Pairs of dual wavelet frames from any two refinable functions
Journal Article (Journal Article)
Starting from any two compactly supported refutable functions in L 2 (R) with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2 (R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible. In particular, when we consider symmetric refinable functions, the constructed dual wavelets are also symmetric or antisymmetric. As a consequence, for any compactly supported refinable function φ in L2 (R), it is possible to construct, explicitly and easily, wavelets that are finite linear combinations of translates φ(d -k), and that generate a wavelet frame with an arbitrarily preassigned number of vanishing moments. We illustrate the general theory by examples of such pairs of dual wavelet frames derived from B-spline functions.
Full Text
Duke Authors
Cited Authors
- Daubechies, I; Han, B
Published Date
- January 1, 2004
Published In
Volume / Issue
- 20 / 3
Start / End Page
- 325 - 352
International Standard Serial Number (ISSN)
- 0176-4276
Digital Object Identifier (DOI)
- 10.1007/s00365-004-0567-4
Citation Source
- Scopus