Reference : A note about non stationary multiresolution analysis
Scientific congresses and symposiums : Unpublished conference/Abstract
Physical, chemical, mathematical & earth Sciences : Mathematics
A note about non stationary multiresolution analysis
Simons, Laurent mailto [Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
International Conference on Applied Harmonic Analysis and Multiscale Computing
du 25 juillet 2011 au 31 juillet 2011
Elena Braverman, Bin Han, Rong-Qing Jia, Yau Shu Wong, Ozgur Yilmaz
[en] Wavelets ; Multiresolution Analysis ; Orthonormal Basis
[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).
Researchers ; Professionals

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