Compactly supported Parseval framelets with symmetry associated to Ed(2)(Z) matrices

A. San Antolín and R.A. Zalik

Applied Mathematics and Computation, 2018, vol. 325, issue C, 179-190

Abstract: Let d ≥ 1. For any A∈Zd×d such that |detA|=2, we construct two families of Parseval wavelet frames with two generators. These generators have compact support, any desired number of vanishing moments, and any given degree of regularity. The first family is real valued while the second family is complex valued. To construct these families we use Daubechies low pass filters to obtain refinable functions, and adapt methods employed by Chui and He and Petukhov for dyadic dilations to this more general case. We also construct several families of Parseval wavelet frames with three generators having various symmetry properties. Our constructions are based on the same refinable functions and on techniques developed by Han and Mo and by Dong and Shen for the univariate case with dyadic dilations.

Keywords: Dilation matrix; Fourier transform; Oblique Extension Principle; Refinable function; Tight framelet (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:325:y:2018:i:c:p:179-190

DOI: 10.1016/j.amc.2017.12.008

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