利用小波分析进行图像数据压缩
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摘要
随着计算机和网络技术的普及，人们对数字图像在质量、大小和应用等方面提出了更高的要求，希望能够用有限的空间和带宽资源存储和传递大幅图像，并且根据实际需要，得到不同分辨率或质量的重构图像。这就要求图像压缩技术不仅有良好的压缩效率，而且还要能灵活地处理压缩码率。基于以上原因，对压缩编码方法的探讨和研究在近几十年来受到了广泛的关注。近20年来，在预测编码、变换编码和其它传统编码方法的基础上，图像压缩编码的理论、方法和技术取得了较大进展；其中小波编码算法因其能量集中特性、多分辨分析概念的提出和小波分解与重构快速算法的实现，使得小波变换在信号处理领域得到了广泛的应用，小波分析应用于图像数据压缩是小波分析应用的一个比较成熟的方面。
本文首先介绍了几种传统的压缩编码方法，并对国际标准JPEG和JPEG2000做了基本阐述，重点讨论了小波的多分辨分析、小波分解、重构算法、小波嵌入零树编码算法和改进的小波编码算法SPIHT。在此基础上提出了对图像进行预处理的想法，结合人眼对图像低频部分比对高频部分敏感的视觉特性对图像各频段提出不同的编码算法。本文在对图像的压缩过程中，对图像低频部分采用无损压缩方法(哈夫曼编码)，对高频部分采用改进的SPIHT编码方法，从而保证了在得到高压缩比的前提下使信噪比恶化程度较轻。本文对几种编码方法得到的重建图像进行了质量比较。最后，讨论了运动图像压缩核心技术——运动补偿技术，并用二维静止图像小波变换与一维时间轴上的小波变换相叠加的方法实现了对运动图像的压缩。
With the popularization of computers and network technology, people brought forward higher requirements on the quality, size and application of digital images, hoping to store and transfer big images by using limited space and bandwidth, and to obtain images of various resolution ration or quality. This requires the image-compression technology to be not only more efficient in compressing images, but also to be more flexible in dealing with compress coding ratio. As a result of all the above, great attention has been paid to the discussion and research of code-compressing method in recent decades. During the latest 20 years, great progress has been made in the theory, method and technology of image-compression coding on the basis of such traditional coding methods as coding forecast and exchanger coding etc; wavelet transformation has been widely used in signal-disposal field, because it has a characteristic of energy focus, it puts forwards a concept of multi-resolution ration analysis and the realization o
f algorithm about wavelet decompose and fast rebuild. Among the applications of wavelet analysis, it is rather mature to apply it to image-data compressing. In the first place, this article introduces several traditional code-compressing methods, and makes a brief introduction about the international standard JPEG and JPEG2000, and dwells on the wavelet multi-resolutions dissecting, decompression and rebuild, EZW algorithm, improved SPIHT. Then, the idea to pre-treat images is put forward on the basis of what has just been discussed, combining with the visual characteristic that people are more sensitive to low-frequency than high-frequency parts of images, different coding algorithms are suggested to use for various frequency. During the image-compressing, lossless-compression method (Huffman-Coding) is used to deal with the low-frequency part, while SPIHT-coding is used to deal with the high-frequency part, so mat high compression scale can be achieved without worsening the SNR. In the article, the quality
of the rebuilt images obtained by using different coding methods is compared. At last, the core technology of compressing moving images is discussed-motive reward technique, and the compression of moving images is realized by using the method that the two wavelet transformations of two-dimensional still images and one-dimensional time-axis are combined together.
