Efficient ML estimation of the shape parameter for generalized Gaussian MRFs

A certain class of Markov random fields (MRF) known as generalized Gaussian MRFs (GGMRF) have been shown to yield good performance in modeling the a priori information in Bayesian image reconstruction and restoration problems. Though the ML estimate of temperature T of a GGMRF has a closed form solution, the optimal estimation of the shape parameter p is a difficult problem due to the intractable nature of the partition function. We present a tractable scheme for ML estimation of p by an off-line numerical computation of the log of the partition function. In image reconstruction or restoration problems, the image itself is not known. To address this problem, we use the EM algorithm to compute the estimates directly from the data. For efficient computation of the expectation step, we propose a fast simulation technique and a method to extrapolate the estimates when the simulations are terminated prematurely prior to convergence. Experimental results show that the proposed methods result in substantial savings in computation and superior quality images.