{"title":"九尺度双正交向量值多元小波包的研究","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":"{\"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}","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}
The survey of biorthogonal vector-valued multivariate wavelet packets with nine-scale
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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