離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: 論文基于矩陣變換和變換矩陣級聯(lián)分解的思想,提出一種新的多相矩陣表示形式,對離散子波提升算法的機理進行了完整的理論分析,對子波提升算法和子波變換雙通道濾波實現(xiàn)的理想重構條件進行了等價性證明,并利用互補濾波器組的對偶性提出一利新的子波提升分解算法的級聯(lián)矩陣分解形式,使提升算法的機理解釋更加完善,然后基于文中提出的矩陣級聯(lián)分解形式,以(2,2)雙正交子波變換為例說明了離散子波提升分解算法的實現(xiàn),并就算法的可逆性、運算量和原位實現(xiàn)等問題進行了簡要討論。
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關鍵詞:
- 子波變換; 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］趙松年,熊小蕓,子波變換與子波分析,北京,電子工業(yè)出版社,1997,第五章.[4]彭玉華,小波變換與工程應用,北京,科學出版社,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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