矢量量化图像编码算法的研究
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摘要
随着计算机和数字通讯技术的普及,数字信号分析和处理技术越来越受到人们的重视并得到了快速发展,现已广泛应用于雷达、通信、航空航天和工业自动化等各个领域。数字信号具有两个突出优点,首先数字传输与存储系统具有抗干扰能力强、保密性好、可靠性高的优点,其次数字信号较易于去除冗余信息。但是由于图像、视频和声音等媒体信息的数据量通常很大,对存储器的存储容量、通信信道的带宽及计算机的处理速度带来了很大的影响。因此在数字通信中通常都要对数字信号进行信源编码。
基于矢量量化的数据压缩思想是数据编码算法的重要方法之一。矢量量化是一种有损压缩方法。其在量化时用输出组集合(码本)中最匹配的一组输出值(码矢量)来代替一组输入采样值(输入矢量)。矢量量化的突出特点是压缩比大、解码简单且能够较好地保存图像细节。矢量量化技术涉及多个学科领域,对矢量量化技术的研究必将给这些学科领域注入新鲜血液。因此无论从理论角度还是从应用角度来讲开展对矢量量化的研究都具有重要的学术、国防和经济意义。
本文针对矢量量化图像编码算法进行了研究,包括两个核心内容:1.码本的设计与优化,主要致力于迭代算法的优化以提高码本性能;2.码矢量搜索算法的优化,主要致力于找寻更有效的码矢量排除准则,以排除不可能匹配的码矢量,进而加快编码速度。归纳起来,本文所做的主要工作如下:
首先分析了国内外矢量量化技术的发展状况,介绍了当前主流的矢量量化器设计方法,并针对经典的码本设计方法和码矢量搜索算法进行了分析研究,介绍了多种具有较高性能的码本的设计方法和基于不等式以及变换域的快速码矢量搜索算法。
接着提出了一种改进的LBG算法,该算法是一种基于矢量空间划分的码本设计算法,通过引入一个距离调节因子λ,使空间划分距离逐渐变小,训练矢量集被逐渐细分。这样逐步细致的划分训练矢量空间,能够使初始码本中的码矢量分散开来。经仿真实验验证,该算法所设计的码本具有较高的性能。
最后提出了一种基于加权方差不等式和哈德码变换的快速码矢量搜索算法,本文将方差不等式与哈德码变换有机地结合起来,提出了一个全新的码矢量排查不等式,较大限度地缩小了码矢量搜索范围,从而大大减小了码矢量搜索时间提高了编码效率。
Along with the popularization of the computer and digital communication, digital signal analysis and processing technology is taken seriously more and more by people and get a rapid development. Now this technology is widely used in radar, communication, aerospace and industrial automation etc. Digital signal has two outstanding advantages. First of all, transmission and storage system of digital has strong anti-interference ability, good secrecy and high reliability advantages. Secondly, digital signal is easy to delete the redundant information. But because the data volume of media information such as images, video and sound is usually very large, so it takes great effect on memory storage capacity, communication channel bandwidth and computer processing speed. Therefore, it is necessary to encode the digital signal in digital communication.
Vector quantization (VQ) is one of the most important methods of data compression. VQ is an effective lossy compression method. In the coding process, VQ uses the most matching codeword in the codebook instead of an input vector. The salient characteristics of VQ are big compression ratio, simple decoding process and maintain the image details well. Many academic fields are involved by vector quantization techniques. The research on VQ will bring fresh blood for these fields. For this reason, the research on VQ has the great significance no matter from the theoretical perspective or from the application perspective.
The study in this paper is the encoding algorithm on image vector quantization. It includes two aspects: 1. Code book design and optimization. It mainly devotes to the optimization of iterative algorithm to improve the code book performance. 2. The optimization of code words search algorithm. It mainly devotes to find more effectively code word exclusion criterion to exclude impossible code words and accelerate the encoding process. All in all, the key work in this paper are as follows:
First of all, the vector quantization technology development situation at home and abroad was analyzed in the beginning of this paper. And then the design methods of current main vector quantizers are introduced. Several of high-performance codebook design method and fast encoding algorithms based on inequality and transform domain are also introduced in this paper.
