Construction and properties of orthogonal matrix-valued wavelets and wavelet packets

被引：25
|
作者：
Chen, Qingjiang [1 ,2 ]
Shi, Zhi [1 ]
机构：
[1] Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Peoples R China
[2] Xian Jiaotong Univ, Fac Sci, Xian 710049, Peoples R China
来源：
CHAOS SOLITONS & FRACTALS | 2008年 / 37卷 / 01期
关键词：
D O I：
10.1016/j.chaos.2007.08.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets with arbitrary integer dilation factor m. A necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets is derived by virtue of paraunitary vector filter bank theory. An algorithm for constructing compactly supported m-scale orthogonal matrix-valued wavelets is presented. The notion of orthogonal matrix-valued wavelet packets is proposed. Their properties are investigated by means of time-frequency method, operator theory and matrix theory. In particular, it is shown how to construct various orthonormal bases of space L(2) (R, C(rxr)) from these wavelet packets, and the orthogonal decomposition relation is also given. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：75 / 86
页数：12
相关论文
共 50 条
  • [1] Orthogonal Matrix-Valued Wavelet Packets
    Qingjiang Chen1
    [J]. Numerical Mathematics(Theory,Methods and Applications), 2007, (01) : 45 - 53
  • [2] The properties of compactly supported orthogonal matrix-valued wavelet packets
    Li, Yan-Ling
    Li, Gang
    [J]. WAVELET ACTIVE MEDIA TECHNOLOGY AND INFORMATION PROCESSING, VOL 1 AND 2, 2006, : 103 - +
  • [3] The properties of orthogonal matrix-valued wavelet packets in higher dimensions
    Chen Q.-J.
    Feng J.-S.
    Cheng Z.-X.
    [J]. Journal of Applied Mathematics and Computing, 2006, 22 (3) : 41 - 53
  • [4] A study of matrix-valued trivariate wavelet packets associated with an orthogonal matrix-valued trivariate scaling function
    Zhang, Jian
    Guo, Shuiwang
    [J]. ADVANCED MEASUREMENT AND TEST, PARTS 1 AND 2, 2010, 439-440 : 1165 - +
  • [5] A study of orthogonal matrix-valued multivariate wavelet packets associated with a dilation matrix
    Lu, Jun
    Li, Tizheng
    [J]. PROCEEDINGS OF THE 2009 WRI GLOBAL CONGRESS ON INTELLIGENT SYSTEMS, VOL IV, 2009, : 360 - +
  • [6] The Characterization of Orthogonal Matrix-valued Multivariable Wavelet Packets Associated with an Integer-valued Dilation Matrix
    Yuan, Deyou
    [J]. PROCEEDINGS OF THE 2009 WRI GLOBAL CONGRESS ON INTELLIGENT SYSTEMS, VOL II, 2009, : 577 - 580
  • [7] A Survey of Orthogonal Matrix-valued Two-dimensional Wavelet Packets with an Integer Quantity Dilation Matrix
    Gao, Hongwei
    Cao, Yanping
    [J]. 2009 INTERNATIONAL CONFERENCE ON ENVIRONMENTAL SCIENCE AND INFORMATION APPLICATION TECHNOLOGY,VOL I, PROCEEDINGS, 2009, : 615 - +
  • [8] Matrix-Valued and Quaternion Wavelets
    Ginzberg, P.
    Walden, A. T.
    [J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2013, 61 (06) : 1357 - 1367
  • [9] On Existence of Matrix-Valued Wavelets
    Yu, Baomin
    [J]. ADVANCED RESEARCH ON MATERIAL ENGINEERING, CHEMISTRY AND BIOINFORMATICS, PTS 1 AND 2 (MECB 2011), 2011, 282-283 : 153 - 156
  • [10] A study on compactly supported orthogonal vector-valued wavelets and wavelet packets
    Chen, Qingjiang
    Cheng, Zhengxing
    [J]. CHAOS SOLITONS & FRACTALS, 2007, 31 (04) : 1024 - 1034
12345