A Bayesian Decision Theoretic Approach to Wavelet Thresholding

Thresholding rules recently became of considerable interest when Donoho and John-stone applied them in the wavelet shrinkage context. Analytically simple, such rules are very eecient in data denoising and data compression problems. In this paper we nd 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 a decision theoretic hard thresholding rule can achieve smaller mean squared error than some standard wavelet thresholding methods, if the prior information on the level noise is precise.