Symmetry-Based Graph Fourier Transforms: Are They Optimal For Image Compression?

Traditional block-based transforms are based on applying a single transform to all blocks. As an alternative, better performance in image and video processing and representation can be achieved by choosing one among a discrete set of transforms for each block. As an example, our recently proposed set of multiple transforms called Symmetry-Based Graph Fourier Transforms (SBGFTs) have shown good performance in terms of energy compaction, improving HEVC intra coding performance when used to replace the Discrete Cosine Transform (DCT). This paper further explores the performance of the SBGFTs in a multiple transforms, non-linear approximation perspective, by comparing them with two alternative sets of orthogonal transforms, namely, the Karhunen-Lo??ve Transform (KLT) and the Sparse Orthonormal Transform (SOT). Experimental results confirm that SBGFTs achieve superior representation ability in this context as well, suggesting that they could assume a central role in image compression.