基于多维矢量矩阵的DCT快速算法的研究
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摘要
多媒体通信是通信技术与计算机技术相结合的产物之一。近年来，伴随着计算机技术与网络技术突飞猛进的发展，应运而生的众多多媒体应用己渐渐延伸到我们生活中的各个方面。与传统数据应用相比，多媒体应用最显著的特点是集成了多种类型的媒体流，而数字化后的媒体流含有巨大的信息量，给图像视频信息的存储与传输带来严峻的挑战。所以对数字图像视频信息进行有效压缩编码以实现节源高效始终是相关领域的永久性研究热点。统计表明，图像或视频都包含着大量的冗余信息：视觉冗余、结构冗余、知识冗余、统计冗余、帧间冗余以及空间冗余等等，压缩编码技术的作用就是大量地削减或压缩数据信息中无关紧要的冗余信息，保留有用信息。
本实验室突破传统思维模式，提出多维矢量矩阵的理论，并且有效利用该理论将图像及视频中存在的相关性更加紧密地结合起来，运用多维矢量矩阵间的运算方法对图像或视频进行有效压缩，在消除多种冗余的同时还能进一步提高压缩比与峰值信噪比等性能。现有图像及视频压缩标准中的核心编码算法，DCT是其中的佼佼者，也正因如此，众多学者对DCT的快速算法的研究也从未停止。
本文主要是针对基于多维矢量DCT正交矩阵的视频流压缩算法进行的后续研究，在多维矢量矩阵乘法准则和多维矢量DCT正交变换矩阵理论基础上，以提高彩色视频流的压缩变换速度、缩短压缩变换的时间为目的，对一种实用性较强的一维快速DCT算法进行了部分校正与补充，并且对两种极具代表性的二维快速DCT算法思想进行深入研究后，将其快速变换算法拓展到多维层面，从而提出一种新颖的快速算法，即基于多维矢量矩阵的快速离散余弦变换算法，并且给出两种基于多维矢量矩阵DCT快速变换的蝶形示意图，并将这两种基于多维矢量矩阵DCT快速变换应用在实验室标准视频库中的视频压缩编码中，在达到压缩目的同时，也能提高压缩速度，缩短压缩变换时间。
实验仿真以C语言为开发工具，在Visual C++6.0软件环境下，编程实现了基于多维矢量矩阵的DCT快速变换算法，本实验选取标准视频库中四种不同大小的视频源数据作为测试视频,大小分别为320×240×8、352×288×8、512×384×8、704×576×8，YUV之比均为4:2:0。首先采用8×8×8子阵分块方法分别对四种不同大小的源视频数据进行子块分割，并根据给出的两种基于多维矢量矩阵DCT快速变换的蝶形示意图，将分割后的每个子块进行快速变换运算。从四组实验结果可看出，本文提出的快速变换算法一方面保证了重构视频的质量，另一方面使得视频的压缩速度得以提高，故本算法是可行的；之后又对基于多维矢量矩阵的快速DCT变换算法中的方法一与方法二进行了比较实验，通过对实验数据详细分析，表明本文所提的两种方法均满足视频实时的要求。最后研究总结了以上算法思想的优缺点和继续研究的方向。
Multimedia communication is the product of the combination of communicationtechnology and computer technology. In recent years, with the rapid development ofcomputer technology and network technology, many multimedia applications havebeen gradually extended to all aspects of our lives. Compared with other traditionaldata applications, the most prominent feature of multimedia applications is theintegration of audio, video and other types of media streams. These digital videosignals generate extremely high data rates which can not be transmitted without firstbeing compressed. The critical challenge for data compression is to reduce the bit ratewithout affecting picture quality. Therefore, video compression technology has been apermanent research focus in digital video technology. According to statistics, there isa lot of redundant information in images and video，such as visual redundancy,structural redundancy, knowledge redundancy, statistical redundancy, inter-frameredundancy, space redundancy and so on. The role of compression coding technologyis to cut or compressed the redundant information and to retain the useful information.
