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.
KeywordsWavelet Packet Fractional Brownian Motion Code Length Minimum Description Length Wavelet Packet Decomposition
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