Smoothing data is an important problem arising in many applications, ranging from analysis of data to sound or image processing. For this reason it has been widely studied in the literature and several methods have been proposed to find a solution in different frameworks (eg, approximation theory, inverse problems, statistics). The most important case is when noise variance is unknown and objective methods are required, that is no user intervention is to be made in deciding the amount of smoothing. In this respect one of the most important contributions is due to Wahba (see [16] for an excellent summarization of the results), whose method relies on the spline approximation and on the GCV criterion for choosing the amount of smoothing objectively. Recently wavelets have been used for the problem of smoothing data, due to their capability of concentrating signal information in a few coefficients. Methods have been developed based on thresholding (see papers by Donoho and Johnstone [8][9]) and regularization [1][5] of the wavelet coefficients. The choice of the amount of smoothing is made in an objective way by a statistical criterion [8] and by GCV [17] in the case of thresholding; again by the statistical criterion [5] and GCV [1] in the case of regularization.Despite of their different origin, thresholding and regularization methods have many common issues and indeed in [4] it has been proved that any thresholding method can be considered as a solution of a suitable regularization method. In the present paper we intend to generalize the wavelet regularization method developed by the authors (in a formulation which takes account of correlated …