scholarly journals Dual Wavelet Frame Transforms on Manifolds and Graphs

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Lihong Cui ◽  
Qiaoyun Wu ◽  
Jiale Liu ◽  
Jianjun Sun
Keyword(s):  
Sufficient Conditions ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Graph Data ◽  
Numerical Example ◽  
Dual Wavelet Frames ◽  
Frame Transformation ◽  
Dual Wavelet ◽  
Discrete Setting

In this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the decomposition and reconstruction for the dual wavelet frame transforms on graphs. Finally, we give a numerical example to illustrate the validity of the dual wavelet frame transformation applied to the graph data.

The Characterization of a Pair of Canonical Frames Generated by Several Compactly Supported Functions

2010 ◽  
Vol 439-440 ◽  
pp. 1135-1140
Author(s):  
Jun Qiu Wang ◽  
Jian Guo Wang
Keyword(s):  
Scaling Functions ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
The Past ◽  
Single Function ◽  
Dual Wavelet Frames ◽  
Popular Subject ◽  
Compactly Supported Functions ◽  
Dual Wavelet

Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function.

The Characteristics of Orthogonal Wavelet Frames and Canonical Frames and Applications in Material Science

2013 ◽  
Vol 721 ◽  
pp. 741-744
Author(s):  
Yong Fan Xu
Keyword(s):  
Material Science ◽  
Scaling Functions ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Orthogonal Wavelet ◽  
The Past ◽  
Single Function ◽  
Dual Wavelet Frames ◽  
Popular Subject ◽  
Dual Wavelet

Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function. Traits of tight wavelet frames are presented.

Study of Periodic Frames and Trivariate Tight Wavelet Frames and Applications in Materials Engineering

2014 ◽  
Vol 1079-1080 ◽  
pp. 878-881
Author(s):  
Song Zhen Sun ◽  
Yi Guo
Keyword(s):  
Time Domain ◽  
Dual Frame ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Materials Engineering ◽  
Number Of Generators ◽  
Dual Wavelet Frames ◽  
The Time Domain ◽  
Dual Wavelet

It is shown that there exists a frame wavelet with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions.

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.

Nonuniform nonhomogeneous dual wavelet frames in Sobolev spaces in $$L^2({\mathbb {K}})$$

2020 ◽  
Vol 31 (7-8) ◽  
pp. 1145-1156 ◽  
Author(s):  
O. Ahmad ◽  
N. A. Sheikh ◽  
M. A. Ali
Keyword(s):  
Sobolev Spaces ◽  
Wavelet Frames ◽  
Dual Wavelet Frames ◽  
Dual Wavelet

Construction of approximate dual wavelet frames

2013 ◽  
Vol 40 (1) ◽  
pp. 273-282 ◽  
Author(s):  
Hans G. Feichtinger ◽  
Darian M. Onchis ◽  
Christoph Wiesmeyr
Keyword(s):  
Wavelet Frames ◽  
Dual Wavelet Frames ◽  
Dual Wavelet

scholarly journals Dualwavelet frames in Sobolev spaces on local fields of positive characteristic

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2091-2099
Author(s):  
Ishtaq Ahmad ◽  
Neyaz Sheikh
Keyword(s):  
Sobolev Spaces ◽  
Local Field ◽  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
The Past ◽  
Dual Wavelet Frames ◽  
Dual Wavelet ◽  
Field Of Positive Characteristic

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. In this article, we obtain the characterization of nonhomogeneous wavelet frames and nonhomogeneous dual wavelet frames in a Sobolev spaces on a local field of positive characteristic by means of a pair of equations.

COMPACTLY SUPPORTED MULTIVARIATE, PAIRS OF DUAL WAVELET FRAMES OBTAINED BY CONVOLUTION

2008 ◽  
Vol 06 (02) ◽  
pp. 183-208 ◽  
Author(s):  
MARTIN EHLER
Keyword(s):  
Approximation Order ◽  
Refinable Functions ◽  
Wavelet Frames ◽  
Refinable Function ◽  
Vanishing Moments ◽  
Wavelet System ◽  
Compactly Supported ◽  
Mask Size ◽  
Dual Wavelet Frames ◽  
Dual Wavelet

In this paper, we present a construction of compactly supported multivariate pairs of dual wavelet frames. The approach is based on the convolution of two refinable distributions. We obtain smooth wavelets with any preassigned number of vanishing moments. Their underlying refinable function is fundamental. In the examples, we obtain symmetric wavelets with small support from optimal refinable functions, i.e. the refinable function has minimal mask size with respect to smoothness and approximation order of its generated multiresolution analysis. The wavelet system has maximal approximation order with respect to the underlying refinable function.

scholarly journals The necessary and sufficient conditions for wavelet frames in Sobolev space over local fields

2021 ◽  
Vol 39 (3) ◽  
pp. 81-92
Author(s):  
Ashish Pathak ◽  
Dileep Kumar ◽  
Guru P. Singh
Keyword(s):  
Sobolev Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Necessary And Sufficient

In this paper we construct wavelet frame on Sobolev space. A necessary condition and sufficient conditions for wavelet frames in Sobolev space are given.

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