A study of biorthogonal multiple vector-valued wavelets

被引：2
|
作者：
Han, Jincang [1 ,2 ]
Cheng, Zhengxing [1 ]
Chen, Qingjiang [3 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Sci, Xian 710049, Peoples R China
[2] Lanzhou Commercial Coll, Sch Informat, Lanzhou 730000, Peoples R China
[3] Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Peoples R China
来源：
CHAOS SOLITONS & FRACTALS | 2009年 / 40卷 / 04期
关键词：
SPACE-TIME; CONSTRUCTION; SIGNAL;
D O I：
10.1016/j.chaos.2007.09.037
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The notion of vector-valued multiresolution analysis is introduced and the concept of biorthogonal multiple vector-valued wavelets which are wavelets for vector fields, is introduced. It is proved that, like in the scalar and multiwavelet case, the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the existence of a pair of biorthogonal multiple vector-valued wavelet functions. An algorithm for constructing a class of compactly supported biorthogonal multiple vector-valued wavelets is presented. Their properties are investigated by means of operator theory and algebra theory and time-frequency analysis method. Several biorthogonality formulas regarding these wavelet packets are obtained. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1574 / 1587
页数：14
相关论文
共 50 条
  • [1] Construction of a class of compactly supported biorthogonal multiple vector-valued wavelets
    Zhang, TQ
    Chen, QJ
    COMPUTATIONAL INTELLIGENCE AND SECURITY, PT 2, PROCEEDINGS, 2005, 3802 : 1134 - 1139
  • [2] Existence and construction of compactly supported biorthogonal multiple vector-valued wavelets
    Chen Q.-J.
    Cheng Z.-X.
    Wang C.-L.
    Journal of Applied Mathematics and Computing, 2006, 22 (3) : 101 - 115
  • [3] Construction of Biorthogonal Compactly Supported Vector-valued Wavelets
    Zhang, Tongqi
    ICNC 2008: FOURTH INTERNATIONAL CONFERENCE ON NATURAL COMPUTATION, VOL 4, PROCEEDINGS, 2008, : 120 - 124
  • [4] Existence and Design of a kind of Biorthogonal Vector-valued Wavelets
    Wang, Junqiu
    Li, Juanfei
    2009 INTERNATIONAL CONFERENCE ON ENVIRONMENTAL SCIENCE AND INFORMATION APPLICATION TECHNOLOGY, VOL III, PROCEEDINGS,, 2009, : 505 - 508
  • [5] The research of a class of biorthogonal compactly supported vector-valued wavelets
    Chen, Qingjiang
    Huo, Ailian
    CHAOS SOLITONS & FRACTALS, 2009, 41 (02) : 951 - 961
  • [6] A METHOD FOR CONSTRUCTING BIORTHOGONAL COMPACTLY SUPPORTED VECTOR-VALUED WAVELETS
    Wang, Xiao-Feng
    Guo, Ming-Pu
    PROCEEDINGS OF 2008 INTERNATIONAL CONFERENCE ON WAVELET ANALYSIS AND PATTERN RECOGNITION, VOLS 1 AND 2, 2008, : 496 - +
  • [7] Construction and decomposition of biorthogonal vector-valued wavelets with compact support
    Chen, Qingjiang
    Cao, Huaixin
    Shi, Zhi
    CHAOS SOLITONS & FRACTALS, 2009, 42 (05) : 2765 - 2778
  • [8] Constructions of Vector-Valued Filters and Vector-Valued Wavelets
    He, Jianxun
    Huang, Shouyou
    JOURNAL OF APPLIED MATHEMATICS, 2012,
  • [9] Existence and construction of biorthogonal comp-actly supported vector-valued wavelets
    Chen, Qing-Jiang
    Cao, Huai-Xin
    2007 INTERNATIONAL CONFERENCE ON WAVELET ANALYSIS AND PATTERN RECOGNITION, VOLS 1-4, PROCEEDINGS, 2007, : 1723 - 1728
  • [10] A Feasible Algorithm for Designing Biorthogonal Bivariate Vector-valued Finitely Supported Wavelets
    Huang Jing
    Lv Bing-Qing
    INTERNATIONAL CONFERENCE ON SOLID STATE DEVICES AND MATERIALS SCIENCE, 2012, 25 : 1507 - 1514
12345