Smoothing Parameter Selection in Image Restoration

Abstract

We consider the problem of the automatic selection of the smoothing parameter in image restoration using the method of regularisation. We consider two new smoothing parameter selectors based on the estimation cross-validation function and compare their performance with some others proposed in the literature and also with some optimal methods. These selectors are assessed with regard to their ability to restore two-dimensional images which have been subjected to different degrees of blur and noise. For most blur-noise combinations, the new methods produced satisfactory restorations except when the blur and noise were both high. The existing methods produced seriously undersmoothed restorations in the high/medium blur and low noise combinations. Although the simulated distributions of the estimated smoothing parameter often did not overlap with the optimal distribution, nevertheless, they were often within the window of acceptable values. The restorations obtained by minimising the estimation and prediction errors, respectively, were of a similar quality which suggests that the choice of error criterion is not a practical issue for the restoration of large degraded images.