High balanced biorthogonal multiwavelets with symmetry
type: Item
instance of: scholarly article
title: High balanced biorthogonal multiwavelets with symmetry
zbMATH Open document ID: 1472.42056
DOI: 10.1155/2014/154269
author: S. Z. Yang
author: Y. F. Shen
author: Youfa Li
author: Gengrong Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Balanced multiwavelet transform can process the vector-valued data sparsely while preserving a polynomial signal. In [Sci. China, Ser. F 49, No. 4, 504--515 (2006; Zbl 1129.42019); Sci. China, Ser. A 49, No. 1, 86--97 (2006; Zbl 1193.42100)], \textit{S. Yang} and \textit{L. Peng} 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.
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 7021821
Wikidata QID: Q59035551
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/154269
OpenAlex ID: W1993664571
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description: scientific article; zbMATH DE number 7021821