中文摘要：

基于稀疏表示的超分辨率（SR）图像重构算法需要求解l1范数优化问题，时间效率不高。本文在该方法的基础上加入平移不变性约束条件，并且考虑到稀疏参数对重构结果影响不大，对重构算法进行简化，避免了求解复杂的l1范数优化问题，实现了一种快速的图像SR重构。数值实验结果表明，本文算法具有更高的时间效率。

英文摘要：

The super resolution （SR） reconstruction of image can be achieved by the locally linear embed- ding algorithm or the sparse representation algorithm. The locally linear embedding algorithm requires the number K of the nearest neighbors as a predefined parameter. Improper choice of K will cause the o- ver-fitting or under-fitting of data, which results in blurring of the reconstructed image. The sparse rep- resentation algorithm could select the neighbors adaptively, but needs to solve a complicated and time consuming ll-norm minimizing problem. In this work, a new super resolution reconstruction algorithm is proprosed by introducing the shift invariance constraints. Since the sparsity parameter affects the recon- struction insignificantly, the proposed algorithm is simplified to avoid solving the minimizing /1-norm problem,which leads to a significant reduction in the time complexity. The time complexity of the pro- posed algorithm is O（mn）, while that of solving the minimizing l1- norm by Lasso is CK m3 ＋ nm2 ）. Ex- perimental results indicate that the proposed algorithm is more efficient than previous algorithms, and holds a good stability in time consumption with the increasing overlap between contiguous image patches and the dictionary size. Thus, the proposed algorithm can be implemented with a bigger dictionary under acceptable time, which can be adopted for the real time super resolution reconstruction applications.