Universal thresholding in the models with non-Gaussian noise

A common assumption in nonparametric signal estimation is that the signal function belongs to a certain class. For example, it may be piecewise continuous or piecewise differentiable and have a compact support. These assumptions, as a rule, make it possible to economically represent a signal function in a specially selected basis in such a way that the useful signal is concentrated in a relatively small number of large expansion coefficients. Then, threshold processing removes noisy coefficients. Typically, the noise distribution is assumed to be Gaussian. This model has been well studied in the literature and optimal thresholding parameters have been calculated for different classes of signal functions. The paper considers the problem of constructing an estimate for the signal function from the observations containing additive noise, whose distribution belongs to quite a wide class. The authors calculate the values of universal thresholding parameters for which the mean-square risk is close to the minimum.