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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/154269 |
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| author | Youfa Li Shouzhi Yang Yanfeng Shen Gengrong Zhang |
| author_facet | Youfa Li Shouzhi Yang Yanfeng Shen Gengrong Zhang |
| author_sort | Youfa Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8d2d7da45f404cef99894b60692576ed |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8d2d7da45f404cef99894b60692576ed2025-02-03T05:44:42ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/154269154269High Balanced Biorthogonal Multiwavelets with SymmetryYoufa Li0Shouzhi Yang1Yanfeng Shen2Gengrong Zhang3College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, ChinaDepartment of Mathematics, Shantou University, Shantou 515063, ChinaDepartment of Mathematics, Dezhou University, Dezhou 253023, ChinaCollege of Mathematics and Information Sciences, Guangxi University, Nanning 530004, ChinaBalanced 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.http://dx.doi.org/10.1155/2014/154269 |
| spellingShingle | Youfa Li Shouzhi Yang Yanfeng Shen Gengrong Zhang High Balanced Biorthogonal Multiwavelets with Symmetry Abstract and Applied Analysis |
| title | High Balanced Biorthogonal Multiwavelets with Symmetry |
| title_full | High Balanced Biorthogonal Multiwavelets with Symmetry |
| title_fullStr | High Balanced Biorthogonal Multiwavelets with Symmetry |
| title_full_unstemmed | High Balanced Biorthogonal Multiwavelets with Symmetry |
| title_short | High Balanced Biorthogonal Multiwavelets with Symmetry |
| title_sort | high balanced biorthogonal multiwavelets with symmetry |
| url | http://dx.doi.org/10.1155/2014/154269 |
| work_keys_str_mv | AT youfali highbalancedbiorthogonalmultiwaveletswithsymmetry AT shouzhiyang highbalancedbiorthogonalmultiwaveletswithsymmetry AT yanfengshen highbalancedbiorthogonalmultiwaveletswithsymmetry AT gengrongzhang highbalancedbiorthogonalmultiwaveletswithsymmetry |