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Homogeneous wavelets and framelets with the refinable structure

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Abstract

Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.

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Acknowledgements

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) (Grant No. RGP 228051).

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

    Bin Han

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  1. Bin Han
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Correspondence to Bin Han.

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Dedicated to the memory of Professor CHENG MinDe

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Han, B. Homogeneous wavelets and framelets with the refinable structure. Sci. China Math. 60, 2173–2198 (2017). https://doi.org/10.1007/s11425-017-9145-4

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