Fast GEM wavelet-based image deconvolution algorithm

The paper proposes a new wavelet-based Bayesian approach to image deconvolution, under the space-invariant blur and additive white Gaussian noise assumptions. Image deconvolution exploits the well known sparsity of the wavelet coefficients, described by heavy-tailed priors. The present approach admits any prior given by a linear (finite of infinite) combination of Gaussian densities. 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.