Compactly supported Parseval framelets with symmetry associated to Ed(2)(Z) matrices
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http://hdl.handle.net/10045/72667
Title: | Compactly supported Parseval framelets with symmetry associated to Ed(2)(Z) matrices |
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Authors: | San Antolín Gil, Ángel | Zalik, Richard A. |
Research Group/s: | Curvas Alpha-Densas. Análisis y Geometría Local |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Dilation matrix | Fourier transform | Oblique Extension Principle | Refinable function | Tight framelet |
Knowledge Area: | Análisis Matemático |
Issue Date: | 15-May-2018 |
Publisher: | Elsevier |
Citation: | Applied Mathematics and Computation. 2018, 325: 179-190. doi:10.1016/j.amc.2017.12.008 |
Abstract: | Let d ≥1. For any A ∈ Z d×d such that | det A | = 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 dila- tions. |
Sponsor: | The first author was partially supported by MEC/ MICINN grant # MTM2011-27998 (Spain) and by Generalitat Valenciana grant GV/2015/035. |
URI: | http://hdl.handle.net/10045/72667 |
ISSN: | 0096-3003 (Print) | 1873-5649 (Online) |
DOI: | 10.1016/j.amc.2017.12.008 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2017 Elsevier Inc. |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1016/j.amc.2017.12.008 |
Appears in Collections: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
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2018_San-Antolin_Zalik_ApplMathComp_final.pdf | Versión final (acceso restringido) | 459,63 kB | Adobe PDF | Open Request a copy |
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