In the blind inversion of digital images, the blur or point spread function (PSF) has to be estimated from the observed image. This general problem can be divided into several levels of difficulty depending mainly on the properties of the blur. Here, the first level of difficulty is addressed and space-invariant analytic PSF are considered. In this case, the generalized cross-validation criterion (GCV), using an AR modeling of the original image, is well known to be a robust estimator. This study use a weak constraint of smoothness on the original image and applies the GCV criterion in a myopic scheme. The problem is to choose which PSF in a set, if any, has blurred the observed image. The minimum of the GCV criterion for each candidate PSF yields a vector of estimated parameters. The actual PSF and its parameters should correspond to the lowest value of the GCV criterion. If the observed image is not blurred, the GCV criterion should attain its lowest value when the candidate PSF is reduce to a single pixel. Simulation results show that this approach yields good results on various kind of images with low signal-to-noise ratio and can discriminate between blurred and unblurred images. A near optimal value of the regularization parameter is estimated at the same time. If the effective PSF does not belong to the set of candidates, the optimization of the regularization operator, as a mean to compensate for the distance between the two PSF, is investigated.