  We consider the estimation of the regularization parameter for the
simultaneous deblurring of multiple noisy images via Tikhonov regularization.
We approach the problem in three ways. We first reduce the problem to a
single-image deblurring for which the regularization parameter can be estimated
through a classic generalized cross-validation (GCV) method. A modification of
this function is used for correcting the undersmoothing typical of the original
technique. With a second method, we minimize an average least-squares fit to
the images and define a new GCV function. In the last approach, we use the
classical $GCV$ on a single higher-dimensional image obtained by concatanating
all the images into a single vector. With a reliable estimator of the
regularization parameter, one can fully exploit the excellent computational
characteristics typical of direct deblurring methods, which, especially for
large images, makes them competitive with the more flexible but much slower
iterative algorithms. The performance of the techniques is analyzed through
numerical experiments. We find that under the independent homoscedastic and
Gaussian assumptions made on the noise, the three approaches provide almost
identical results with the first single image providing the practical advantage
that no new software is required and the same image can be used with other
deblurring algorithms.
