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We propose using the generalized Gaussian Markov random field (GGMRF) image model with MAP estimation to solve the problem of restoration for a blurred and noise corrupted image. The restoration algorithm is adapted to specific characteristics of the true image by estimating the GGMRF shape parameter used in computing the MAP estimation. This shape parameter, p, is estimated based on the sample kurtosis of the image. It is shown that higher quality restorations are obtained when the estimated p value is used, rather than some arbitrary choice as other investigators have used.