A Symmetric Graph Transformation Framework for Image Compression

In this paper, a framework for image and video intra-frame coding able to effectively employ the multiple transform paradigm using Symmetry-Based Graph Fourier Transforms (SBGFTs) is proposed. As data representation relies heavily on the characteristics of signal classes in high dimensional spaces, over the years it has been understood that signal instances for a given class, e.g., images, typically lie on a manifold which is not a single linear subspace. Accordingly, standards for image/video compression have considered to introduce multiple representation models to encode the data, i.e., multiple linear block transforms. However, the advantages are currently limited typically due to implementation complexity and the high signaling cost of the representation mode. As a result, only a small set of alternative transforms is typically considered, which restricts the adaptation capabilities to the data. In this paper, we instead argue that it is feasible to incorporate into the image coding framework a large set of SBGFTs which can overcome the aforementioned drawbacks. Specifically, we demonstrate the ability to derive the block encoding transform index from the quantization pattern fingerprint using a Multilayer Perceptron (MLP) architecture, achieving prediction with high confidence, surpassing 80% for 4-top accuracy. This translates into a more efficient entropy coding strategy for the index, allowing to save on the average more than 3 bits per block. These experimental results highlight the significant benefits of SBGFTs for multiple transform coding, particularly when combined with the proposed MLP based index prediction, with only a limited increase in computational complexity.