Simple shape parameter estimation from blurred observations for a generalized Gaussian MRF image prior used in MAP image restoration

The generalized Gaussian Markov random field (GGMRF) is used as an image prior model in MAP restoration of blurred and noise corrupted images. This model is adapted to the characteristics of the true image by jointly estimating the true image and the GGMRF shape parameter, p, from the corrupted observation. A simple estimator for p based on sample kurtosis is introduced. It is shown that the value of p ranges widely when modeling typical images and texture fields. Higher quality restorations can be obtained when the estimated p value is used, rather than commonly used arbitrary choices.