图像小波压缩编码的比特分配算法的研究与实现
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摘要
图像信息作为传递信息的媒体和手段是十分重要的。但广泛使用数字图像还有一个主要的障碍，就是数字图像的数据量非常大，需要很多的比特数，因而需要对图像进行压缩。所谓图像压缩就是在保证一定的图像质量和满足一定要求的前提下，减少图像原始数据量的一种过程。针对图像中存在的相关冗余信息，采用某种方法，去除多余成分，就能实现图像的压缩。由于小波分析具有时—频分析、多分辨率分析等优点，易与人类视觉特性相结合，可获得较好的压缩效果，所以小波变换的方法受到人们的高度重视，出现了各种基于小波变换的图像编码方法。
图像压缩编码的根本目的，是在给定比特率(Bit Rate)下，力求使图像失真(Distortion)达到最小。小波变换的图像压缩算法虽然是一种有效的算法，但因为它利用了不同子带间和各个子带内部的相关性，所以复杂度比较高，有时不能实现实时的要求，因而小波变换编码方案的有效性很大程度上依靠比特分配，即给定的比特数必须被有效地分配在不同子带中。一种优秀的比特分配算法可使最终的量化失真达到最小。
本课题着重研究基于小波变换的数字图像压缩编码中的比特分配问题。由率失真理论我们知道，对于给定的码率，可以找到一种比特分配算法对小波变换后的各个子带进行比特分配，使重建图像的失真达到最小。论文中重点介绍了两种不同的比特分配算法的理论和具体实现的算法。这两种比特分配算法的差别在于，第一种是在率失真曲线是下凸的情况下进行的，这种方法算法是以率失真曲线的斜率为基础的。第二种是在任意率失真曲线的情况下进行的，这种算法的关键是求解Lagrangian方程。具体的压缩效果将在第五章中给出，并将论文中的压缩效果与JPEG、JPEG2000等标准，零树编码等其他压缩方案进行比较，得出结论。
As the method of passing information, image information is very important. However, the predominant drawback to apply digital image is the bulk data that need many bits. In order to overcome that drawback, we must compress the digital image. The definition of image compression is the processing of decreasing original data in the position of insuring the image quality. Because of the redundancy of digital image data, we can compress the image. Wavelet analysis have a variety of advantages, so there are a lot of image compression methods based on wavelet transform.
The basic aim of image compression is minimizing the distortion with the needed Bit-Rate. The image compression based on wavelet transform is a valid method, but because it uses subbands' redundancy, the complexity is so much that the compressing process consumes much time. So the efficiency of wavelet coding depends on bit allocation, that is , definite bits must be allocated to a serial of quantizations validly. By using kinds of quantization tables, each quantization can work at kinds of rates. In a word, bit allocation is the method deciding how to allocate definite bits to a variety of subbands. A excellent bit allocation can minimizing the overall distortion..
The emphasis of this thesis is studying the methods of bit allocations of digital image compression based on wavelet transform and managing to minimizing the overall distortion. We know from the Rate-Distortion theory that the aim is gainable. In the thesis, I describe the theories of two bit allocation methods and also give the realizable algorithms. The difference of the two methods is that the first is in the position of convex Rate-Distortion and the second is in the position of arbitrary Rate-Distortion curve. The results is gave in the character five, and in the character, I compare results of the thesis with those of JPEG, JPEG2000, ZTE and also conclude from the comparison of results that get form the two bit allocation.
