

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 Frame Multiresolution Analysis on Local Fields of Positive Characteristic

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Firdous A. Shah
Keyword(s):  
Multiresolution Analysis ◽  
Positive Characteristic ◽  
Scaling Function ◽  
Local Fields ◽  
Wavelet Frames ◽  
Shift Invariant Spaces ◽  
Frame Multiresolution Analysis ◽  
Invariant Spaces ◽  
The Scaling Function

We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces. In contrast to the standard setting, the associated subspace V0 of L2(K) has a frame, a collection of translates of the scaling function φ of the form φ(·-u(k)):k∈N0, where N0 is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local field K of positive characteristic using the shift-invariant space theory.

Nonuniform wavelet frames in L2(ℝ)

2015 ◽  
Vol 08 (02) ◽  
pp. 1550034 ◽  
Author(s):  
Vikram Sharma ◽  
P. Manchanda
Keyword(s):  
Multiresolution Analysis ◽  
Sufficient Condition ◽  
Wavelet Frame ◽  
Necessary And Sufficient Condition ◽  
Wavelet Frames ◽  
Spectral Pairs ◽  
Necessary And Sufficient ◽  
Funct Anal

Gabardo and Nashed, [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal. 158 (1998) 209–241] introduced the nonuniform multiresolution analysis (NUMRA) whose translation set is not necessarily a group. The translation set is taken for elements in [Formula: see text], N ≥ 1 (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. In this paper, we construct wavelet frame over the translation set Λ on L2(ℝ). We call it nonuniform wavelet frame. We establish necessary and sufficient condition for such wavelet frame. An example is presented at the end.

scholarly journals Recent Advances in bis-Chalcone-Based Photoinitiators of Polymerization: From Mechanistic Investigations to Applications

Molecules ◽  
2021 ◽  
Vol 26 (11) ◽  
pp. 3192
Author(s):  
Nicolas Giacoletto ◽  
Frédéric Dumur
Keyword(s):  
Free Radical ◽  
Radical Polymerization ◽  
Cationic Polymerization ◽  
Free Radical Polymerization ◽  
Research Field ◽  
4D Printing ◽  
Unique Structure ◽  
The Past ◽  
Mechanistic Investigations ◽  
Active Research

Over the past several decades, photopolymerization has become an active research field, and the ongoing efforts to develop new photoinitiating systems are supported by the different applications in which this polymerization technique is involved—including dentistry, 3D and 4D printing, adhesives, and laser writing. In the search for new structures, bis-chalcones that combine two chalcones’ moieties within a unique structure were determined as being promising photosensitizers to initiate both the free-radical polymerization of acrylates and the cationic polymerization of epoxides. In this review, an overview of the different bis-chalcones reported to date is provided. Parallel to the mechanistic investigations aiming at elucidating the polymerization mechanisms, bis-chalcones-based photoinitiating systems were used for different applications, which are detailed in this review.

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