Lifting scheme of symmetric tight wavelets frames  

作　　者：ZHUANG BoJin YUAN WeiTao PENG LiZhong 

机构地区：[1]Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University,Beijing 100871, China

出　　处：《Science in China(Series F)》2008年第8期1117-1124,共8页中国科学（F辑英文版）

基　　金：the National Natural Science Foundation of China(Grant No.10471002);the Major State Basic Research Development Program of China(Grant No.20060001010)

摘　　要：This paper proposes a method to realize the lifting scheme of tight frame wavelet filters. As for 4-channel tight frame wavelet filter, the tight frame transforms＇ matrix is 2×4, but the lifting scheme transforms＇ matrix must be 4×4. And in the case of 3-channel tight frame wavelet filter, the transforms＇ matrix is 2×3, but the lifting scheme transforms＇ matrix must be 3×3. In order to solve this problem, we introduce two concepts： transferred polyphase matrix for 4-channel filters and transferred unitary matrix for 3-channel filters. The transferred polyphase matrix is symmetric/antisymmetric. Thus, we use this advantage to realize the lifting scheme.This paper proposes a method to realize the lifting scheme of tight frame wavelet filters. As for 4-channel tight frame wavelet filter, the tight frame transforms＇ matrix is 2×4, but the lifting scheme transforms＇ matrix must be 4×4. And in the case of 3-channel tight frame wavelet filter, the transforms＇ matrix is 2×3, but the lifting scheme transforms＇ matrix must be 3×3. In order to solve this problem, we introduce two concepts： transferred polyphase matrix for 4-channel filters and transferred unitary matrix for 3-channel filters. The transferred polyphase matrix is symmetric/antisymmetric. Thus, we use this advantage to realize the lifting scheme.

关 键 词：lifting scheme tight frame wavelet transform 

分 类 号：O17[理学—数学]