图像压缩编码的根本目的，是在给定比特率(Bit Rate)下，力求使图像失真(Distortion)达到最小。小波变换的图像压缩算法虽然是一种有效的算法，但因为它利用了不同子带间和各个子带内部的相关性，所以复杂度比较高，有时不能实现实时的要求，因而小波变换编码方案的有效性很大程度上依靠比特分配，即给定的比特数必须被有效地分配在不同子带中。一种优秀的比特分配算法可使最终的量化失真达到最小。
本课题着重研究基于小波变换的数字图像压缩编码中的比特分配问题。由率失真理论我们知道，对于给定的码率，可以找到一种比特分配算法对小波变换后的各个子带进行比特分配，使重建图像的失真达到最小。论文中重点介绍了两种不同的比特分配算法的理论和具体实现的算法。这两种比特分配算法的差别在于，第一种是在率失真曲线是下凸的情况下进行的，这种方法算法是以率失真曲线的斜率为基础的。第二种是在任意率失真曲线的情况下进行的，这种算法的关键是求解Lagrangian方程。具体的压缩效果将在第五章中给出，并将论文中的压缩效果与JPEG、JPEG2000等标准，零树编码等其他压缩方案进行比较，得出结论。
As the method of passing information, image information is very important. However, the predominant drawback to apply digital image is the bulk data that need many bits. In order to overcome that drawback, we must compress the digital image. The definition of image compression is the processing of decreasing original data in the position of insuring the image quality. Because of the redundancy of digital image data, we can compress the image. Wavelet analysis have a variety of advantages, so there are a lot of image compression methods based on wavelet transform.
The basic aim of image compression is minimizing the distortion with the needed Bit-Rate. The image compression based on wavelet transform is a valid method, but because it uses subbands' redundancy, the complexity is so much that the compressing process consumes much time. So the efficiency of wavelet coding depends on bit allocation, that is , definite bits must be allocated to a serial of quantizations validly. By using kinds of quantization tables, each quantization can work at kinds of rates. In a word, bit allocation is the method deciding how to allocate definite bits to a variety of subbands. A excellent bit allocation can minimizing the overall distortion..
The emphasis of this thesis is studying the methods of bit allocations of digital image compression based on wavelet transform and managing to minimizing the overall distortion. We know from the Rate-Distortion theory that the aim is gainable. In the thesis, I describe the theories of two bit allocation methods and also give the realizable algorithms. The difference of the two methods is that the first is in the position of convex Rate-Distortion and the second is in the position of arbitrary Rate-Distortion curve. The results is gave in the character five, and in the character, I compare results of the thesis with those of JPEG, JPEG2000, ZTE and also conclude from the comparison of results that get form the two bit allocation.
引文
[1] 王汇源．数字图像通信原理与技术．北京：国防工业出版社．2000
[2] 沈兰荪．图像编码与异步传输．北京：人民邮电出版社．1998
[3] 蔡士杰，岳华，刘小燕．连续色调静止图像的压缩与编码—JPEG．第1版．南京大学出版．1995：11—13页 15—19页
[4] 崔锦泰，程正兴译。小波分析导论．西安交通大学出版社，1995
[5] 程正兴．小波分析算法与应用．西安交通大学出版社，1998
[6] 秦前清等．实用小波分析．西安电子科技大学出版社，1995
[7] 阮秋琦．数字图像处理学．电子工业出版社，2001
[8] 余松煜．现代图像信息压缩技术．北京：科学出版社．1998
[9] 黄贤武．数字图像处理与压缩编码技术．电子科技大学出版社．2000
[10] 吴乐南．数据压缩的原理与应用．北京：电子工业出版社．1995
[11] 黎洪松．数字视频技术及其应用．第二版．北京：清华大学出版社．1998
[12] 胡昌华等．基于MATLAB的系统分析与设计——小波分析．西安电子科技大学出版社，2000
[13] 何斌等．Visual C++数字图像处理．人民邮电出版社．2001
[14] Efficient bit allocation for an arbitrary set of quantizers,IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol.36, No.9 pp. 1445-1453, Sept 1988.
[15] DAVID S. TAUBMAN, MICHAEL W. MARCELLIN JPEG2000 Image Compression Fundamentals, Standards and Practice Kluwer Academic Publishers, 2002
[16] 周剑平《JPEG2000展望》《软件世界》1999，(10)64-65
[17] Eve A.Riskin.Optimal Bit Allocation via the Generalized BFOS Algorithm.IEEE Trans.Infor.Theory, VOL 37, NO.2, March 1991
[18] David Taubman.Embedded block coding in JPEG2000.Signal Processing:Image Communication 17(2002) 49-72
[19] Majid Rabbani, Rajan Joshi.An overview of the JPEG2000 still image compression standard. Signal Procesing:Image Communication 17(2002)
3-48
[20] 丁贵广，郭宝龙．新一代静止图像压缩编码标准：JPEG2000 概述．西安电子科技大学
[21] D.Taubman, "High Performance Scalable Image Compression With EBCOT", Proc. IEEE Int. Conference Image Processing, Vol.Ⅲ, pp. 343-348, Kobe, Japan, October 1999.
