A method that applies Bayes theory on using wavelet packets to the problem of estimating an unknown signal currupted by noise has been proposed in the previous research. Despite its Bayesian approach, it is not completely Bayes optimal when the loss function is something useful in estimating the signal like the squared error loss. In this paper, we deal with the Bayesian optimized estimator of the squared error loss. When applying Bayesian optimization, it involves wavelet packet basis weighting which requires high computational complexity. We propose an algorithm with takes account the binary tree structure of the wavelet packet bases which computes the Bayes optimal estimator in O(N log N) We will confirm the Bayesian optimality through some experiments.
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