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Parametric Multi-Wavelets on a Hexagonal Sampling Lattice

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Abstract

An orthogonal basis is a dictionary of minimum size that can yield a sparse representation if designed to concentrate the signal energy over a set of few vectors. In this paper we construct such dictionary for a two dimensional hexagonal sampling lattice with the 1-parametric family of wavelets associated with Haar scaling function for scale factor 3. We also provide reconstruction formulae at various scales associated with these parametric multi wavelets.

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Authors and Affiliations

  1. Department of Engineering, Sciences and Humanities, Vishwakarma Institute of Technology, Pune, 411037, India

    Rupali Sadashiv Deshpande

  2. Savitribai Phule Pune University, Pune, 411007, India

    Rupali Sadashiv Deshpande

  3. Department of Mathematics, Savitribai Phule Pune University, Pune, 411007, India

    Hemant Dattatray Bhate

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  1. Hemant Dattatray Bhate
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  2. Rupali Sadashiv Deshpande
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Correspondence to Rupali Sadashiv Deshpande.

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Bhate, H.D., Deshpande, R.S. Parametric Multi-Wavelets on a Hexagonal Sampling Lattice. Results Math 73, 49 (2018). https://doi.org/10.1007/s00025-018-0804-y

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