基于多维矢量矩阵的离散余弦变换快速算法  

Fast DCT algorithms based on multi-dimensional vector matrix

作　　者：桑爱军[1] 吴杨[1] 崔海廷[1] 陈贺新[1] 

机构地区：[1]吉林大学通信工程学院,吉林长春130022

出　　处：《光学精密工程》2013年第3期799-806,共8页Optics and Precision Engineering

基　　金：国家自然科学基金资助项目(No.61171078);吉林大学科学前沿与交叉学科创新项目(No.201103256)

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。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.

关 键 词：彩色视频压缩编码 多维矢量矩阵 快速离散余弦变换 正交变换 

分 类 号：TN919.81[电子电信—通信与信息系统]