Recursive-in-order least squares parameter estimation for 2D Gaussian Markov random field model

Presents two recursive-in-order least squares algorithms for parameter estimation of 2D Gaussian Markov random field (GMRF) models. Algorithm I implements the recursive computation by introducing auxiliary variables without changing the structure of the model, while algorithm II realizes the recursive computation by replacing the noncausal symmetric GMRF model by an equivalent causal nonsymmetric model. The concept of recursive path, which is used to increase the speed of computation of the model parameters and accomplish the choice of the optimal model support, is proposed. The computational complexity of both algorithms is O(M²m) multiplications per order, where m is the total number of parameters and M² is the size of a sample image