Fast scheme for downsampling and upsampling in the DCT domain

Given a video frame or image in terms of its 8×8 block-DCT coefficients we wish to obtain a downsized or upsized (by factor of two) version of this frame also in terms of 8×8 block-DCT coefficients. We propose an algorithm for achieving this directly in the DCT domain which is computationally much faster, produces visually sharper images and gives significant improvements in PSNR (typically 4 dB better) compared to other compressed domain methods based on bilinear interpolation. The downsampling and upsampling schemes combined together preserve all the low-frequency DCT coefficients of the original image. This implies tremendous savings for coding the difference between the original (unsampled image) and its prediction (the upsampled image). This is desirable for many applications based on scalable encoding of video.