Image super resolution is very important and is also considered as a challenging problem in image applications. The main researches are about how to bring back missing information in generating higher resolution image given that there is only information from a single low resolution image. Conventional methods such as interpolation could be applied to estimate the missing pixel information. However, there is still not enough information to generate the high resolution image. Thus, the resulting image may look blurred and lacks high resolution detail. In this thesis, sparse representation is used as a fundamental method to solve the problem. In training step, we propose an efficient clustering dictionary to design an overcomplete dictionary. Firstly, we prepare training set as an initial dictionary. We then perform efficient sparse coding to generate basis matrix. The error of the dictionary is reduced using singular value decomposition. In solution step, we propose Elastic Net as a solution of sparse representation problem. Experiments demonstrated that our proposed method can generate high resolution images with better visual quality when compared with conventional method such as Bicubic interpolation. Our method can give smaller Root Mean Square Error (RMSE) value than other known interpolation methods. Smaller RMSE implies the higher accuracy in the recognition of face, license plate, and other objects. Experiments also proved that our proposed method is applicable in video super-resolution. We use combination of sparse-representation method and analytical method to reduce number of skipped frames while retained the acceptable quality of generated high resolution video.