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Article Dans Une Revue Journal of Fourier Analysis and Applications Année : 2000

An algebraic approach to discrete dilations. Application to discrete wavelet transforms

Résumé

We investigate the connections between continuous and discrete wavelet transforms on the basis of algebraic arguments. The discrete approach is formulated abstractly in terms of the action of a semidirect product $\cA\times\Gamma$ on $\ell^2(\Gamma)$, with $\Gamma$ a lattice and $\cA$ an abelian semigroup acting on $\Gamma$. We show that several such actions may be considered, and investigate those which may be written as deformations of the canonical one. The corresponding deformed dilations (the pseudodilations) turn out to be characterized by compatibility relations of a cohomological nature. The connection with multiresolution wavelet analysis is based on families of pseudodilations of a different type.
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Dates et versions

hal-00814185 , version 1 (16-04-2013)

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Jean-Pierre Antoine, Yebeni B. Kouagou, Dominique Lambert, Bruno Torrésani. An algebraic approach to discrete dilations. Application to discrete wavelet transforms. Journal of Fourier Analysis and Applications, 2000, 6 (2), pp.113-141. ⟨10.1007/BF02510656⟩. ⟨hal-00814185⟩
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