Directional discrete cosine transforms--a new framework for image coding

Nearly all block-based transform schemes for image and video coding developed so far choose the 2-D discrete cosine transform (DCT) of a square block shape. With almost no exception, this conventional DCT is implemented separately through two 1-D transforms, one along the vertical direction and another along the horizontal direction. In this paper, we develop a new block-based DCT framework in which the first transform may choose to follow a direction other than the vertical or horizontal one. The coefficients produced by all directional transforms in the first step are arranged appropriately so that the second transform can be applied to the coefficients that are best aligned with each other. Compared with the conventional DCT, the resulting directional DCT framework is able to provide a better coding performance for image blocks that contain directional edges--a popular scenario in many image signals. By choosing the best from all directional DCTs (including the conventional DCT as a special case) for each image block, we will demonstrate that the rate-distortion coding performance can be improved remarkably. Finally, a brief theoretical analysis is presented to justify why certain coding gain (over the conventional DCT) results from this directional framework. Index Terms--Directional discrete cosine transform, discrete cosine transform (DCT), image coding, video coding.