Regularization parameter estimation for iterative image restoration in a weighted Hilbert space

A method for obtaining optimal estimates of the regularization parameter for iterative image restoration in a weighted Hilbert space is presented. The method is a modified form of the cross-validation technique. It requires no a priori knowledge of either the amount of noise or its distribution. Results are presented which demonstrate the effectiveness of the technique for different weighting matrices. Cross-validation is based on the concept of prediction error. For a fixed value of the regularization parameter, a restored image is determined using all the values from the observed image but one, and the restored image is reblurred in order to predict the blurred and noisy observation that was left out of the restoration. A different restored image is formed for each observation. The regularization parameter which minimizes the mean-square prediction error over all the observations is chosen as the estimated optimal parameter. A simplified version of cross-validation that is computationally manageable is presented