Directional Discrete Cosine Transforms: A Theoretical Analysis

Nearly all block-based transform techniques developed so far for image and video coding applications choose the 2-D discrete cosine transform (DCT) of a square block shape. With almost no exception, this conventional DCT is always implemented separately through two 1-D transforms, along the vertical and horizontal directions, respectively. In one of our recent works, we have developed a directional DCT framework in which the first transform may choose to follow a direction other than the vertical or horizontal one, while the second transform is arranged to be a horizontal one. Compared to the conventional DCT, our directional DCT framework has been demonstrated to provide a better coding performance for image blocks that contain directional edges - a popular scenario in many image and video signals. In this paper, we attempt to pursue an in-depth theoretical analysis to understand how the coding gain is produced in the directional DCTframework and how big it can be.