中文摘要：

正则化是图像复原领域为获取理想复原结果,将图像复原的优化模型与约束条件整合为统一的优化目标的重要手段.针对传统正则化复原模型中仅基于单一先验的假设的不足,提出了流形正则化的方法,将图像空间看作一个＂弯曲＂的图像流形,通过修正绝对高斯曲率和对图像中的不同特征进行标识和分类,然后针对不同特征区域采用不同的先验形式进行正则约束,并针对多种正则化约束的模型设计了基于E-M算法的交叉迭代图像复原方法.实验验证了该方法在去噪和去模糊方面取得了比经典全局单一范数约束方法更好的信噪比.

英文摘要：

The regularization method used in image restoration area is an effective means for obtaining the restored image with higher quality. This paper improves the traditional single prior assumptions for the regularization term with a novel prior assumption which we call manifold regularization. According to the idea of manifold regularization,all images lie on the ＂bending＂manifold. By the modified absolute value of Gaussian curvature,the feature of images can be identified. And images can be classified into different classes. Based on the classification,the model can decide the form of the regularization term by using the different prior assumptions. Furthermore,this operation can be taken on different regions of an image.For the proposed restoration model with several kinds of regularization term,a cross iterative algorithm based on E-M method is designed for the experiments. By some tests,it is verified that the manifold regularization based restoration model achieves the desired results.