Design of non-separable transforms for directional 2-D sources

Traditionally, a 2-D block-based transform is always implemented through two separate 1-D transforms along each block´s vertical and horizontal dimensions. Such a framework is however not highly suitable for a directional 2-D source in which the dominant directional information is neither horizontal nor vertical. On the other hand, the R-D performance upper bound for all block-based transform coding schemes applied on such 2-D directional sources can be obtained by the non-separable Karhunen-Loève transform (KLT) — which is unfortunately very expensive computationally. In this paper, we present a new framework for designing some non-separable transforms that offer an R-D performance closer to that of the KLT, but can be implemented with nearly the same complexity as that of the discrete cosine transform (DCT).