It is well-known that the application of the Discrete Cosine Transform
(DCT) in transform coding schemes is justified by the fact that
it belongs to a family of transforms asymptotically equivalent to the
Karhunen-Loève Transform (KLT) of a first order Markov process.
However, when the pixel-to-pixel correlation is low the DCT does
not provide a compression performance comparable with the KLT.
In this paper, we propose a set of symmetry-based Graph Fourier
Transforms (GFT) whose associated graphs present a totally or partially
symmetric grid. We show that this family of transforms well
represents both natural images and residual signals outperforming
the DCT in terms of energy compaction. We also investigate how
to reduce the cardinality of the set of transforms through an analysis
that studies the relation between efficient symmetry-based GFTs and
the directional modes used in H.265 standard. Experimental results
indicate that coding efficiency is high.