The lifting factorization of wavelet bi-frames with arbitrary generators

Yan Shi and Xiaoyuan Yang

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 82, issue 4, 570-589

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.

Keywords: Wavelet bi-frames; The lifting scheme; Generalized Bernstein basis; Symmetric framelets; Vanishing moments (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2011:i:4:p:570-589

DOI: 10.1016/j.matcom.2011.10.001

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