Symmetric Line Graph Transforms for Inter Predictive Video Coding

In this paper, we study graph-based transforms for inter predictive video coding. We are motivated by the fact that symmetries in the transform basis are very beneficial for computational efficiency. Based on this, we describe the relationship between bisymmetric matrices and the butterfly structure in fast transform algorithms. We introduce a new class of transforms called Symmetric Line Graph Transforms (SLGTs), of which the discrete cosine transform (DCT) is one particular case. As is well known in the case of the DCT, the bisymmetry property allows us to reduce the number of multiplications by half. We show that, beyond the DCT, useful SLGTs can be defined that have efficient implementation. We propose a specific SLGT that is shown to outperform the DCT for classes of inter residual blocks. While the proposed SLGT approaches the performance of a Karhunen Loeve Transform (KLT) at certain distortion levels, it has lower computation cost.