Orthogonality criteria for compactly supported refinable functions and refinable function vectors

2000 ◽  
Vol 6 (2) ◽  
pp. 153-170 ◽  
Author(s):  
Jeffrey C. Lagarias ◽  
Yang Wang
Keyword(s):  
Refinable Functions ◽  
Refinable Function ◽  
Compactly Supported ◽  
Refinable Function Vectors

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.

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 Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Yeon Ju Lee ◽  
Jungho Yoon
Keyword(s):  
Riesz Bases ◽  
Refinable Functions ◽  
Biorthogonal Wavelet ◽  
Wavelet Bases ◽  
Refinable Function ◽  
B Splines ◽  
Compactly Supported ◽  
Mathematical Properties ◽  
The Stability

This paper is concerned with analyzing the mathematical properties, such as the regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines. We first discuss the biorthogonality condition of the nonstationary refinable functions, and then we show that the refinable functions based on exponential B-splines have the same regularities as the ones based on the polynomial B-splines of the corresponding orders. In the context of nonstationary wavelets, the stability of wavelet bases is not implied by the stability of a refinable function. For this reason, we prove that the suggested nonstationary wavelets form Riesz bases for the space that they generate.

A CLASS OF ORTHOGONAL TWO-DIRECTION REFINABLE FUNCTIONS AND TWO-DIRECTION WAVELETS

2008 ◽  
Vol 06 (06) ◽  
pp. 883-894 ◽  
Author(s):  
SHOUZHI YANG ◽  
CHANGZHEN XIE
Keyword(s):  
Refinable Functions ◽  
Refinable Function

In this paper, an algorithm for constructing a class of orthogonal two-direction refinable functions and the corresponding orthogonal two-direction wavelets is obtained. In addition, the relation of both two-direction refinable functions and multiwavelets is discussed. We discover that Chui–Lian's orthogonal symmetric/antisymmetric multiscaling functions and the corresponding multiwavelets can be recovered by using an orthogonal two-direction refinable function and the corresponding two-direction wavelets, respectively. Finally, some construction examples are given.

scholarly journals Generalized interpolating refinable function vectors

2009 ◽  
Vol 227 (2) ◽  
pp. 254-270 ◽  
Author(s):  
Bin Han ◽  
Soon-Geol Kwon ◽  
Xiaosheng Zhuang
Keyword(s):  
Refinable Function ◽  
Refinable Function Vectors
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