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