A generalized Gaussian image model for edge-preserving MAP estimation

Abstract

The authors present a Markov random field model which allows realistic edge modeling while providing stable maximum a posterior (MAP) solutions. The model, referred to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the a posteriori log-likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography.