Approximation order provided by refinable function vectors

1997 ◽  
Vol 13 (2) ◽  
pp. 221-244 ◽  
Author(s):  
G. Plonka
Keyword(s):  
Approximation Order ◽  
Refinable Function ◽  
Refinable Function Vectors

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

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 High Balanced Biorthogonal Multiwavelets with Symmetry

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Youfa Li ◽  
Shouzhi Yang ◽  
Yanfeng Shen ◽  
Gengrong Zhang
Keyword(s):  
General Scheme ◽  
Refinable Function ◽  
Antisymmetric Component ◽  
Multiwavelet Transform ◽  
Refinable Function Vectors ◽  
Function Vector ◽  
Biorthogonal Multiwavelets ◽  
Vector Valued

Balanced multiwavelet transform can process the vector-valued data sparsely while preserving a polynomial signal. Yang et al. (2006) constructed balanced multiwavelets from the existing nonbalanced ones. It will be proved, however, in this paper that if the nonbalanced multiwavelets have antisymmetric component, it is impossible for the balanced multiwavelets by the method mentioned above to have symmetry. In this paper, we give an algorithm for constructing a pair of biorthogonal symmetric refinable function vectors from any orthogonal refinable function vector, which has symmetric and antisymmetric components. Then, a general scheme is given for high balanced biorthogonal multiwavelets with symmetry from the constructed pair of biorthogonal refinable function vectors. Moreover, we discuss the approximation orders of the biorthogonal symmetric refinable function vectors. An example is given to illustrate our results.

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