Choice of Edge-preserving and Sparse Prior Models in Image Restoration

The choice of the prior image models in image restoration is discussed in the Bayesian framework. The paper studies the properties of two classes of stochastic models for natural images, the generalized Gaussian model and the Markov random field, and constructs two corresponding cost functions of the image restoration problem. It surveys the edge-preserving abilities of the two classes of models, and proposes the conditions that the models need to satisfy to ensure the preservation of edges, and defines the edge-preserving prior. The theory of the sparse prior is considered, and it shows that the above two classes of models will be sparse under some constraints. The relationship between the edge-preserving prior and the sparse prior is analysed, and it concludes that an edge-preserving prior model is a sparse prior model. The work provides a criterion of the choice of a prior model in the process of image restoration. The numerical simulations show that a proper choice of prior image model can improve the restoration performance dramatically.