Biorthogonal bases of compactly supported wavelets

Journal Article (Journal Article)

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual Riesz bases of compactly supported wavelets. We give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions, and we present a sufficient conditions for the decay of their Fourier transforms. We study the regularity of these biorthogonal bases. We provide several families of examples, all symmetric (corresponding to “linear phase” filters). In particular we can construct symmetric biorthogonal wavelet bases with arbitraily high preassigned regularity; we also show how to construct symmetric biorthogonal wavelet bases “close” to a (nonsymmetric) orthonormal basis. Copyright © 1992 Wiley Periodicals, Inc., A Wiley Company

Full Text

Duke Authors

Cited Authors

  • Cohen, A; Daubechies, I; Feauveau, J

Published Date

  • January 1, 1992

Published In

Volume / Issue

  • 45 / 5

Start / End Page

  • 485 - 560

Electronic International Standard Serial Number (EISSN)

  • 1097-0312

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/cpa.3160450502

Citation Source

  • Scopus