Unbiased risk estimate of stabilized hard thresholding in the model with a long-range dependence

De-noising methods for processing signals and images, based on the thresholding of wavelet decomposition coefficients, have become popular due to their simplicity, speed, and the ability to adapt to signal functions that have a different degree of regularity at different locations. An analysis of inaccuracies of these methods is an important practical task, since it makes it possible to evaluate the quality of both the methods themselves and the equipment used for processing. The present author considers the recently proposed stabilized hard thresholding method which avoids the main disadvantages of the popular soft and hard thresholding techniques. The statistical properties of this method are studied. In the model with an additive Gaussian noise, the author analyzes the unbiased risk estimate. Assuming that the noise coefficients have a long-range dependence, the author formulates the conditions under which strong consistency and asymptotic normality of the unbiased risk estimate take place. The results obtained make it possible to construct asymptotic confidence intervals for the threshold processing errors using only observable data.