2M维矢量余弦整数变换核矩阵

桑爱军; 王艇; 栾晓利; 崔海廷; 陈贺新

doi:10.3788/OPE.20132107.1891

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2M维矢量余弦整数变换核矩阵

信息科学 | 更新时间：2020-08-12

- 2M维矢量余弦整数变换核矩阵
- 2 M-dimensional vector integer DCT transform kernel matrix
- 光学精密工程 2013年21卷第7期页码：1891-1897
- 作者机构：
  
  1. 吉林大学通信工程学院,吉林长春,中国,130012
  2. 长春空军航空大学,吉林长春,130022
- 作者简介：
- 基金信息：
  
  国家自然科学基金项目（基于可交换clifford代数的彩色图像矩不变量研究）();吉林大学科学前沿与交叉学科创新项目()
- DOI：10.3788/OPE.20132107.1891
  中图分类号： TP391
- 收稿日期：2012-11-12，
  
  修回日期：2013-03-05，
  
  网络出版日期：2013-07-15，
  
  纸质出版日期：2013-07-15
- 稿件说明：
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桑爱军王艇栾晓利崔海廷陈贺新. 2M维矢量余弦整数变换核矩阵[J]. 光学精密工程, 2013,21(7): 1891-1897

. 2 M-dimensional vector integer DCT transform kernel matrix[J]. Editorial Office of Optics and Precision Engineering, 2013,21(7): 1891-1897
桑爱军王艇栾晓利崔海廷陈贺新. 2M维矢量余弦整数变换核矩阵[J]. 光学精密工程, 2013,21(7): 1891-1897 DOI： 10.3788/OPE.20132107.1891.

. 2 M-dimensional vector integer DCT transform kernel matrix[J]. Editorial Office of Optics and Precision Engineering, 2013,21(7): 1891-1897 DOI： 10.3788/OPE.20132107.1891.

摘要

为了减少处理多维数据的运算时间，提出了2M维矢量离散余弦变换（DCT）整数核矩阵，并分析了该整数变换核矩阵的正交性和能量集中性。首先，根据原有浮点型2M维矢量DCT变换核矩阵的理论及性质介绍了2M维矢量DCT整数变换核矩阵的实现算法；验证了2M维矢量整数变换核矩阵的正交性。然后，简述了对*.yuv格式视频文件进行分块与重组的基本原理。最后，以四阶整数变换核为例，分析了2M维矢量整数变换核矩阵，即讨论多维数据在整数变换后的能量集中性。实验结果表明：采用2M维矢量整数变换相对浮点型变换仍然具有较好的能量集中性，而且Y分量能量集中性均值已达到97.3%以上，U分量和V分量的能量集中性均值也已达到99.9%以上，此结果会对后来的多维数据压缩编码处理提供有力依据。

Abstract

To reduce the computation time of multidimensional data processing

a 2 M-dimensional vector integer Discrete Cosine Transformation(DCT) kernel matrix was proposed and the orthogonality and energy concentration of the integer transform kernel matrix were analyzed. First

according to the theory and properties of original floating-point 2 M-dimensional vector DCT transform kernel matrix

the algorithm for the 2 M-dimensional vector DCT integer transform kernel matrix was introduced and the orthogonality of 2 M-vector integer transform kernel matrix was validated. Then

the basic principles of blocking and reorganizing the *.yuv format video files were given. Finally

by taking the four order and eight order integer transform kernels as examples

the 2 M-dimensional vector integer transform kernel matrix was analyzed

namely

the energy concentration of multidimensional data after integer transform was discussed. The experimental results show that 2 M-vector transform relative floating-point transformation has good energy concentration. The average value of energy concentration for the Y component has reached more than 97.3%

and those for the U component and V component have been more than 99.9%. It concludes that the results will provide a strong basis for compression processing of multi-dimensional data.

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references

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