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
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摘要: 论文基于矩阵变换和变换矩阵级联分解的思想,提出一种新的多相矩阵表示形式,对离散子波提升算法的机理进行了完整的理论分析,对子波提升算法和子波变换双通道滤波实现的理想重构条件进行了等价性证明,并利用互补滤波器组的对偶性提出一利新的子波提升分解算法的级联矩阵分解形式,使提升算法的机理解释更加完善,然后基于文中提出的矩阵级联分解形式,以(2,2)双正交子波变换为例说明了离散子波提升分解算法的实现,并就算法的可逆性、运算量和原位实现等问题进行了简要讨论。
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关键词:
- 子波变换; 多相表示; 提升
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. -
C.K. Chui, An Introduction to Wavelets, San Diego, Academic Press, 1992, Chapter 1. ［2］I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Series in Appl. Math 61,SIAM, 1992.[2]W. Sweldens, The lifting scheme: A custom-design construction of biorthogonal wavelets, J. Appl.Comp. Harm. Anal, 1996, 3(2), 186-200.[3]I. Daubechies, W. Sweldens, Factoring wavelet transforms into lifting steps, Tech. Rep, Bell Lab,1997. ［5］W. Sweldens, The lifting scheme: A new philosophy in biorthorgonal wavelet constructions, Tech.Rep., University of South Carolina, 1995. ［6］赵松年,熊小芸,子波变换与子波分析,北京,电子工业出版社,1997,第五章.[4]彭玉华,小波变换与工程应用,北京,科学出版社,2000,第四、六章.[5]W. Sweldens, B. Jawerth, An overview of wavelet based multiresolution analysis, Tech. Rep.,University of South Carolina, 1995. ［9］M. Vetterli, C. Herley, Wavelets and filter banks: Theory and design, IEEE Trans. on ASSP,1992, 40(9), 2207-2232 .[6]W. Sweldens, P. Schroder, Building your own wavelets at home, Tech. Rep., University of South Carolina, 1995 . -
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