本文首先介绍了几种传统的压缩编码方法，并对国际标准JPEG和JPEG2000做了基本阐述，重点讨论了小波的多分辨分析、小波分解、重构算法、小波嵌入零树编码算法和改进的小波编码算法SPIHT。在此基础上提出了对图像进行预处理的想法，结合人眼对图像低频部分比对高频部分敏感的视觉特性对图像各频段提出不同的编码算法。本文在对图像的压缩过程中，对图像低频部分采用无损压缩方法(哈夫曼编码)，对高频部分采用改进的SPIHT编码方法，从而保证了在得到高压缩比的前提下使信噪比恶化程度较轻。本文对几种编码方法得到的重建图像进行了质量比较。最后，讨论了运动图像压缩核心技术——运动补偿技术，并用二维静止图像小波变换与一维时间轴上的小波变换相叠加的方法实现了对运动图像的压缩。
With the popularization of computers and network technology, people brought forward higher requirements on the quality, size and application of digital images, hoping to store and transfer big images by using limited space and bandwidth, and to obtain images of various resolution ration or quality. This requires the image-compression technology to be not only more efficient in compressing images, but also to be more flexible in dealing with compress coding ratio. As a result of all the above, great attention has been paid to the discussion and research of code-compressing method in recent decades. During the latest 20 years, great progress has been made in the theory, method and technology of image-compression coding on the basis of such traditional coding methods as coding forecast and exchanger coding etc; wavelet transformation has been widely used in signal-disposal field, because it has a characteristic of energy focus, it puts forwards a concept of multi-resolution ration analysis and the realization o
f algorithm about wavelet decompose and fast rebuild. Among the applications of wavelet analysis, it is rather mature to apply it to image-data compressing. In the first place, this article introduces several traditional code-compressing methods, and makes a brief introduction about the international standard JPEG and JPEG2000, and dwells on the wavelet multi-resolutions dissecting, decompression and rebuild, EZW algorithm, improved SPIHT. Then, the idea to pre-treat images is put forward on the basis of what has just been discussed, combining with the visual characteristic that people are more sensitive to low-frequency than high-frequency parts of images, different coding algorithms are suggested to use for various frequency. During the image-compressing, lossless-compression method (Huffman-Coding) is used to deal with the low-frequency part, while SPIHT-coding is used to deal with the high-frequency part, so mat high compression scale can be achieved without worsening the SNR. In the article, the quality
of the rebuilt images obtained by using different coding methods is compared. At last, the core technology of compressing moving images is discussed-motive reward technique, and the compression of moving images is realized by using the method that the two wavelet transformations of two-dimensional still images and one-dimensional time-axis are combined together.
引文
1 唐向宏，贺振华，杨绍国．利用二维小波变换和视觉模型进行图像压缩编码．西南师范大学学报(自然科学版)，1999，24(4)：137～177
2 肖忠，刘钊．采用树特征平面的小波变换图像编码压缩方法[J]．通信学报，1999，20(11)：19～24
3 崔锦泰．小波分析导论．程正兴译．第一版．西安：西安交通大学出版社，1995．1～354
4 刘贵忠，邸双亮．小波分析及其应用．第一版．西安：西安电子科技大学出版社，1992．1～35
5 程正兴．小波分析算法与应用．第一版．西安：西安交通大学出版社，1998．57～70
6 王江晴．图像压缩中小波变换技术的研究．武汉理工大学学报．2002，24(3)：28～30
7 李建平，唐远炎．小波分析方法的应用．第一版．重庆：重庆大学出版社，1999．32～34
8 秦前清，杨宗凯．实用小波分析．第二版．西安：西安电子科技大学出版社，1994．41～53
9 杨福生．小波变换的工程分析与应用．第一版．北京：科学出版社，1999．95～97
10 陈武凡．小波分析及其在图像处理中的应用．北京：科学出版社，2002．131～132
11 柳斌，田金文，柳健．一种基于零树量化的小波变换图像压缩方法．华中理工大学学报．2000，28(3)：68～70
