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.

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.

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 A SINISTER VIEW OF DILATION EQUATIONS

2005 ◽  
Vol 03 (01) ◽  
pp. 67-77
Author(s):  
DAVID MALONE
Keyword(s):  
Refinable Functions ◽  
Refinable Function ◽  
Compactly Supported ◽  
Rate Of Growth ◽  
Dilation Equation ◽  
Dilation Equations

We present a technique for studying refinable functions which are compactly supported. Refinable functions satisfy dilation equations and this technique focuses on the implications of the dilation equation at the edges of the support of the refinable function. This method is fruitful, producing new results regarding existence, uniqueness, smoothness and rate of growth of refinable functions.

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.

CONSTRUCTION OF COMPACTLY SUPPORTED CONJUGATE SYMMETRIC COMPLEX TIGHT WAVELET FRAMES

2010 ◽  
Vol 08 (06) ◽  
pp. 861-874 ◽  
Author(s):  
SHOUZHI YANG ◽  
YANMEI XUE
Keyword(s):  
Wavelet Frames ◽  
Refinable Function ◽  
Compactly Supported ◽  
Symmetric Complex ◽  
Low Pass ◽  
Tight Wavelet Frame ◽  
Free Parameters ◽  
Low Pass Filters ◽  
The Given ◽  
High Pass

Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function ϕ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function ϕ is compactly supported conjugate symmetric, then we prove that there exists a compactly supported conjugate symmetric/anti-symmetric complex tight wavelet frame Ψ = {ψ1, ψ2, ψ3} associated with ϕ. Secondly, under the conditions that both the low-pass filters and high-pass filters are unknown, we give a parametric formula for constructing a class of smooth conjugate symmetric/anti-symmetric complex tight wavelet frames. Free parameters in the algorithm are explicitly identified, and can be used to optimize the result with respect to other criteria. Finally, two examples are given to illustrate how to use our method to construct conjugate symmetric complex tight wavelet frames.

scholarly journals Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
A. San Antolín ◽  
R. A. Zalik
Keyword(s):  
Closed Form ◽  
Spectral Factorization ◽  
Extension Principle ◽  
Refinable Functions ◽  
Wavelet Frames ◽  
Compactly Supported ◽  
Slight Generalization ◽  
Dilation Matrix ◽  
Transcendental Functions ◽  
Low Degrees

For any dilation matrix with integer entries and , we construct a family of smooth compactly supported tight wavelet frames with three generators in . Our construction involves some compactly supported refinable functions, the oblique extension principle, and a slight generalization of a theorem of Lai and Stöckler. Estimates for the degrees of smoothness are given. With the exception of a polynomial whose coefficients must in general be computed by spectral factorization, the framelets are expressed in closed form in the frequency domain, in terms of elementary transcendental functions. By means of two examples we also show that for low degrees of smoothness the use of spectral factorization may be avoided.

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.

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