From Frame-like Wavelets to Wavelet Frames keeping approximation properties and symmetry

2018/06/18 by Krivoshein, A. V.
#42C40 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1806.06810

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 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.

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