An EM algorithm for Gaussian Markov Random Fields
Lavine [7] has shown how 1-dimensional Linear Dynamical Systems (LDS’s) can be used for exact inference in 2(or higher) dimensional Gaussian Markov Random Fields (GMRFs). His trick is to relate the row of an image to the state of the LDS and introduce pseudoobservations (which turn out to be zero) such that the evolution equation implements vertical neighbour contstraints and the observation equation implements horizontal neighbour constraints. Thus, exact inference can take place using Kalman smoothing. In this report we show how nonstationary smoothness parameters can be estimated using the M-step of the EM algorithm for LDS’s.