中文摘要：

传统的基于稀疏表示的超分辨率重建算法对所有图像块，应用单一冗余字典表示而不能反映不同几何结构类型图像块间的区别。针对这一问题，本文探索图像局部几何结构特性，提出一种基于结构特性聚类的几何字典学习和耦合约束的超分辨率重建方法。该方法首先对训练样本图像块进行几何特性聚类，然后应用K-SVD算法为每个聚类块联合训练得到高低分辨率字典。此外，在重建过程中引入局部可控核回归和非局部相似性耦合约束，以提高重建图像质量。实验结果表明，与单一字典超分辨率算法相比，本文方法重建图像边缘和细节部分明显改善，评价参数较大提高。

英文摘要：

Traditional super-resolution algorithms based on sparse representation of image patches exploit single redundant dictionary to represent the image patches that contain various textures, which can not reflect the differences of various image patches types. In order to overcome this disadvantage, this paper proposes a single image super resolution reconstruction method based on geometric dictionary learning and coupled regularization, by exploring the local geometric property of image patches. A large number of training image patches are clustered into several groups by their geometric property, from which the corresponding ＂geometric dictionaries＂ are learned via K-SVD algorithm which is combined with the idea that the high and low resolution dictionaries can be co-trained. In addition, a coupled regularization of local steering kernel regression and non-local similarity is introduced into the proposed method to further improve the quality of the reconstructed images. Experiment results show that the proposed method both increases the evaluation parameters and improves the visual quality of the edges and the details significantly.