Two-Dimensional Orthogonal Wavelets and Wavelet Packets

2018 ◽  
pp. 73-82
Author(s):  
Amir Z. Averbuch ◽  
Pekka Neittaanmäki ◽  
Valery A. Zheludev
Keyword(s):  
Wavelet Packets ◽  
Two Dimensional ◽  
Orthogonal Wavelets

Periodic Orthogonal Wavelets and Wavelet Packets

2018 ◽  
pp. 41-72
Author(s):  
Amir Z. Averbuch ◽  
Pekka Neittaanmäki ◽  
Valery A. Zheludev
Keyword(s):  
Wavelet Packets ◽  
Orthogonal Wavelets

SPECTRA AND FILTERING: A CLARIFICATION

2007 ◽  
Vol 05 (03) ◽  
pp. 465-483 ◽  
Author(s):  
CH.-H. BRUNEAU ◽  
P. FISCHER
Keyword(s):  
Wavelet Packets ◽  
Two Dimensional ◽  
Wavelet Filtering

Filtering methods have been introduced in the early nineties, in 1988 by Farge et al. for a wavelet filtering, in 1987 by Benzi et al. and in 1994 by Borue for a direct cut-off filtering. The aim of these methods is to filter the velocity and/or the vorticity fields of two-dimensional turbulence experiments in order to enhance the various components of the fluid. Using this king of methods allows us to separate the vortices from the background essentially composed by vorticity filaments. We have also shown the ability of the wavelet packets in performing this filtering. However, we had underestimated, like Borue in 1994, the influence of the filtering process in the computation of the energy and/or enstrophy spectra. We will show in the present paper how the introduction of discontinuities due to the filtering process can subsequently modify the spectra.

scholarly journals A Wavelet Approach to Representing Background Error Covariances in a Limited-Area Model

2005 ◽  
Vol 133 (5) ◽  
pp. 1279-1294 ◽  
Author(s):  
Alex Deckmyn ◽  
Loïk Berre
Keyword(s):  
Correlation Matrix ◽  
Wavelet Function ◽  
Limited Area ◽  
Two Dimensional ◽  
Background Error ◽  
Orthogonal Wavelets ◽  
Wavelet Space ◽  
Powers Of 2 ◽  
Correlation Scale ◽  
Meyer Wavelets

Abstract The use of orthogonal wavelets for the representation of background error covariances over a limited area is studied. Each wavelet function contains both information on position and information on scale: using a diagonal correlation matrix in wavelet space thus gives the possibility of representing the local variations of correlation scale. To this end, a generalized family of orthogonal Meyer wavelets that are not restricted to dyadic domains (i.e., powers of 2) is introduced. A three-bases approach is used, which allows one to take advantage of the respective properties of the spectral, wavelet, and gridpoint spaces. While the implied local anisotropies are relatively small, the local changes in the two-dimensional length scale are rather well represented.

scholarly journals Two-dimensional orthogonal wavelets with vanishing moments

1996 ◽  
Vol 44 (10) ◽  
pp. 2579-2590 ◽  
Author(s):  
D. Stanhill ◽  
Y.Y. Zeevi
Keyword(s):  
Two Dimensional ◽  
Vanishing Moments ◽  
Orthogonal Wavelets

A Study on Characteristics of Biorthogonal Two-Dimensional Wavelet Packets

2010 ◽  
Vol 439-440 ◽  
pp. 1159-1164
Author(s):  
De Yao Song ◽  
Xiao Feng Wang
Keyword(s):  
Wavelet Analysis ◽  
Science Research ◽  
Wavelet Packets ◽  
Two Dimensional ◽  
Popular Subject ◽  
Definition Of

Wavelet analysis is a popular subject in science research. The notion of univariate orthog- onal wavelet packets is generalized. The definition of biorthogonal nonseparable two-dimensional wavelet packets is presented and a procedure for constructing them is proposed. The biorthogonality property of bivariate wavelet packets is investigated. Two biorthogonality formulas regarding these wavelet packets are established.

scholarly journals THE COMPUTATIONAL EFFICIENCY OF WALSH APPROXIMATION FOR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS

2011 ◽  
Vol 04 (02) ◽  
pp. 263-270 ◽  
Author(s):  
S. Anderyance ◽  
M. Hadizadeh
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Volterra Integral Equation ◽  
Computational Efficiency ◽  
Numerical Scheme ◽  
Operational Matrix ◽  
Wavelet Packets ◽  
Walsh Functions ◽  
Two Dimensional ◽  
Operational Matrix Of Integration

In this research, we give details of a new numerical method for the approximate solution of a general two-dimensional Volterra integral equation, using the discontinuous wavelet packets e.g. Walsh functions. The double Walsh approximation we have adopted utilizes a simple robust numerical scheme for approximate solution of the equations. The two-dimensional operational matrix of integration for each subinterval [Formula: see text] is explicitly constructed, where m is a power of 2. Finally the reliability and efficiency of the proposed scheme are demonstrated by some numerical results.

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