Secondly, an improved LBG algorithm is proposed in the third chapter. It is an effective codebook design algorithm base on space division. By introducing a distance adjustment factorλ, the clustering vector will be decreased gradually with the increase of iteration times. Thus, the input vector set is refined and the initial codewords are spread well among the input vector set.
Last, a fast encoding algorithm for vector quantization based on weighted Variance Inequality and Hadamard Transform (HT) is proposed in the forth chapter. A new inequality which combined Variance Inequality and HT is used. By this inequality, more non-similar codewords will be rejected and the search range will decrescent. The experiment results show that the efficiency of the encoding process is improved observably.
基于矢量量化的数据压缩思想是数据编码算法的重要方法之一。矢量量化是一种有损压缩方法。其在量化时用输出组集合(码本)中最匹配的一组输出值(码矢量)来代替一组输入采样值(输入矢量)。矢量量化的突出特点是压缩比大、解码简单且能够较好地保存图像细节。矢量量化技术涉及多个学科领域,对矢量量化技术的研究必将给这些学科领域注入新鲜血液。因此无论从理论角度还是从应用角度来讲开展对矢量量化的研究都具有重要的学术、国防和经济意义。
本文针对矢量量化图像编码算法进行了研究,包括两个核心内容:1.码本的设计与优化,主要致力于迭代算法的优化以提高码本性能;2.码矢量搜索算法的优化,主要致力于找寻更有效的码矢量排除准则,以排除不可能匹配的码矢量,进而加快编码速度。归纳起来,本文所做的主要工作如下:
首先分析了国内外矢量量化技术的发展状况,介绍了当前主流的矢量量化器设计方法,并针对经典的码本设计方法和码矢量搜索算法进行了分析研究,介绍了多种具有较高性能的码本的设计方法和基于不等式以及变换域的快速码矢量搜索算法。
接着提出了一种改进的LBG算法,该算法是一种基于矢量空间划分的码本设计算法,通过引入一个距离调节因子λ,使空间划分距离逐渐变小,训练矢量集被逐渐细分。这样逐步细致的划分训练矢量空间,能够使初始码本中的码矢量分散开来。经仿真实验验证,该算法所设计的码本具有较高的性能。
最后提出了一种基于加权方差不等式和哈德码变换的快速码矢量搜索算法,本文将方差不等式与哈德码变换有机地结合起来,提出了一个全新的码矢量排查不等式,较大限度地缩小了码矢量搜索范围,从而大大减小了码矢量搜索时间提高了编码效率。
Along with the popularization of the computer and digital communication, digital signal analysis and processing technology is taken seriously more and more by people and get a rapid development. Now this technology is widely used in radar, communication, aerospace and industrial automation etc. Digital signal has two outstanding advantages. First of all, transmission and storage system of digital has strong anti-interference ability, good secrecy and high reliability advantages. Secondly, digital signal is easy to delete the redundant information. But because the data volume of media information such as images, video and sound is usually very large, so it takes great effect on memory storage capacity, communication channel bandwidth and computer processing speed. Therefore, it is necessary to encode the digital signal in digital communication.
Vector quantization (VQ) is one of the most important methods of data compression. VQ is an effective lossy compression method. In the coding process, VQ uses the most matching codeword in the codebook instead of an input vector. The salient characteristics of VQ are big compression ratio, simple decoding process and maintain the image details well. Many academic fields are involved by vector quantization techniques. The research on VQ will bring fresh blood for these fields. For this reason, the research on VQ has the great significance no matter from the theoretical perspective or from the application perspective.
The study in this paper is the encoding algorithm on image vector quantization. It includes two aspects: 1. Code book design and optimization. It mainly devotes to the optimization of iterative algorithm to improve the code book performance. 2. The optimization of code words search algorithm. It mainly devotes to find more effectively code word exclusion criterion to exclude impossible code words and accelerate the encoding process. All in all, the key work in this paper are as follows:
First of all, the vector quantization technology development situation at home and abroad was analyzed in the beginning of this paper. And then the design methods of current main vector quantizers are introduced. Several of high-performance codebook design method and fast encoding algorithms based on inequality and transform domain are also introduced in this paper.
