The traditional discrete cosine transform (DCT) can only sparsely represent the horizontal and vertical edges in images.The computation complexity of directional prediction DCT (DPDCT), which has the ability to represent more directions, is much higher.To overcome these shortcomings, the fast directional discrete cosine transforms (FDDCT) is proposed in this paper, in which the transformation is performed on the predefined direction mode.Compared with DPDCT, no interpolation is needed in FDDCT, so FDDCT can sparsely represent the anisotropic edges in much faster images.A special lifting algorithm is designed between adjacent blocks to ensure the perfect reconstruction, which compacts energy in edges lying across the blocks.The experimental results show that the computation of FDDCT is no more than 1.4 times that of DCT's.Coding with the same set partition method,PSNR compressed images that are combined with FDDCT are 0.4～1.6dB higher than those with DCT and DPDCT.Also, the edges and the details in the images are much clearer and less distortion exists.%传统的二维DCT(discrete cosine transform)无法稀疏表示除水平或垂直方向以外的边缘,而具有强方向表示能力的方向预测离散余弦变换(directional prediction DCT,简称DPDCT)计算复杂度又过高.针对这些问题,提出了一种快速方向离散余弦变换(fast directional discrete cosine transform,简称FDDCT).该算法沿给定的方向模式进行变换.避免了DPDCT中的插值运算,可以快速、稀疏地表示图像中各向异性边缘信息.此外,FDDCT通过设计块边界提升,在进一步集中边缘能量的同时保证了算法的完全重构.实验结果表明,FDDCT计算复杂度不超过DCT的1.4倍;采用同样的编码方法,基于FDDCT的压缩图像与基于DCT以及DPDCT的压缩图像相比,峰值信噪比可提高0.4dB～1.6dB,而且边缘细节更加清晰、完整.
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