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The lifting factorization of wavelet bi-frames with arbitrary generators

Author

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  • Shi, Yan
  • Yang, Xiaoyuan

Abstract

In this paper, we present the lifting scheme of wavelet bi-frames with arbitrary generators. The Euclidean algorithm for arbitrary n Laurent polynomials and the factorization theorem of polyphase matrices of wavelet bi-frames are proposed. We prove that any wavelet bi-frame with arbitrary generators can be factorized into a finite number of alternating lifting and dual lifting steps. Based on this concept, we present a new idea for constructing bi-frames by lifting. For the construction, by using generalized Bernstein basis functions, we realize a lifting scheme of wavelet bi-frames with arbitrary prediction and update filters and establish explicit formulas for wavelet bi-frame transforms. By combining the different designed filters for the prediction and update steps, we can devise practically unlimited forms of wavelet bi-frames. Furthermore, we present an algorithm for increasing the number of vanishing moments of wavelet bi-frames to arbitrary order by the presented lifting scheme, which adopts an iterative algorithm. Several examples are constructed to illustrate the conclusion.

Suggested Citation

  • Shi, Yan & Yang, Xiaoyuan, 2011. "The lifting factorization of wavelet bi-frames with arbitrary generators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 570-589.
    • Handle: RePEc:eee:matcom:v:82:y:2011:i:4:p:570-589
    DOI: 10.1016/j.matcom.2011.10.001
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