### 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 language | English |
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Title of host publication | Approximation Theory XI : Gatlinburg 2004 |

Editors | Charles K. Chui, Marian Neamtu, Larry Schumaker |

Number of pages | 12 |

Place of Publication | Brentwood, Tennessee |

Publisher | Nashboro Press |

Publication date | 2005 |

Pages | 93-104 |

ISBN (Print) | 00972848258 |

Publication status | Published - 2005 |

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## Cite this

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.