Best Basis Representations with Prior Statistical Models

Wavelet packets and local trigonometric bases provide an efficient framework and fast algorithms to obtain a “best representation” of a deterministic signal. Applying these deterministic search techniques to stochastic signals may, however, lead to statistically unreliable results. In this chapter, we revisit this problem and introduce prior models on the underlying signal in noise. We propose several techniques to derive the prior parameters and develop a Bayesian-based approach to the best basis problem. As illustrated by applications to signal denoising, this leads to reduced estimation errors while preserving the classical tree search algorithm.

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