Nonlinear approximation with bi-framelets

Lasse Borup, Morten Nielsen, Rémi Gribonval

Research output: Contribution to book/anthology/report/conference proceedingBook chapterResearch

Abstract

We study the approximation in Lebesgue spaces of wavelet 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.
Original languageEnglish
Title of host publicationApproximation Theory XI : Gatlinburg 2004
EditorsCharles K. Chui, Marian Neamtu, Larry Schumaker
Number of pages12
Place of PublicationBrentwood, Tennessee
PublisherNashboro Press
Publication date2005
Pages93-104
ISBN (Print)00972848258
Publication statusPublished - 2005

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    Borup, L., Nielsen, M., & Gribonval, R. (2005). Nonlinear approximation with bi-framelets. In C. K. Chui, M. Neamtu, & L. Schumaker (Eds.), Approximation Theory XI: Gatlinburg 2004 (pp. 93-104). Nashboro Press.