Graduated nonconvexity algorithm for image estimation using compound Gauss Markov field models

The authors describe the development of a deterministic algorithm for obtaining the global maximum a posteriori probability (MAP) estimate from an image corrupted by additive Gaussian noise. The MAP algorithm requires the probability density function of the original undegraded image and the corrupting noise. It is assumed that the original image is represented by a compound model consisting of a 2-D noncausal Gaussian-Markov random field (GMRF) to represent the homogeneous regions and a line process model to represent the discontinuities. The MAP algorithm is written in terms of the compound GMRF model parameters. The solution to the MAP equations is realized by a deterministic relaxation algorithm that is an extension of the graduated nonconvexity (GNC) algorithm and finds the global MAP estimate in a small number of iterations. As a byproduct, the line process configuration determined by the MAP estimate produces an accurate edge map without any additional cost. Experimental results are given to illustrate the usefulness of the method