High Balanced Biorthogonal Multiwavelets with Symmetry

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 antisymmetr...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014, Vol.2014 (2014), p.936-943
Main Authors: Zhang, Gengrong, Shen, Y. F., Yang, S. Z., Li, Youfa
Format: Article
Language:English
Subjects:
Algorithms
Mathematical functions
Mathematical research
Mathematics
Music
Vector spaces
Wavelet transforms
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/154269