Stabilized hard thresholding with an unknown noise level
In this paper we consider the method of stabilized hard thresholding for wavelet coefficients of the signal function. We study the effect of estimating the noise variance on the statistical properties of this method. The unbiased estimate of the mean-square risk is analyzed. It is shown that under certain conditions the distribution of this estimate converges to a normal law with the variance depending on the type of noise variance estimate.