Asymptotic properties of wavelet thresholding risk estimate in the model of data with correlated noise

Wavelet thresholding techniques of denoising are widely used in signal and image processing. These methods are easily implemented through fast algorithms; so, they are very appealing in practical situations. Besides, they adapt to function classes with different amounts of smoothness in different locations more effectively than the usual linear methods. Wavelet thresholding risk analysis is an important practical task because it allows determining the quality of techniques themselves and equipment which is being used. In the present paper, asymptotical properties of mean-square risk estimate of wavelet thresholding techniques have been studied in the model of data with correlated noise. The conditions under which the unbiased risk estimate is consistent and asymptotically normal are given. These results allow constructing asymptotical confidence intervals for wavelet thresholding risk, using only the observed data.