In this paper we develop a wavelet-based statistical method for solving the image restoration problem. In this approach, a signal prior is set up by modeling the image wavelet coefficients as independent Gaussian mixture random variables. We first specify a uniform (non-informative) distribution on the mixing parameters, which leads to a simple and efficient iterative algorithm for MAP estimation. This algorithm is similar to the EM algorithm in that it alternates between a state estimation step and a maximization step. Moreover, we show that our algroithm converges monotonically to a local maximum of the posterior distribution. We next generalize the result to non-uniform priors and develop an efficient integer programming algorithm that enables a similar alternating optimization procedure.