A Bayesian decision theoretic approach to the choice of thresholding parameter

Thresholding rules recently became of considerable interest when Donoho and Johnstone applied them in the wavelet shrinkage context. Analytically simple, such rules are very efficient in data denoising and data compression problems. In this paper we find hard thresholding decision rules that minimize Bayes risk for broad classes of underlying models. Standard Donoho-Johnstone test signals are used to evaluate performance of such rules. We show that an optimal Bayesian decision theoretic (BDT) hard thresholding rule can achieve smaller mean squared error than some standard wavelet thresholding methods, if the prior information on the noise level is precise.