R-D Performance Upper Bound of Transform Coding for 2-D Directional Sources

Traditionally, any 2D transform (such as 2D DCT) is implemented through two separable 1D transforms along the vertical and horizontal dimensions. Such a framework is however not most suitable for a 2D directional source in which the dominant directional information is neither horizontal nor vertical. In this letter, we attempt to determine the R-D performance upper bound for block-based transform coding schemes applied on such 2D directional sources. It is not a surprise that the Karhunen-Loeve transform (KLT) plays a critical role here. Specifically, we show that a nonseparable KLT can be determined directly from the given 2D directional source model to yield the R-D performance upper bound. We also show that there exists a significant gap between this upper bound and the R-D performance that can be achieved by using the traditional 2D DCT.