The sparse representation models have been widely applied in image super-resolution. The certain optimization problem is supposed and can be solved by the iterative shrinkage algorithm. During iteration, the update of dictionaries and similar patches is necessary to obtain prior knowledge to better solve such ill-conditioned problem as image super-resolution. However, both the processes of iteration and update often spend a lot of time, which will be a bottleneck in practice. To solve it, in this paper, we present the concept of image quality difference based on generalized Gaussian distribution feature which has the same trend with the variation of Peak Signal to Noise Ratio (PSNR), and we update dictionaries or similar patches from the termination strategy according to the adaptive threshold of the image quality difference. Based on this point, we present two sparse representation algorithms for image super-resolution, one achieves the further improvement in image quality and the other decreases running time on the basis of image quality assurance. Experimental results also show that our quantitative results on several test datasets are in line with exceptions.