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In this paper we propose novel algorithms for image restoration and parameter estimation with a generalized Gaussian Markov random field (GGMRF) prior utilizing variational distribution approximation. The restored image and the unknown hyperparameters for both the image prior and the image degradation noise are simultaneously estimated within a hierarchical Bayesian framework. We develop two algorithms resulting from this formulation which provide approximations to the posterior distributions of the latent variables. Experimental results are provided to demonstrate the performance of the algorithms.