Beyond the traditional ways of thinking, our laboratory proposed the theory ofmulti-dimensional vector matrix. The theory of multi-dimensional vector matrix caneffectively decrease the redundancies。Mufti-dimensional transform is carried out inorder to achieve good compression results with good image quality. In the image andvideo compression standard, DCT is one of the core coding algorithm, so manyacademics have been studying the fast DCT algorithm.
This paper is the follow-up study of DCT-based multi-dimensional vectororthogonal matrix transform algorithm. Based on Multi-dimensional vector matrixmultiplication and DCT-based multi-dimensional vector orthogonal matrix transformalgorithm and in order to reduce color video stream compression transform time, we partly correct and supplement the fast1D-DCT algorithm which has strongpracticality. After in-depth research the two most representative fast algorithm of2D-DCT, the Fast transform algorithm is extended to the multi-dimensional field.We propose a new fast algorithm that is the fast discrete cosine transform algorithmbased on multi-dimensional vector matrix. We also give two butterfly diagram of thefast DCT based on the multi-dimensional vector matrix. And both the twotransformational methods are used in video compression coding, thus it not only canachieve compression, also can improve speed of the compression and shorten the timeof the compression transformation.
We simulate fast DCT algorithm based on multi-dimensional vector matrixtheory. C language is used in visual C++6.0. Source data which are selected as testdata are four different size and have the same YUV proportion (4:2:0). First, we usesub-matrix method divide source data into sub-blocks. Then, two new kinds ofbutterfly diagrams based on multidimensional vector matrix fast DCT algorithm areproposed. Finally, we process all blocks by the new fast transform algorithm. Asshown in four group results, the algorithm is feasible. We compare the first methodwith the second method. After detail data analyzing, we find that both the twomethods can meet the need of real time video. In the end of this paper, we summarizealgorithms and point out the continued research direction.
本实验室突破传统思维模式，提出多维矢量矩阵的理论，并且有效利用该理论将图像及视频中存在的相关性更加紧密地结合起来，运用多维矢量矩阵间的运算方法对图像或视频进行有效压缩，在消除多种冗余的同时还能进一步提高压缩比与峰值信噪比等性能。现有图像及视频压缩标准中的核心编码算法，DCT是其中的佼佼者，也正因如此，众多学者对DCT的快速算法的研究也从未停止。
本文主要是针对基于多维矢量DCT正交矩阵的视频流压缩算法进行的后续研究，在多维矢量矩阵乘法准则和多维矢量DCT正交变换矩阵理论基础上，以提高彩色视频流的压缩变换速度、缩短压缩变换的时间为目的，对一种实用性较强的一维快速DCT算法进行了部分校正与补充，并且对两种极具代表性的二维快速DCT算法思想进行深入研究后，将其快速变换算法拓展到多维层面，从而提出一种新颖的快速算法，即基于多维矢量矩阵的快速离散余弦变换算法，并且给出两种基于多维矢量矩阵DCT快速变换的蝶形示意图，并将这两种基于多维矢量矩阵DCT快速变换应用在实验室标准视频库中的视频压缩编码中，在达到压缩目的同时，也能提高压缩速度，缩短压缩变换时间。
实验仿真以C语言为开发工具，在Visual C++6.0软件环境下，编程实现了基于多维矢量矩阵的DCT快速变换算法，本实验选取标准视频库中四种不同大小的视频源数据作为测试视频,大小分别为320×240×8、352×288×8、512×384×8、704×576×8，YUV之比均为4:2:0。首先采用8×8×8子阵分块方法分别对四种不同大小的源视频数据进行子块分割，并根据给出的两种基于多维矢量矩阵DCT快速变换的蝶形示意图，将分割后的每个子块进行快速变换运算。从四组实验结果可看出，本文提出的快速变换算法一方面保证了重构视频的质量，另一方面使得视频的压缩速度得以提高，故本算法是可行的；之后又对基于多维矢量矩阵的快速DCT变换算法中的方法一与方法二进行了比较实验，通过对实验数据详细分析，表明本文所提的两种方法均满足视频实时的要求。最后研究总结了以上算法思想的优缺点和继续研究的方向。
Multimedia communication is the product of the combination of communicationtechnology and computer technology. In recent years, with the rapid development ofcomputer technology and network technology, many multimedia applications havebeen gradually extended to all aspects of our lives. Compared with other traditionaldata applications, the most prominent feature of multimedia applications is theintegration of audio, video and other types of media streams. These digital videosignals generate extremely high data rates which can not be transmitted without firstbeing compressed. The critical challenge for data compression is to reduce the bit ratewithout affecting picture quality. Therefore, video compression technology has been apermanent research focus in digital video technology. According to statistics, there isa lot of redundant information in images and video，such as visual redundancy,structural redundancy, knowledge redundancy, statistical redundancy, inter-frameredundancy, space redundancy and so on. The role of compression coding technologyis to cut or compressed the redundant information and to retain the useful information.
