四元数及其相关理论已成为近年来彩色图像处理的一种有效方法，被广泛应用于多维信号分析领域。为克服传统的彩色图像超分辨率重建方法中基于主分量或者多通道分别处理的不足，本项目采用四元数表示并从四元数域非局部均值、稀疏表示及它们的组合研究彩色图像的整体超分辨率重建，以充分考虑不同颜色通道的联系，进一步提高重建图像的质量，着重开展以下三个方面的研究：(1) 联合四元数矩，构建四元数域基于混合相似度的非局部均值模型，将其应用于彩色图像超分辨率重建；(2) 考虑到训练样本数量，分别研究四元数域基于双字典、自训练字典的超分辨率重建算法；(3) 利用图像自身冗余性质，研究四元数域非局部稀疏编码的超分辨率重建算法。

Quaternion and the relevant theories has become an effective method for color image processing and widely utilized in the field of multidimensional signal analysis. To overcome the shortcomings of color image super-resolution reconstruction by means of traditional algorithms based on principal component or multichannel separately processing, the project adopts quaternion representation to fully regard the relationship between different color channels and investigates the color image super-resolution reconstruction in a holistic way from non-local means, sparse representation and the combination of them in quaternion domain, aiming to further improve the quality of reconstructed image. We will place emphasis on the following three aspects: (1) by combining the quaternion moments, to establish the non-local means based on hybrid similarity in quaternion domain and apply it to color image super-resolution reconstruction; (2) considering the number of trained samples, to investigate the super-resolution algorithms based on double dictionaries in quaternion domain as well as self-training dictionary; (3) by exploiting the redundancy of the image, to investigate non-local sparse coding based super-resolution algorithm in quaternion domain.