The authors wish to warn the readers that while the analytical justification of the RGCV method appears to be valid, and several examples (including real HST data) demonstrate its ability, there have been cases in simulated data sets where the RGCV criterion failed to perform as a stopping rule. In other words, for some images, the RGCV criterion continues to decrease indefinitely, even after the noise amplification has completely destroyed the restoration. Other authors have noticed similar problems with other GCV based measurements (Thompson et al. 1989).
The authors have noticed this problem in several scenarios, and have tried to qualify the situations where it may occur. The factors that the authors have witnessed as contributing to the problem are a complex point-spread functions (PSF) and a low ratio of data points to PSF points.