Analysis and research on a novel method of constructing wavelets: lifting factorization
离散子波提升算法研究及其性能分析

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 ard computational complexity is also analyzed in brief.