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Abstract and Applied Analysis
Volume 2014, Article ID 154269, 8 pages
http://dx.doi.org/10.1155/2014/154269
Research Article

High Balanced Biorthogonal Multiwavelets with Symmetry

1College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China
2Department of Mathematics, Shantou University, Shantou 515063, China
3Department of Mathematics, Dezhou University, Dezhou 253023, China

Received 10 June 2014; Accepted 28 August 2014; Published 10 November 2014

Academic Editor: Thanh Tran

Copyright © 2014 Youfa Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.