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| Analysis and research on a novel method of constructing wavelets: lifting factorization |
| Wang Buhong; Wang Yongliang; Li Rongfeng |
| Key Research Lab Air Force Radar Academy Wuhan 430010 China |
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Abstract Analysis and research on a novel method of constructing wavelets-lifting factorization is addressed. To arrive at a generalized interpretation of lifting based on the linear transform and transform matrix factorization, a new polyphase matrix representation is proposed. Moreover the equivalence of the conditions for perfect reconstruction between dual-subband FIR filtering implementation and the lifting is also proved. Additionally based on the duality theorem of complementary filter pairs, a new lifting factorization representation is suggested which brings lifting factorization to completion. Finally, to clarify the theory a concrete example of lifting factorization corresponding to (2,2) biorthogonal wavelet transform is presented, and the algorithm performance including reversibility, in-place implementation and computational complexity is also analyzed in brief.
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Received: 08 May 2001
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2002, Vol. 24 
