Optimal biorthogonal wavelet bases for signal decomposition
- 1 June 1996
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 44 (6) , 1406-1417
- https://doi.org/10.1109/78.506607
Abstract
The selection of scaling functions for optimal signal representation by general multidimensional biorthogonal wavelet bases is investigated. Criterion for optimality is the minimization of the mean-square approximation error at each level of the decomposition. Conditions are given under which the approximation error of the decomposition approaches zero as the level increases. Given arbitrary synthesis filters, the optimal corresponding analysis filters are determined. Globally optimal families of filters are also found, and suboptimal linear and nonlinear-phase filters for the realization of the optimal scaling functions are explicitly determinedKeywords
This publication has 20 references indexed in Scilit:
- Hierarchical partition priority wavelet image compressionIEEE Transactions on Image Processing, 1996
- Optimal filters for the generation of multiresolution sequencesSignal Processing, 1994
- Invariant image classification using triple-correlation-based neural networksIEEE Transactions on Neural Networks, 1994
- Sampling procedures in function spaces and asymptotic equivalence with shannon's sampling theoryNumerical Functional Analysis and Optimization, 1994
- On the optimality of ideal filters for pyramid and wavelet signal approximationIEEE Transactions on Signal Processing, 1993
- Wavelets and recursive filter banksIEEE Transactions on Signal Processing, 1993
- Image coding using wavelet transformIEEE Transactions on Image Processing, 1992
- On the optimal choice of a wavelet for signal representationIEEE Transactions on Information Theory, 1992
- Wavelets and filter banks: theory and designIEEE Transactions on Signal Processing, 1992
- Polynomial spline signal approximations: filter design and asymptotic equivalence with Shannon's sampling theoremIEEE Transactions on Information Theory, 1992