12 张益贞，刘滔．Visual C++实现MPEG／JPEG编解码技术．第一版．北京：人民邮电出版社，2002．87～106
13 解梅，顾德仁．一种基于小波变换的多分辨率门限选取方法．电子学报，1991，25(1)：95～97
14 王向阳，杨红颖．零树小波图像压缩算法的改进小型微型计算机系统，2002，23(10)：1245～1248
15 杨云峰，钟似玢．一种改进的基于小波零树的图像编码算法．中国图像图形学报，2001，6(6)：523～546
16 曾凡永，谷东兵，宋正勋．基于小波变换的图像压缩方法中小波基的选取问题探讨．长春光学精密机械学院学报，2000，23(2)：73～74
17 朱广进，祝建．二维非均匀取样图像编码．上海大学学报．1999，5(4)：231～234
18 何斌，马天予等．Visual C++数字图像处理．第二版．北京：人民邮电出版社，2001．233～235
19 张宗平，刘贵忠．基于小波的视频图像压缩研究进展．电子学报，2002，30(6)：886～888
20 林刚，刘泽民．基于运动补偿的三维小波视频编码．中国图像图形学报，1998，3(11)：24～26
21 毛玉星．基于小波分析的活动图像压缩方法．计算机应用．2002，22(2)：53～55
22 张文忠，沈兰荪．一种新的3-D小波变换图像编码方法．电子学报，1997，25(10)：49～52
23 JPEG2000 Part Ⅰ Final Committee Draft Version 1.0[S]
24 FCD15444-1, JPEG2000 [S/OL]. http://www.JPEG.org/FCD15444-1.htm
25 Chailaos christopoulos, Joel Askelof and Mathias Larsson, "Efficient Methods For Encoding Regions Of In The Upcoming JPEG2000 Still Image Coding Standard". IEEE Signal Proceedings Letters, 2000, 7 (9):247～249
26 Mallat S.A theory of multiresolution signal decomposition: the wavelet representation. IEEE Trans. PAMI, 1989,11 (7):674～693
27 I.Daubechies, Orthogonal bases of compactly supported wavelet, Comm. On Pure and App. Math. 1998, 41,909～996,
28 Shapiro J M. Embedded Image Coding Using Zerotrees of Wavelet Cofficients. IEEE Trans on SP,1993,41 (12):3445～3462
29 Said A, Peal man W A. A New, Fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees. IEEE Trans on Circuits and Systems for Video Technology, 1996,6(6): 1441～1554
30 J.Villasensor, et al. Wavelet filter evaluation for image compression. IEEE Trans. Image Proc. 1995,2(8):
1053～1060
31 Said A, Pealman W A. An Image Multiresolution Representation for Lossless and Lossy Compression. IEEE Trans on IP, 1996,5(9): 1003～1010
32 J. Shapiro. Embedded image coding Zero-tress of wavelet coefficients. IEEE Trans. Signal Processing. 1993, 41:3445～3462
33 Daubechies I. Orthonormal bases of compactly supported wavelets[J]. Comm. Pure and Appl. Math, 1988,41(7); 909～996
34 T Sikara. MPEG digital video-coding standards: delivering picture-perfect compression for storage, transmission, and multimedia application. IEEE Signal Processing Magazine, 1997, 14(5): 82～100
35 S.A. Carlucci, I Sod agar, T Chiang, Y-Q Zhang.A zero-tree wavelet video coder. IEEE Trans on Circuits and System ms for Video Tech, 1997,7(1): 109～118
36 J Vass, B-B char, K Palaniappan, X Zhuang. Significance-linked connected component. Analysis for low bit-rate wavelet video coding [J]. IEEE Trans on Circuits and Systems for Video Tech, 1999,9(4): 630～647.
37 Y-Q Zhang, S Zafar. Motion compensated wavelet transform coding for color video compression[J]. IEEE Trans on Circuits and Systems for Video Tech, 1992,2(3):285～296
38 X Yang, K Ramchandram. Scalable wavelet video coding using aliasing reduced hierarchical motion compensation. IEEE Trans on Image Processing,2000,9(5):778～791
39 D Taubman, A Zakhor. MultiMate 3-Dsubband coding of video. IEEE Trans on Image Processing, 1994,3(5):559～588
40 J-R Ohm. Three dimensional sub band coding with motion compensation. IEEE Trans on Image Processing, 1994,3(5):559～571
2 肖忠，刘钊．采用树特征平面的小波变换图像编码压缩方法[J]．通信学报，1999，20(11)：19～24
3 崔锦泰．小波分析导论．程正兴译．第一版．西安：西安交通大学出版社，1995．1～354
4 刘贵忠，邸双亮．小波分析及其应用．第一版．西安：西安电子科技大学出版社，1992．1～35
5 程正兴．小波分析算法与应用．第一版．西安：西安交通大学出版社，1998．57～70
6 王江晴．图像压缩中小波变换技术的研究．武汉理工大学学报．2002，24(3)：28～30
