Bayesian wavelet-shrinkage methods are defined through a prior distribution on the space of wavelet coefficients after a Discrete Wavelet Transformation (DWT) has been applied to the data. Posterior summaries of the wavelet coefficients establish a Bayes shrinkage rule. After the Bayes shrinkage is performed, an Inverse DWT can be used to recover the signal that generated the observations. This article reviews some of the main approaches for Bayesian wavelet shrinkage that span both smooth and multivariate types of shrinkage. WIREs Comp Stat 2010 2 668–672 DOI: 10.1002/wics.127
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