COMPOUND GAUSS-MARKOV RANDOM-FIELDS FOR IMAGE ESTIMATION

This paper is concerned with algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound Gauss-Markov random fields. We consider both the maximum a posteriori probability (MAP) estimate and the minimum meansquared error (MMSE) estimate for both image estimation and image restoration. Compound image models consist of several submodels having different characteristics along with an underlying structure model which governs transitions between these image submodels. Compound Gauss-Markov field models can be attractive for image estimation because the resulting estimates do not suffer the oversmoothing of edges that usually occurs with Gaussian image models. Two different compound random field models are employed in this paper, the doubly stochastic Gaussian (DSG) random field and a newly defined compound Gauss-Markov (CGM) random field. We present MAP estimators for DSG and CGM random fields using simulated annealing, a powerful optimization method best suited to massively parallel processors. A fast converging algorithm called deterministic relaxation, which however converges to only a locally optimal MAP estimate, is also presented as an alternative for reducing computational loading on sequential machines. For comparison purposes, we also include results on the fixed-lag smoothing MMSE estimator for the DSG field and its suboptimal M-algorithm approximation. The incorporation of causal and noncausal modeling together with causal and noncausal estimates on the same data sets allows meaningful visual comparisons to be made. We also include Wiener and reduced update Kalman filter (RUKF) estimates to allow visual comparison of the near optimal estimates based on compound Gauss-Markov models to those based on simple Gaussian image models.