7 李建平，唐远炎．小波分析方法的应用．第一版．重庆：重庆大学出版社，1999．32～34
8 秦前清，杨宗凯．实用小波分析．第二版．西安：西安电子科技大学出版社，1994．41～53
9 杨福生．小波变换的工程分析与应用．第一版．北京：科学出版社，1999．95～97
10 陈武凡．小波分析及其在图像处理中的应用．北京：科学出版社，2002．131～132
11 柳斌，田金文，柳健．一种基于零树量化的小波变换图像压缩方法．华中理工大学学报．2000，28(3)：68～70
12 张益贞，刘滔．Visual C++实现MPEG／JPEG编解码技术．第一版．北京：人民邮电出版社，2002．87～106
13 解梅，顾德仁．一种基于小波变换的多分辨率门限选取方法．电子学报，1991，25(1)：95～97
14 王向阳，杨红颖．零树小波图像压缩算法的改进小型微型计算机系统，2002，23(10)：1245～1248
15 杨云峰，钟似玢．一种改进的基于小波零树的图像编码算法．中国图像图形学报，2001，6(6)：523～546
16 曾凡永，谷东兵，宋正勋．基于小波变换的图像压缩方法中小波基的选取问题探讨．长春光学精密机械学院学报，2000，23(2)：73～74
17 朱广进，祝建．二维非均匀取样图像编码．上海大学学报．1999，5(4)：231～234
18 何斌，马天予等．Visual C++数字图像处理．第二版．北京：人民邮电出版社，2001．233～235
19 张宗平，刘贵忠．基于小波的视频图像压缩研究进展．电子学报，2002，30(6)：886～888
20 林刚，刘泽民．基于运动补偿的三维小波视频编码．中国图像图形学报，1998，3(11)：24～26
21 毛玉星．基于小波分析的活动图像压缩方法．计算机应用．2002，22(2)：53～55
22 张文忠，沈兰荪．一种新的3-D小波变换图像编码方法．电子学报，1997，25(10)：49～52
23 JPEG2000 Part Ⅰ Final Committee Draft Version 1.0[S]
24 FCD15444-1, JPEG2000 [S/OL]. http://www.JPEG.org/FCD15444-1.htm
25 Chailaos christopoulos, Joel Askelof and Mathias Larsson, "Efficient Methods For Encoding Regions Of In The Upcoming JPEG2000 Still Image Coding Standard". IEEE Signal Proceedings Letters, 2000, 7 (9):247～249
26 Mallat S.A theory of multiresolution signal decomposition: the wavelet representation. IEEE Trans. PAMI, 1989,11 (7):674～693
27 I.Daubechies, Orthogonal bases of compactly supported wavelet, Comm. On Pure and App. Math. 1998, 41,909～996,
28 Shapiro J M. Embedded Image Coding Using Zerotrees of Wavelet Cofficients. IEEE Trans on SP,1993,41 (12):3445～3462
29 Said A, Peal man W A. A New, Fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees. IEEE Trans on Circuits and Systems for Video Technology, 1996,6(6): 1441～1554
30 J.Villasensor, et al. Wavelet filter evaluation for image compression. IEEE Trans. Image Proc. 1995,2(8):
1053～1060
31 Said A, Pealman W A. An Image Multiresolution Representation for Lossless and Lossy Compression. IEEE Trans on IP, 1996,5(9): 1003～1010
32 J. Shapiro. Embedded image coding Zero-tress of wavelet coefficients. IEEE Trans. Signal Processing. 1993, 41:3445～3462
33 Daubechies I. Orthonormal bases of compactly supported wavelets[J]. Comm. Pure and Appl. Math, 1988,41(7); 909～996
34 T Sikara. MPEG digital video-coding standards: delivering picture-perfect compression for storage, transmission, and multimedia application. IEEE Signal Processing Magazine, 1997, 14(5): 82～100
35 S.A. Carlucci, I Sod agar, T Chiang, Y-Q Zhang.A zero-tree wavelet video coder. IEEE Trans on Circuits and System ms for Video Tech, 1997,7(1): 109～118
36 J Vass, B-B char, K Palaniappan, X Zhuang. Significance-linked connected component. Analysis for low bit-rate wavelet video coding [J]. IEEE Trans on Circuits and Systems for Video Tech, 1999,9(4): 630～647.
37 Y-Q Zhang, S Zafar. Motion compensated wavelet transform coding for color video compression[J]. IEEE Trans on Circuits and Systems for Video Tech, 1992,2(3):285～296
38 X Yang, K Ramchandram. Scalable wavelet video coding using aliasing reduced hierarchical motion compensation. IEEE Trans on Image Processing,2000,9(5):778～791
39 D Taubman, A Zakhor. MultiMate 3-Dsubband coding of video. IEEE Trans on Image Processing, 1994,3(5):559～588
40 J-R Ohm. Three dimensional sub band coding with motion compensation. IEEE Trans on Image Processing, 1994,3(5):559～571