Canonical angles, subspace partitioning, and hyrbrid wavelet packets

Robert A. Hedges

doi:10.1117/12.408643

4 December 2000 Canonical angles, subspace partitioning, and hyrbrid wavelet packets

Robert A. Hedges

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408643
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

In previous work, hybrid wavelet packets were introduced as a generalization of wavelet packets in which the choice of quadrature mirror filter (QMF) is selected adaptively within the wavelet packet analysis. This was motivated by the observation that for certain classes of signals, the choice of appropriate QMF is not only signal dependent, but may be scale dependent as well. Best Basis selection was generalized to provide a means of optimizing the representation of a given signal. This method can be viewed as an adaptive partitioning of signal subspaces. In such a scheme it is important to determine a small number of QMFs which will provide some diversity in the partitioning of the subspaces. In the current work, canonical correlations and canonical angles are used to quantify the difference between subspaces spanned by two filter pairs. Preliminary results indicate the utility of this method as a data independent metric for filter comparison.

Citation Download Citation

Robert A. Hedges "Canonical angles, subspace partitioning, and hyrbrid wavelet packets", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408643

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KEYWORDS

Wavelets

Matrices

Digital filtering

Mirrors

Analytical research

Electronic filtering

Time-frequency analysis

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