Nonlinear approximation with bi-framelets

Lasse Borup 1 Rémi Gribonval 2 Morten Nielsen 1
2 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : We study the approximation in Lebesgue spaces of wave- let bi-frame systems given by translations and dilations of a finite set of generators. A complete characterization of the approximation spaces associated with best m-term approximation of wavelet bi-framelet systems is given. The characterization depends, in general, on the number of vanishing moments of the generators. However, in some cases it is possible to get rid of this restriction, but at the price of replacing the canonical expansion by another linear expansion. This is done by expanding a suitable wavelet in the wavelet bi-frame system.
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Chui, Charles K. and Neamtu, M. and Schumaker, L.L. Approximation Theory XI, 2004, Gatlinburg, United States. Nashboro Press, Brentwood, TN, pp.101-112, 2005, Approximation theory XI: Gatlinburg 2004
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Lasse Borup, Rémi Gribonval, Morten Nielsen. Nonlinear approximation with bi-framelets. Chui, Charles K. and Neamtu, M. and Schumaker, L.L. Approximation Theory XI, 2004, Gatlinburg, United States. Nashboro Press, Brentwood, TN, pp.101-112, 2005, Approximation theory XI: Gatlinburg 2004. 〈inria-00564761〉

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