Coding of Image Intra Prediction Residuals Using Symmetric Graphs

The Discrete Cosine Transform (DCT) is widely deployed by modern image and video coding standards such as JPEG and H.26x. In most cases, the DCT is applied in a separable manner to rows and columns, which limits its ability to represent signals with diagonal orientation. As an alternative, non-separable transforms can represent signals with different orientations, but are significantly more computationally complex. To address this problem, in this paper we propose a set of non-separable Symmetry-Based Graph Fourier Transforms (SBGFTs), whose symmetric structures lead to a faster implementation. We study a practical image coding scenario that exploits the proposed SBGFTs, where for each intra predicted image residual block the optimal graph is chosen by solving a graph-based Rate-Distortion (R-D) problem. Experimental results indicate a coding efficiency higher than JPEG and JPEG2000.