Unpublished conference/Abstract (Scientific congresses and symposiums)
A note about non stationary multiresolution analysis
Simons, Laurent
2011International Conference on Applied Harmonic Analysis and Multiscale Computing
 

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Keywords :
Wavelets; Multiresolution Analysis; Orthonormal Basis
Abstract :
[en] An orthonormal basis of wavelets of $L^2(\mathbb{R})$ is an orthonormal basis of $L^2(\mathbb{R})$ of type \[ \psi_{j,k}=2^{j/2}\psi(2^j\cdot-k),\quad j,k\in\mathbb{Z}. \] A classical method to obtain such bases consists in constructing a multiresolution analysis. When the mother wavelet $\psi$ depends on the scale (i.e. the index $j$), a non stationary version of multiresolution analysis is then used. We generalize different characterizations of orthonormal bases of wavelets to the non stationary case (as main reference for the stationary case, we used results presented in "A First Course of Wavelets" of E. Hernandez and G. Weiss).
Disciplines :
Mathematics
Author, co-author :
Simons, Laurent ;  Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
A note about non stationary multiresolution analysis
Publication date :
28 July 2011
Event name :
International Conference on Applied Harmonic Analysis and Multiscale Computing
Event organizer :
Elena Braverman, Bin Han, Rong-Qing Jia, Yau Shu Wong, Ozgur Yilmaz
Event place :
Edmonton, Canada
Event date :
du 25 juillet 2011 au 31 juillet 2011
Audience :
International
Available on ORBi :
since 06 March 2012

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