Fast DCT algorithm based on multi-dimensional vector matrix

SANG Ai-jun; CUI Hai-ting; CHEN He-xin

doi:10.3788/OPE.20132103.0799

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Fast DCT algorithm based on multi-dimensional vector matrix

更新时间：2020-08-12

- Fast DCT algorithm based on multi-dimensional vector matrix
- Optics and Precision Engineering Vol. 21, Issue 3, Pages: 799-806(2013)
- 作者机构：
  
  吉林大学通信工程学院,吉林长春,中国,130012
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20132103.0799
  CLC： TN919.81
- Received：26 June 2012，
  
  Revised：12 September 2012，
  
  Published Online：20 March 2013，
  
  Published：15 March 2013
- 稿件说明：
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桑爱军吴杨崔海廷陈贺新. 基于多维矢量矩阵的DCT快速算法[J]. 光学精密工程, 2013,21(3): 799-806

SANG Ai-jun CUI Hai-ting CHEN He-xin. Fast DCT algorithm based on multi-dimensional vector matrix[J]. Editorial Office of Optics and Precision Engineering, 2013,21(3): 799-806
桑爱军吴杨崔海廷陈贺新. 基于多维矢量矩阵的DCT快速算法[J]. 光学精密工程, 2013,21(3): 799-806 DOI： 10.3788/OPE.20132103.0799.

SANG Ai-jun CUI Hai-ting CHEN He-xin. Fast DCT algorithm based on multi-dimensional vector matrix[J]. Editorial Office of Optics and Precision Engineering, 2013,21(3): 799-806 DOI： 10.3788/OPE.20132103.0799.

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，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0.25 s，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。

Abstract

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-dimensional vector matrix. The algorithm combined fast a DCT based on multi-dimensional vector orthogonal matrix transform algorithm with existing a 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 combination method

to the multi-dimensional field. Then

two DCT fast algorithms and their butterfly diagrams were deduced by combining multi-dimensional vector matrix theory

and the times of multiplications were analyzed. Finally

two methods were applied to test of the video in the standard video library and meanwhile comparative experiments were performed. The experimental results show that the required time of the two methods are 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 DCT fast algorithm from low-dimension to multi-dimension.

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references

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