Applying generalised cross-validation to image restoration

Generalised cross-validation (GCV) is a method often used to choose the order of a model or the degree of smoothing for fitting a function to noisy values. It can also help in the design of a restoration filter for an image degraded by known uniform blur and the addition of an unknown amount of uncorrelated noise. Inefficiencies in its use can be removed by processing in the Fourier domain and reducing constraints on the filter to a carefully-chosen few. The analysis gives a useful insight into how GCV works and how to improve it. Examples of its application to image restoration are given.<>