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.

On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle

2014 ◽  
Vol 57 (2) ◽  
pp. 254-263 ◽  
Author(s):  
Ole Christensen ◽  
Hong Oh Kim ◽  
Rae Young Kim
Keyword(s):  
Extension Principle ◽  
Sufficient Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Number Of Generators ◽  
Unitary Extension

AbstractThe unitary extension principle (UEP) by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.

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.

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.

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.

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

scholarly journals The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates

2006 ◽  
Vol 58 (6) ◽  
pp. 1121-1143 ◽  
Author(s):  
Marcin Bownik ◽  
Darrin Speegle
Keyword(s):  
Regularity Condition ◽  
Finite Union ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Weak Regularity

AbstractThe Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.

Constructing totally interpolating wavelet frame systems

2015 ◽  
Vol 13 (03) ◽  
pp. 1550017
Author(s):  
Baobin Li
Keyword(s):  
Filter Banks ◽  
Scaling Function ◽  
Tight Frame ◽  
Special Structure ◽  
Dual Frame ◽  
Wavelet Frame ◽  
Continuous Linear ◽  
Wavelet Frames ◽  
Frame Systems ◽  
The Scaling Function

The system of totally interpolating wavelet frames is discussed in this paper, in which both the scaling function and one of wavelet functions are interpolating. It will be shown that corresponding filter banks possess the special structure, and the parametrization of filter banks is present. Moreover, we show that when considering tight frame systems with two generators, the Ron–Shen's continuous-linear-spline-based tight frame is the only one with totally interpolating property and symmetry. But in the dual frame context, more good examples of bi-frames with symmetric/antisymmetric property can be obtained and constructed, which in particular, include frames with the uniform symmetry.

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
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