On the Statistics of Best Bases Criteria
Wavelet packets are a useful extension of wavelets providing an adaptive time- scale analysis. In using noisy observations of a signal of interest, the criteria for best bases representation are random variables. The search may thus be very sensitive to noise. In this paper, we characterize the asymptotic statistics of the criteria to gain insight which can in turn, be used to improve on the performance of the analysis. By way of a well-known information-theoretic principle, namely the Minimum Description Length, we provide an alternative approach to Minimax methods for deriving various attributes of nonlinear wavelet packet estimates.
KeywordsEntropy Covariance Radar Shrinkage Pyramid
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- [CH1]Cambanis, S., Houdré., C.: On the continuous wavelet transform of second order random processes, preprint (1993)Google Scholar
- [DJ1]Donoho, D. L., Johnstone, I. M.: Ideal spatial adaptation by wavelet shrinkage. Bio-metrika (to appear)Google Scholar
- [DJ2]Donoho, D. L., Johnstone, I. M.: Ideal denoising in an orthogonal basis chosen from a library of bases. Note CRAS Paris (to appear)Google Scholar
- [KPW]Krim, H., Pesquet, J.-C., Willsky, A. S.: Robust multiscale representation of processes and optimal signal reconstruction. Proceedings of IEEE Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, USA. (1994) 1–4Google Scholar
- [LP+]Lumeau, B., Pesquet, J.-C., Bercher, J.-F., Louveau, L.: Optimisation of bias-variance tradeoff in non parametric spectral analysis by decomposition into wavelet packets. Progress in wavelet analysis and applications, Editions Frontieres. (1993) 285–290Google Scholar
- [PC1]Pesquet, J.-C., Combettes, P. L.: Wavelet synthesis by alternating projections, submitted to IEEE Trans, on S.P.Google Scholar
- [Sa1]Saito, N.: Local feature extraction and its applications using a library of bases. PhD thesis, Yale University (1994)Google Scholar
- [Wi1]Wickerhauser, M. V.: INRIA lectures on wavelet packet algorithms. Ondelettes et paquets d’ondelettes, Roquencourt, France. (1991) 31–99Google Scholar