Existence and design of biorthogonal matrix-valued wavelets

被引：7
|
作者：
Cui, Lihong [1 ]
Zhai, Bolan [1 ]
Zhang, Tongbing [2 ]
机构：
[1] Beijing Univ Chem Technol, Sch Sci, Beijing 100029, Peoples R China
[2] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2009年 / 10卷 / 05期
关键词：
Biorthogonal; Existence; Matrix-valued wavelets; Filter; Factorization; MULTIFILTER BANKS; FILTER BANKS; MULTIWAVELETS; BASES;
D O I：
10.1016/j.nonrwa.2008.07.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study biorthogonal matrix-valued wavelets for analyzing matrix-valued signals based on matrix multiresolution analysis. Firstly, sufficient conditions for the existence of biorthogonal matrix-valued scaling function are established in terms of two-scale matrix symbols. Then we focus on the construction of biorthogonal matrix-valued wavelet. Two designs based on factorizations of biorthogonal two-scale matrix symbol are presented. In particular, explicit constructing formulations for biorthogonal matrix-valued wavelets are given. With these formulations, highpass filters {G(k)} and {(G) over tilde (k)} of biorthogonal matrix-valued wavelets can be given explicitly by lowpass filters {H(k)} and {(H) over tilde (k)} of their corresponding biorthogonal scaling functions. Finally, according to our designs, two examples of two-scale matrix filters are given. (C) 2008 Elsevier Ltd. All rights reserved.
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页码：2679 / 2687
页数：9
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