A fast scheme for image size change in the compressed domain

Given a video frame in terms of its 8×8 block-DCT coefficients, we wish to obtain a downsized or upsized version of this frame also in terms of 8×8 block-DCT coefficients. The DCT being a linear unitary transform is distributive over matrix multiplication. This fact has been used for downsampling video frames in the DCT domain. However, this involves matrix multiplication with the DCT of the downsampling matrix. This multiplication can be costly enough to trade off any gains obtained by operating directly in the compressed domain. We propose an algorithm for downsampling and also upsampling in the compressed domain which is computationally much faster, produces visually sharper images, and gives significant improvements in PSNR (typically 4-dB better compared to bilinear interpolation). Specifically the downsampling method requires 1.25 multiplications and 1.25 additions per pixel of original image compared to 4.00 multiplications and 4.75 additions required by the method of Chang et al. (1995). Moreover, 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 frame (unsampled image) and its prediction (the upsampled image). This is desirable for many applications based on scalable encoding of video. The method presented can also be used with transforms other than DCT, such as Hadamard or Fourier