Nonlinear approximation with redundant dictionaries

Lasse Borup 1 Morten Nielsen 1 Rémi Gribonval 2
2 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non- oversampled wavelet bi-frames we can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion.
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Communication dans un congrès
Acoustics, Speech and Signal Processing, 2005. ICASSP 2005. IEEE International Conference on, Mar 2005, Philadeplhia, PA, United States. IEEE, 4, pp.IV/261 -- IV/264, 2005, 〈10.1109/ICASSP.2005.1415995〉
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Dernière modification le : mercredi 11 avril 2018 - 01:54:24
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Lasse Borup, Morten Nielsen, Rémi Gribonval. Nonlinear approximation with redundant dictionaries. Acoustics, Speech and Signal Processing, 2005. ICASSP 2005. IEEE International Conference on, Mar 2005, Philadeplhia, PA, United States. IEEE, 4, pp.IV/261 -- IV/264, 2005, 〈10.1109/ICASSP.2005.1415995〉. 〈inria-00564480〉

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