Generalized Graduated Non-Convexity Algorithm for Maximum A Posteriori Image Estimation'

We are interested in restoring a degraded scene while preserving the edges. Edges are represented as line pr& cesses and are estimated along with the intensities in a Maximum A Posien'ori (MAP) framework. Aasumptions regarding the prior and degradation distributions reduce the problem to one of energy function minimization. The energy function is highly non-convex and finding the global minimum is a non-trivial problem. When constraints on the interactions between line processes are removed, the deterministic, Graduated Non-Convexity (GNC) algorithm has been shown to find close to optimum solutions. We have generalized the GNC model. Any number of constraints on the line processes can now be added. This has been achieved by using the adiabalie approzimaiion, a well known technique in synergetics. Our resulting algorithm is a combination of the Conjugate Gradient (CG) and the Iterated Conditional Modes (ICM) algorithms and is completely deterministic. Since the GNC algorithm can be obtained as a special case of our approach, we refer to our algorithm as the Generalized GNC or GZNC algorithm. The algorithm was executed on two aerial images. Results are presented along with comparisons to the GNC algorithm.