Cross-validation and other criteria for estimating the regularizing parameter

The application of regularization to ill-conditioned problems necessitates the choice of a regularizing parameter which trades fidelity to the data for smoothness of the solution. Methods based on the properties of the residuals and on the generalized cross-validation have been proposed for estimating the regularizing parameter. Alternative methods to compute the regularizing parameter are proposed. The resulting values of the regularizing parameter are compared with the values obtained from the above-mentioned methods. Furthermore, it is shown that under certain conditions all the above-mentioned methods result in the same value for the regularizing parameter. Experimental results are presented which verify theoretical results