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From frame-like wavelets to wavelet frames keeping approximation properties and symmetry

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  • Krivoshein, A.V.

Abstract

For a given symmetric refinable mask obeying the sum rule of order n, an explicit method is suggested for the construction of mutually symmetric almost frame-like wavelet system providing approximation order n. A transformation based on the lifting scheme is described that allows to improve almost frame-like wavelets up to dual wavelet frames and preserve other properties. A direct method for the construction of dual wavelet frames providing approximation order n and mutual symmetry properties is also discussed. For an abelian symmetry group H, a technique providing the H-symmetry property for each wavelet function is given for the above three methods.

Suggested Citation

  • Krivoshein, A.V., 2019. "From frame-like wavelets to wavelet frames keeping approximation properties and symmetry," Applied Mathematics and Computation, Elsevier, vol. 344, pages 204-218.
    • Handle: RePEc:eee:apmaco:v:344-345:y:2019:i::p:204-218
    DOI: 10.1016/j.amc.2018.10.004
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    References listed on IDEAS

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    1. San Antolín, A. & Zalik, R.A., 2018. "Compactly supported Parseval framelets with symmetry associated to Ed(2)(Z) matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 179-190.
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