Secondly, an improved LBG algorithm is proposed in the third chapter. It is an effective codebook design algorithm base on space division. By introducing a distance adjustment factorλ, the clustering vector will be decreased gradually with the increase of iteration times. Thus, the input vector set is refined and the initial codewords are spread well among the input vector set.
Last, a fast encoding algorithm for vector quantization based on weighted Variance Inequality and Hadamard Transform (HT) is proposed in the forth chapter. A new inequality which combined Variance Inequality and HT is used. By this inequality, more non-similar codewords will be rejected and the search range will decrescent. The experiment results show that the efficiency of the encoding process is improved observably.
引文
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2.孙圣和,陆哲明.矢量量化技术及应用[M].科学出版社, 2002
3.胡征,杨有为,矢量量化原理与应用[M].西安:西安电子科技大学出版社, 1988
4. Y. Linde, A. Buzo, R. M. Gray. An algorithm for vector quantizer design[J]. IEEE Trans. Communications, 1980, 28(1):84-95
5. C. Q. Chen, S. N. Koh, P. Sivaprakasapillai. A novel scheme for optimizing partitioned VQ using a modified resolution measure[J]. Signal Processing, 2007, 56:157-163
6. T. Berger. Rate Distortion Theory[J]. New Jersey: Prentice-Hall, Englewood Cliffs, 1991
7. R. G. Gallager. Information theory and reliable communications[J]. New York: John Wiley &Sons, 1968
8. A. Buzo, A. H. RM. Cray and J. D. Market. Speech coding based upon Vector Quantization[J]. Trans. Acoustics Speech and Signal Processing, 1980, 28(5):562-574
9. PA. Chou, T. Lookabaugh, RM. Cray. Optimal pruning with applications to tree -structured source coding and modeling[J]. IEEE Trans. Information Theory, 1999, 35(2):299-315
10. B. Mahesh, W. A. Pearlman, L. Lu. Variable-rate tree structured vector quantizers. Information Theory[J]. 2005, 41(4):917-930
11. V. Ramasubramanian, K. K. Paliwal. Fast k-dimensional tree algorithm for nearest neighbor search with application to Vector Quantization encoding[J]. IEEE Trans. Signal Processing, 2002, 40(3):471-480
12. G. Poggi, A. R. P. Gagozini. Tree-structured product-codebook vector quantization[J]. Signal Processing: Image Communication, 2001, 16:421-430
13. R Baker, R. Gray. Image compression using nonadaptive spatial vector quantization[C]. The 16th Asilomar Conference on Circuits, Systems and Computers, 1982, 55-61
14. R. A. King, N. M. Nasrabadi. Image coding using Vector Quantization in the transform domain[J]. Pattern Recognition Letters, 1983, 1:323-329
15. P. C. Chang, R. M. Gray, J. May. Fourier transform Vector Quantization for speech coding[J]. IEEE Trans. Communication, 2007, 35(10):1059-1068
16.王磊,戚飞虎,赵雪春.基于BWT和FVQ的极低比特率图像编码算法[J].电子科学学刊, 2000, 22(4):667-671
17.李弼程,胡宗云.基于小波变换的图像矢量量化[J].信号处理, 2000, 26 (1):32-36
18.赵键,李勇,廉保旺等.一种基于小波变换的图像压缩方法[J].数据采集与处理, 2000, 15(2):166-169
19. WS. Chen, F. C. Ou, L. C. Lin, etc. Image coding using Vector Quantization with a hierarchical codebook in wavelet domain[J]. IEEE Trans. Consumer Electronics, 2005, 45(1):36-45
20. S. Adlersberg, V. Cuperman. Transform domain Vector Quantization for speech signals[C]. International Conference on Acoustics, Speech, and Signal Processing, 1997, 4:45.4.1-45.4.4
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