Maximum likelihood scale estimation for a class of Markov random fields

This paper presents the exact maximum likelihood (ML) estimate of temperature for a class of Markov random fields (MRF) known as generalized Gaussian MRFs. The ML estimate has a simple closed form which is analogous to variance estimation for Gaussian random variables. This result is useful because the temperature parameter plays the important role of determining the amount of smoothing in problems such as Bayesian image reconstruction and restoration. Two extensions of the basic result are also given: 1) numerical scale estimation for the general class of continuous MRFs; and 2) parameter estimation from incomplete data using the EM algorithm. Preliminary numerical experiments support the usefulness of the technique