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Lifting scheme of symmetric tight wavelets frames

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Abstract

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.

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Authors and Affiliations

  1. Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    BoJin Zhuang, WeiTao Yuan & LiZhong Peng

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  1. BoJin Zhuang
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  2. WeiTao Yuan
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  3. LiZhong Peng
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Correspondence to LiZhong Peng.

Additional information

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

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Zhuang, B., Yuan, W. & Peng, L. Lifting scheme of symmetric tight wavelets frames. Sci. China Ser. F-Inf. Sci. 51, 1117–1124 (2008). https://doi.org/10.1007/s11432-008-0090-5

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  • DOI: https://doi.org/10.1007/s11432-008-0090-5

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