{"title":"The survey of biorthogonal vector-valued multivariate wavelet packets with nine-scale","authors":"Qingjiang Chen, Z. An","doi":"10.1109/ICWAPR.2009.5207453","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce a class of vector-valued wavelet packets of space L<sup>2</sup>(R<sup>s</sup>,C<sup>v</sup>), which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued higher-dimensional wavelet packets is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formu-las regarding these wavelet packets are derived. Moreover, it is shown how to obtain new Riesz bases of space L<sup>2</sup>(R<sup>s</sup>,C<sup>v</sup>) from these wavelet packets.","PeriodicalId":424264,"journal":{"name":"2009 International Conference on Wavelet Analysis and Pattern Recognition","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Conference on Wavelet Analysis and Pattern Recognition","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICWAPR.2009.5207453","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we introduce a class of vector-valued wavelet packets of space L2(Rs,Cv), which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued higher-dimensional wavelet packets is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formu-las regarding these wavelet packets are derived. Moreover, it is shown how to obtain new Riesz bases of space L2(Rs,Cv) from these wavelet packets.
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