中文摘要：

为了提高彩色视频流压缩变换的速度，缩短变换时间，将基于多维矢量离散余弦变换（DCT）正交矩阵的视频流压缩算法同现有的快速DCT算法相结合，提出了基于多维矢量矩阵DCT的快速算法。首先，对一种实用性较强的一维快速DCT算法进行部分校正与补充，并将两种极具代表性的二维快速DCT算法，即行列分解法和线性组合法拓展到了多维层面。然后，结合多维矢量矩阵理论，推导出了两种DCT快速算法及其蝶形示意图，并分析了算法的乘法运算次数。最后，将这两种基于多维矢量矩阵的DCT快速算法应用在标准视频库中测试视频的压缩编码中，同时做了对比实验。实验结果表明：两种算法在DCT时所需的时间均小于0．25s，满足视频实时性的要求。该算法在保证重建视频质量的同时降低了运算时间，并将DCT快速算法从低维扩展到了多维，可以处理更多维数的视频。

英文摘要：

With the aim to improve the speed and reduce the time of color video stream compression transform, this paper proposed a fast Discrete Cosine Transform （DCT） algorithm based on multi-di- mensional vector matrix. The algorithm combined a fast DCT based on multi-dimensional vector or- thogonal matrix transform algorithm with a existing fast DCT algorithm for the first time. Firstly, it corrected and supplemented the fast 1D-DCT algorithm with strong practicality, and extended two most representative 2D-DCT fast algorithms, the rank decomposition method and the linear combina- tion method, to the multi-dimensional field. Then, two DCT fast algorithms and their butterfly dia- grams were deduced by combining multi-dimensional vector matrix theory, and the times of multipli- cations were analyzed. Finally, two methods were applied to test of the video in the standard video li- brary meanwhile comparative experiments were performed. The experimental results show that the required time of the two methods is both less 0.25 s in DCT and these meet the real-time requirements of video. The proposed two methods ensure the reconstructed video quality, and not only reduce the computation time significantly, but also expand the DCT fast algorithm from a low-dimension to the multi-dimension.