Some Smooth Compactly Supported Tight Wavelet Frames with Vanishing Moments

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Título: Some Smooth Compactly Supported Tight Wavelet Frames with Vanishing Moments
Autor/es: San Antolín Gil, Ángel | Zalik, Richard A.
Grupo/s de investigación o GITE: Curvas Alpha-Densas. Análisis y Geometría Local
Centro, Departamento o Servicio: Universidad de Alicante. Departamento de Matemáticas
Palabras clave: Dilation matrix | Fourier transform | Refinable function | Tight framelet | Unitary Extension Principle
Área/s de conocimiento: Análisis Matemático
Fecha de publicación: ago-2016
Editor: Birkhäuser
Cita bibliográfica: Journal of Fourier Analysis and Applications. 2016, 22(4): 887-909. doi:10.1007/s00041-015-9442-x
Resumen: Let A∈Rd×d, d≥1 be a dilation matrix with integer entries and |detA|=2. We construct several families of compactly supported Parseval framelets associated to A having any desired number of vanishing moments. The first family has a single generator and its construction is based on refinable functions associated to Daubechies low pass filters and a theorem of Bownik. For the construction of the second family we adapt methods employed by Chui and He and Petukhov for dyadic dilations to any dilation matrix A. The third family of Parseval framelets has the additional property that we can find members of that family having any desired degree of regularity. The number of generators is 2d+d and its construction involves some compactly supported refinable functions, the Oblique Extension Principle and a slight generalization of a theorem of Lai and Stöckler. For the particular case d=2 and based on the previous construction, we present two families of compactly supported Parseval framelets with any desired number of vanishing moments and degree of regularity. None of these framelet families have been obtained by means of tensor products of lower-dimensional functions. One of the families has only two generators, whereas the other family has only three generators. Some of the generators associated with these constructions are even and therefore symmetric. All have even absolute values.
Patrocinador/es: The first author was partially supported by MEC/MICINN Grant #MTM2011-27998 (Spain).
URI: http://hdl.handle.net/10045/58074
ISSN: 1069-5869 (Print) | 1531-5851 (Online)
DOI: 10.1007/s00041-015-9442-x
Idioma: eng
Tipo: info:eu-repo/semantics/article
Derechos: © Springer Science+Business Media New York 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/s00041-015-9442-x
Revisión científica: si
Versión del editor: http://dx.doi.org/10.1007/s00041-015-9442-x
Aparece en las colecciones:INV - CADAGL - Artículos de Revistas

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