[22] D.Taubman, "High Performance Scalable Image Compression With EBCOT", IEEE Trans. Image Processing, Vol.9, No.7, pp. 1158-1170, July 2000.
[23] 王相海，张福炎．静态图像编码研究发展．《计算机研究与发展》Vol．38，No．11．Nov．2001
[24] 向逾．小波变换图像压码延拓匹配与变换系数研究．《电子科技大学学报》．Vol．28 No．3 Jun，1999
[25] 周建鹏，杨义先．图像压缩编码中的小波变换技术．《电路与系统学报》Vol．2 No．2 June 1997
[26] 郑勇 周正华等．一种快速零树编码的小波图像压缩算法．《电子科技大学学报》．Vol．70 No．3 Aug，1999
[2] 沈兰荪．图像编码与异步传输．北京：人民邮电出版社．1998
[3] 蔡士杰，岳华，刘小燕．连续色调静止图像的压缩与编码—JPEG．第1版．南京大学出版．1995：11—13页 15—19页
[4] 崔锦泰，程正兴译。小波分析导论．西安交通大学出版社，1995
[5] 程正兴．小波分析算法与应用．西安交通大学出版社，1998
[6] 秦前清等．实用小波分析．西安电子科技大学出版社，1995
[7] 阮秋琦．数字图像处理学．电子工业出版社，2001
[8] 余松煜．现代图像信息压缩技术．北京：科学出版社．1998
[9] 黄贤武．数字图像处理与压缩编码技术．电子科技大学出版社．2000
[10] 吴乐南．数据压缩的原理与应用．北京：电子工业出版社．1995
[11] 黎洪松．数字视频技术及其应用．第二版．北京：清华大学出版社．1998
[12] 胡昌华等．基于MATLAB的系统分析与设计——小波分析．西安电子科技大学出版社，2000
[13] 何斌等．Visual C++数字图像处理．人民邮电出版社．2001
[14] Efficient bit allocation for an arbitrary set of quantizers,IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol.36, No.9 pp. 1445-1453, Sept 1988.
[15] DAVID S. TAUBMAN, MICHAEL W. MARCELLIN JPEG2000 Image Compression Fundamentals, Standards and Practice Kluwer Academic Publishers, 2002
[16] 周剑平《JPEG2000展望》《软件世界》1999，(10)64-65
[17] Eve A.Riskin.Optimal Bit Allocation via the Generalized BFOS Algorithm.IEEE Trans.Infor.Theory, VOL 37, NO.2, March 1991
[18] David Taubman.Embedded block coding in JPEG2000.Signal Processing:Image Communication 17(2002) 49-72
[19] Majid Rabbani, Rajan Joshi.An overview of the JPEG2000 still image compression standard. Signal Procesing:Image Communication 17(2002)
3-48
[20] 丁贵广，郭宝龙．新一代静止图像压缩编码标准：JPEG2000 概述．西安电子科技大学
[21] D.Taubman, "High Performance Scalable Image Compression With EBCOT", Proc. IEEE Int. Conference Image Processing, Vol.Ⅲ, pp. 343-348, Kobe, Japan, October 1999.
[22] D.Taubman, "High Performance Scalable Image Compression With EBCOT", IEEE Trans. Image Processing, Vol.9, No.7, pp. 1158-1170, July 2000.
[23] 王相海，张福炎．静态图像编码研究发展．《计算机研究与发展》Vol．38，No．11．Nov．2001
[24] 向逾．小波变换图像压码延拓匹配与变换系数研究．《电子科技大学学报》．Vol．28 No．3 Jun，1999
[25] 周建鹏，杨义先．图像压缩编码中的小波变换技术．《电路与系统学报》Vol．2 No．2 June 1997
[26] 郑勇 周正华等．一种快速零树编码的小波图像压缩算法．《电子科技大学学报》．Vol．70 No．3 Aug，1999