Implementation and practical comparison of two estimators of the smoothing parameter in linear image restoration

The restoration of a 2-D discrete object from its degraded image observed on a finite lattice is considered. The solution, interpreted as a Bayesian estimate of the original object modeled as a Gaussian random field, can be computed using Kalman filtering techniques. The problem of choosing the value of the smoothing parameter is addressed. Two methods for this are discussed: generalized cross validation (GXV) and maximum likelihood (ML). Particular attention is paid to implementation problems. The use of Chandrasehar equations allows an exact computation of a GXV criterion with a modest increase in the computational cost with respect to image restoration itself. In th Gaussian case, the ML gives better results than GXV, but GXV is generally far more robust with respect to modeling errors. The prior covariance matrix is assumed to be known