Beyond the traditional ways of thinking, our laboratory proposed the theory ofmulti-dimensional vector matrix. The theory of multi-dimensional vector matrix caneffectively decrease the redundancies。Mufti-dimensional transform is carried out inorder to achieve good compression results with good image quality. In the image andvideo compression standard, DCT is one of the core coding algorithm, so manyacademics have been studying the fast DCT algorithm.
This paper is the follow-up study of DCT-based multi-dimensional vectororthogonal matrix transform algorithm. Based on Multi-dimensional vector matrixmultiplication and DCT-based multi-dimensional vector orthogonal matrix transformalgorithm and in order to reduce color video stream compression transform time, we partly correct and supplement the fast1D-DCT algorithm which has strongpracticality. After in-depth research the two most representative fast algorithm of2D-DCT, the Fast transform algorithm is extended to the multi-dimensional field.We propose a new fast algorithm that is the fast discrete cosine transform algorithmbased on multi-dimensional vector matrix. We also give two butterfly diagram of thefast DCT based on the multi-dimensional vector matrix. And both the twotransformational methods are used in video compression coding, thus it not only canachieve compression, also can improve speed of the compression and shorten the timeof the compression transformation.
We simulate fast DCT algorithm based on multi-dimensional vector matrixtheory. C language is used in visual C++6.0. Source data which are selected as testdata are four different size and have the same YUV proportion (4:2:0). First, we usesub-matrix method divide source data into sub-blocks. Then, two new kinds ofbutterfly diagrams based on multidimensional vector matrix fast DCT algorithm areproposed. Finally, we process all blocks by the new fast transform algorithm. Asshown in four group results, the algorithm is feasible. We compare the first methodwith the second method. After detail data analyzing, we find that both the twomethods can meet the need of real time video. In the end of this paper, we summarizealgorithms and point out the continued research direction.
引文
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[9]沈鹏.基于多维矢量DCT正交矩阵变换即熵编码算法的研究[D]，吉林大学通信与信息系,2009.
[10]胡铁根，基于多维矢量DCT正交矩阵的视频流压缩算法的研究[D]，吉林大学通信与信息系统，2008.
[11]冯华.基于多维Wlash矢量正交矩阵的视频流压缩算法的研究[D].吉林大学通信与信息系,2009.
[12]刘丽丽.基于采样模型的多维矢量矩阵DCT整数变换编解码器研究[D].吉林大学通信与信息系统，2011.
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[28]郝丽.基于多维矢量矩阵的快速Wlash变换算法的研究[D].吉林大学电子与通信工程,2011.
[29] Nahum Mohamed. Digital Filters Design for Signal and Image Processing(Digital Signal&Image Processing Series (ISTE-DSP))[M]. Wiley-ISTE,2006-10-31.
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[2] Yun Q Shi, Huifang Sun. Image and Video Compression for MultimediaEngineering: Fundamentals, Algorithms, and Standards[M]. SecondEdition(Image Processing). CRC,2008.
[3] Robert J. McEliece. The Theory of Information and Coding[M]. AddisonWesley Publishing Company,1977.
[4] Gilbert Held, Thomas R. Marshall Data and Image Compression: Tools andTechni-ques[M].4th Edition. John Wiley&Sons,1996.
[5]桑爱军.三维立体矩阵理论及彩色图像的变换编码[D].吉林大学通信与信息系统，2002.
