Parametric Graph-based Separable Transforms for Video Coding

In many video coding systems, separable transforms (such as two-dimensional DCT-2) have been used to code block residual signals obtained after prediction. This paper proposes a parametric approach to build graph-based separable transforms (GBSTs) for video coding. Specifically, a GBST is derived from a pair of line graphs, whose weights are determined based on two non-negative parameters. As certain choices of those parameters correspond to the discrete sine and cosine transform types used in recent video coding standards (including DCT-2, DST-7 and DCT-8), this paper further optimizes these graph parameters to better capture residual block statistics and improve video coding efficiency. The proposed GBSTs are tested on the Versatile Video Coding (VVC) reference software, and the experimental results show that about 0.4% average coding gain is achieved over the existing set of separable transforms constructed based on DCT-2, DST-7 and DCT-8 in VVC.