Down-sampling in the discrete cosine transform (DCT) domain is preferable for images coded by DCT transform, such as JPEG/MJPEG/H.264, etc. Recent researches show that the truncated high-frequency DCT coefficients during the DCT down-sampling process can be estimated by learning the correlations between low-frequency and high-frequency DCT coefficients. In this paper, we propose to utilize the powerful super-resolution framework using sparse dictionaries with anchored neighborhood regression to significantly improve the accuracy of the estimated high-frequency DCT coefficients. Experimental results show that the proposed framework outperforms the state-of-the-art DCT-based up-sampling methods in terms of PSNR (0.3-1.63dB) and SSIM values for standard image datasets Set5 and Set14, while the computational time of the proposed method is 23× times faster than the state-of-the-art learning-based method using k-NN MMSE due to pre-computation of the ridge regression during the training process.