The development of image acquisition technology and display technology provide the base for popularization of high-resolution images. On the other hand, the available bandwidth is not always enough to data stream such high-resolution images. Down- and up-sampling, which decreases the data volume of images and increases back to high-resolution images, is a solution for the transmission of high-resolution images. In this paper, motivated by the observation that the high-frequency DCT components are sparse in the spatial domain, we propose a scheme combined with Discrete Cosine Transform (DCT) and Compressed Sensing (CS) to achieve arbitrary-ratio down-sampling. Our proposed scheme makes use of two properties: First, the energy of a image concentrates on the low-frequency DCT components. Second, the high-frequency DCT components are sparse in the spatial domain. The scheme is able to preserve the most information and avoid absolutely blindly estimating the high-frequency components. Experimental results show that the proposed down- and up-sampling scheme produces better performance compared with some state-of-the-art schemes in terms of peak signal to noise ratio (PSNR), structural similarity index measurement (SSIM) and processing time.