Transforms for the motion compensation residual

The Discrete-Cosine-Transform (DCT) is the most widely used transform in image and video compression. Its use in image compression is often justified by the notion that it is the statistically optimal transform for first-order Markov signals, which have been used to model images. In standard video codecs, the motion-compensation residual (MC-residual) is also compressed with the DCT. The MC-residual may, however, possess different characteristics from an image. Hence, the question that arises is if other transforms can be developed that can perform better on the MC-residual than the DCT. Inspired by recent research on direction-adaptive image transforms, we provide an adaptive auto-covariance characterization for the MC-residual that shows some statistical differences between the MC-residual and the image. Based on this characterization, we propose a set of block transforms. Experimental results indicate that these transforms can improve the compression efficiency of the MC-residual.