[6] Byeong Lee. A New A lgorithm to Compute the Discrete Cosine Transform[C].IEEE Trans on ASSP,1984,32(6):1243-1245.
[7] J David Frost. Digital Image Processing:Techniques and Applications in CivilEngineer-ing: Keauhou Beach Hotel, Kona, Hawaii Februar[M]. AmericanSociety of Civil Engin-eers,1993.
[8]陈贺新，桑爱军，赵岩，陈绵书，胡铁根.一种高效的多维视频流编解码方法:中国，200810050395[P].2008-07-30.
[9]沈鹏.基于多维矢量DCT正交矩阵变换即熵编码算法的研究[D]，吉林大学通信与信息系,2009.
[10]胡铁根，基于多维矢量DCT正交矩阵的视频流压缩算法的研究[D]，吉林大学通信与信息系统，2008.
[11]冯华.基于多维Wlash矢量正交矩阵的视频流压缩算法的研究[D].吉林大学通信与信息系,2009.
[12]刘丽丽.基于采样模型的多维矢量矩阵DCT整数变换编解码器研究[D].吉林大学通信与信息系统，2011.
[13]张鹤.基于四维n阶矩阵的彩色图像正交变换算法的研究[D].吉林大学通信与信息系统，2007.
[14] Kenneth R, Castleman. Digital Image Processing[M]. Prentice Hall,1995.
[15] Harald Grossauer. Digital Image Inpainting[M]. VDM Verlag Dr,Mueller e K,2008.
[16] Jerry D. Gibson,Toby Berger, Tom Lookabaugh, Rich Baker, David Lindbergh.Digital Compression for Multimedia: Principles&Standards (The MorganKaufmann Series in Multimedia Information and Systems)[M]. MorganKaufmann,1998.
[17] Wilhelm Burger, Mark James Burge. Digital Image Processing:AnAlgorithmic Introducti-on using Java[M]. Springer,2007.
[18] Gerard Blanchet, Maurice Charbit. Digital Signal and Image Processing UsingMatlab (Digital Signal and Image Processing series)[M]. ISTE PublishingCompany,2006.
[19] Pratt, William K. Digital Image Processing[M]. John Wiley&Sons Inc,2007.
[20]桑爱军，陈贺新.三维矩阵彩色图像WDCT压缩编码[J].电子学报，2002,30(4):594-597.
[21]赵岩，陈贺新，王长青.一种基于四维离散余弦变换的视频编码方法[D].吉林大学通信工程学院，2002.
[22] Peter Symes. Digital Video Compression[M]. McGraw-Hill, TAB Electronics,2003.
[23] Rafael C Gonzalez, Richard E Woods, Steven L Eddins. Digital ImageProcessing Using MATLAB[M].2nd ed. Gatesmark Publishing,2009.
[24] Chad Fogg, Didier J LeGall, Joan L Mitchell, William B Pennebaker. MPEGVideo Compression Standard (Digital Multimedia Standards Series)[M].Springer,1996.
[25] Geoff Dougherty. Digital Image Processing for Medical Applications[M].Cambridge University Press,2009-05-11.
[26] Sebastian Montabone. Beginning Digital Image Processing: Using Free Toolsfor Phot-ographers[M]. Apress,2010-07-31.
[27] Ahmed N, Rao K R.Orthogonal Transforms for Digigital SignalProcessing.Springer-Verlag,New York,1975.
[28]郝丽.基于多维矢量矩阵的快速Wlash变换算法的研究[D].吉林大学电子与通信工程,2011.
[29] Nahum Mohamed. Digital Filters Design for Signal and Image Processing(Digital Signal&Image Processing Series (ISTE-DSP))[M]. Wiley-ISTE,2006-10-31.
[30] Ahmed N,Natarajan T,Rao K R.Discrete Cosine Transforms[C].IEEE TransComp,1974, vol C-23, pp90-93.
[31]胡广书.数字信号处理-理论、算法与实现[M].清华大学出版社，2003.
[32] Wang Z. On computing the discrete Fourier and consine transforms[J]. IEEETrans Acoust Speech, Signal Processing,1985,33(4):1341~1344.
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