The paper introduces modelling and optimization contributions on a class of Bayesian wavelet-based image deconvolution problems. Main assumptions of this class are: 1) space-invariant blur and additive white Gaussian noise; 2) prior given by a linear (finite of infinite) decomposition of Gaussian densities. Many heavy-tailed priors on wavelet coefficients of natural images admit this decomposition. To compute the maximum a posteriori (MAP) estimate, we propose a generalized expectation maximization (GEM) algorithm where the missing variables are the Gaussian modes. The maximization step of the EM algorithm is approximated by a stationary second order iterative method. The result is a GEM algorithm of O(N log N) computational complexity. In comparison with state-of-the-art methods, the proposed algorithm either outperforms or equals them, with low computational complexity.
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