Analysis of the unbiased mean-square risk estimate of the block thresholding method

Signal and image processing methods based on wavelet decomposition and thresholding have become very popular in solving problems of compression and noise suppression. This is due to their ability to adapt to local features of functions, high speed of processing algorithms and optimality of estimates obtained. In this paper, a block thresholding method is considered, in which expansion coefficients are processed in groups, which makes it possible to take into account information about neighboring coefficients. In the model with additive noise, an unbiased estimate of the mean-square risk is analyzed and it is shown that, under certain conditions of regularity, this estimate is strongly consistent and asymptotically normal. These properties allow using the risk estimate as a quality criterion for the method and constructing asymptotic confidence intervals for the theoretical mean-square risk.