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Biorthogonal bases of compactly supported wavelets
Abstract
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.
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Cites
The wavelet transform, time-frequency localization and signal analysis
Daubechies, I. (1990) · IEEE Transactions on Information Theory · doi:10.1109/18.57199 · Cited by 6,483
Self-citationThe Laplacian pyramid as a compact image code
Burt, P., & Adelson, E. (1983) · IEEE Transactions on Communications · doi:10.1109/tcom.1983.1095851 · Cited by 6,077
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Multiresolution analysis for surfaces of arbitrary topological type
Lounsbery, M., DeRose, T. D., & Warren, J. (1997) · ACM Transactions on Graphics · doi:10.1145/237748.237750 · Cited by 760
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Donoho, D. L. (1995) · Applied and Computational Harmonic Analysis · doi:10.1006/acha.1995.1008 · Cited by 608
Metadata
- Authors
- Cohen, A., Daubechies, I., & Feauveau, J. ‐.
- Venue
- Communications on Pure and Applied Mathematics
- Publisher
- Wiley
- Published
- 1992-06
- Volume
- 45
- Issue
- 5
- Pages
- 485-560
- ISSN
- 0010-3640 (ISSN-L)
- 1097-0312
- OpenAlex
- W3005363104
- Cited by
- 2,667
- References
- 2
- FWCI
- 81.84
- Type
- journal article
- Language
- en
- Open access
- closed
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- Cohen, A., Daubechies, I., & Feauveau, J. ‐. (1992). Biorthogonal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics. https://doi.org/10.1002/cpa.3160450502
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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