中文摘要：

考虑了广义高斯分布和马尔科夫随机场两类随机图像模型,提出相应的图像复原目标函数。分析了这两类模型在图像复原中的边缘保持性能,给出了它们具有边缘保持能力所需的条件。根据稀疏型先验的理论,指出在一定条件下这两类先验模型对图像具有稀疏表示特性,因此可以用于图像超分辨率复原处理。说明了边缘保持和稀疏先验之间的关系,为复原中图像先验模型的选择提供了参考。仿真实验表明,合理选择图像的先验模型,可以显著提高图像复原效果。

英文摘要：

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.