The problem of constructing an estimate of a signal function from noisy observations, assuming that this function is uniformly Lipschitz regular, is considered. The thresholding of empirical wavelet coefficients is used to reduce the noise. As a rule, it is assumed that the noise distribution is Gaussian and the optimal parameters of thresholding are known for various classes of signal functions. In this paper a model of additive noise whose distribution belongs to a fairly wide class, is considered. The mean-square risk estimate of thresholding is analyzed. It is shown that under certain conditions, this estimate is strongly consistent and asymptotically normal.
Moscow University Computational Mathematics and Cybernetics – Springer Journals
Published: May 30, 2018
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