A fast scheme for image size change in the compressed domain

Given a video frame in terms of its 8 x 8 block-DCT coefficients, we wish t o obtain a downsized or upsized version of this frame also in terms of 8 x 8 block-DCT coefficients. The DCT being a linear unitary transform is distr ibutive over matrix multiplication. This fact has been used for downsamplin g video frames in the DCT domain. However, this involves matrix multiplicat ion with the DCT of the downsampling matrix. This multiplication can be cos tly enough to trade off any gains obtained by operating directly in the com pressed domain. We propose an algorithm for downsampling and also upsamplin g in the compressed domain which is computationally much faster, produces v isually sharper images, and gives significant improvements in PSNR (typical ly 4-dB better compared to bilinear interpolation). Specifically the downsa mpling method requires 1.25 multiplications and 1.25 additions per pixel of original image compared to 4.00 multiplications and 4.75 additions require d by the method of Chang ct at, Moreover, the downsampling and upsampling s chemes combined together preserve all the low-frequency DCT coefficients of the original image. This implies tremendous savings for coding the differe nce between the original frame (unsampled image) and its prediction (the up sampled image). This is desirable for many applications based on scalable e ncoding of video. The method presented can also be used with transforms oth er than DCT, such as Hadamard or Fourier.