Bayesian approach to best basis selection

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. 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.