Abstract

Wavelet packets and local trigonometric bases provide an efficient framework and fast algorithms to obtain a "best basis" or "best representation" of deterministic signals. Applying these deterministic techniques to stochastic processes may, however, lead to variable results. In this paper we revisit this problem and introduce a prior model on the underlying signal in noise and account for the contaminating noise model as well. We thus develop a Bayesian-based approach to the best basis problem, while preserving the classical tree search efficiency. 1. INTRODUCTION Research interest in a "best representation" of a signal x(t) when given a finite dictionary of possible bases, has greatly increased recently [1, 2, 3, 4]. In [1], it was established that wavelet packets and Malvar's wavelets (or local cosine bases) led to interesting choices of timefrequency dictionaries based on binary tree structures. These structures, in turn, allowed for a very efficient and fast dynamic programming ...

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