[1]李洪刚,吴乐南.基于任意小波的提升格式的设计[J].东南大学学报(自然科学版),2001,31(4):22-26.[doi:10.3969/j.issn.1001-0505.2001.04.006]
　Li Honggang,Wu Lenan.Design of Lifting Scheme of Arbitrary Wavelets[J].Journal of Southeast University (Natural Science Edition),2001,31(4):22-26.[doi:10.3969/j.issn.1001-0505.2001.04.006]
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基于任意小波的提升格式的设计()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
31
期数:
2001年第4期
页码:
22-26
栏目:
信息与通信工程
出版日期:
2001-07-20

文章信息/Info

Title:
Design of Lifting Scheme of Arbitrary Wavelets
作者:
李洪刚;  吴乐南
东南大学无线电工程系, 南京 210096
Author(s):
Li Honggang;  Wu Lenan
Department of Radio Engineering, Southeast University, Nanjing 210096, China)
关键词:
双正交小波;  提升格式;  第2代小波;  完全可恢复
Keywords:
biorthogonal wavelet;  lifting scheme;  second generation wavelet;  perfect reconstruction
分类号:
TN911.6
DOI:
10.3969/j.issn.1001-0505.2001.04.006
摘要:
在Sweldens等人提出的提升格式(lifting scheme)基础上,利用小波消失矩与其对应的滤波器在z=1处零点阶数的关系,提出了一种新颖的提升系数设计方法.它克服了过去的提升格式设计方法只能设计基于Lazy Wavelet的插值小波的缺陷,通过求解一组简单的线性方程组来设计基于任意双正交小波的提升系数,从而实现了根据具体要求动态地、迭代地设计小波的目的.为了便于算法的工程实现,本文根据最佳提升格式的惟一性,提出并论证了一种最佳提升系数的迭代设计算法.此外,上述2种算法均可以用于设计对称和非对称的小波.
Abstract:
Adopting the lifting scheme, introduced by Sweldens, a novel algorithm is proposed to design the lifting scheme of an arbitrary wavelet. Based on the relationship between the vanishing moments of wavelets and the multiplicity of zero at z=1 of corresponding filter, this algorithm only needs to solve simple linear equations. It overcomes the shortcoming in former algorithm, which can only be used to design the lifting scheme for interpolating wavelets starting from lazy wavelet. Therefore, the wavelets for special purpose can be constructed by iteration. According to the uniqueness of the shortest lifting scheme, an iterative algorithm to simplify its design is presented. These algorithms can be used to design both symmetrical and asymmetrical wavelets.

参考文献/References:

[1] Sweldens W.The lifting scheme:a new philosophy in biorthogonal wavelet constructions.In:Laine A F,Unser M,eds.Wavelet Applications in Signal and Image Processing III Proc SPIE 2569,1995.68～79
[2] Sweldens W.The lifting scheme:a custom-design construction of biorthogonal wavelets.Appl Comput Harmon Anal,1996,3(2):186～200
[3] Sweldens W.The lifting scheme:a construction of second generation wavelets.SIAM J Math Anal,1997,29(2):511～546
[4] Mallat S G.Multiresolution approximation and wavelet orthogonal bases of L2(R).Trans Amer Math Soc,1989,315(1):69～87
[5] Daubechies I,Sweldens W.Factoring wavelet transforms into lifting steps.J Fourier Anal App,1998,4(3):245～267
[6] Vetterli M,Herley C.Wavelets and filter banks:theory and design.IEEE Trans on Acoust Speech Signal Processing,1992,40(9):2207～2232

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备注/Memo

备注/Memo:
作者简介:李洪刚,男,1974年生,博士研究生.
基金项目:国家自然科学基金资助项目(60002008).
更新日期/Last Update: 2001-07-20