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 21 条
[1]   El Naschie's ε(∞) space-time and scale relativity theory in the topological dimension D=4 [J].
Agop, M. ;
Murgulet, C. .
CHAOS SOLITONS & FRACTALS, 2007, 32 (03) :1231-1240
[2]   Wavelets for multichannel signals [J].
Bacchelli, S ;
Cotronei, M ;
Sauer, T .
ADVANCES IN APPLIED MATHEMATICS, 2002, 29 (04) :581-598
[3]   A study on compactly supported orthogonal vector-valued wavelets and wavelet packets [J].
Chen, Qingjiang ;
Cheng, Zhengxing .
CHAOS SOLITONS & FRACTALS, 2007, 31 (04) :1024-1034
[4]   NONORTHOGONAL WAVELET PACKETS [J].
CHUI, CK ;
LI, C .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (03) :712-738
[5]   ON THE INSTABILITY OF ARBITRARY BIORTHOGONAL WAVELET PACKETS [J].
COHEN, A ;
DAUBECHIES, I .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (05) :1340-1354
[6]   Data-driven and optimal denoising of a signal and recovery of its derivative using multiwavelets [J].
Efromovich, S ;
Lakey, J ;
Pereyra, MC ;
Tymes, N .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2004, 52 (03) :628-635
[7]   A guide to the mathematics of E-infinity Cantorian spacetime theory [J].
El Naschie, MS .
CHAOS SOLITONS & FRACTALS, 2005, 25 (05) :955-964
[8]   Hilbert space, the number of Higgs particles and the quantum two-slit experiment [J].
El Naschie, MS .
CHAOS SOLITONS & FRACTALS, 2006, 27 (01) :9-13
[9]   Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets [J].
Fowler, JE ;
Hua, L .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2002, 50 (12) :3018-3027
[10]   Home network power-line communication signal processing based on wavelet packet analysis [J].
He, HB ;
Cheng, SJ ;
Zhang, YB ;
Nguimbis, J .
IEEE TRANSACTIONS ON POWER DELIVERY, 2005, 20 (03) :1879-1885
123