基于小波变换的静止图像压缩编码技术研究
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摘要
随着图像应用范围和深度的不断扩大，不仅要求实现高压缩率、高保真度和快速性，还应满足诸如渐进传输等网络应用的需要。因此，图像／视频的压缩技术成为国际上热门的研究课题。
本文在对图像压缩编码理论与实际应用技术的的现状和发展趋势进行简要分析的基础上，从一定理论深度较为详细阐述了基于小波变换的静止图像压缩编码技术，重点探讨了编码器结构、编码步骤、小波基的选取以及影响压缩编码性能因素等几个关键问题。对基于图像压缩性能的小波特性进行了分析与仿真，通过仿真比较了具有相似小波特性的正交与双正交小波的压缩性能。
在基于小波变换的图像压缩方案中，嵌入式零树小波(EZW)编码能够很好地利用小波系数的特性使得输出的码流具有嵌入特性。论文在深入分析了EZW算法的原理、步骤、实现过程和优缺点的基础上，针对EZW算法计算复杂度高的缺陷，从探求算法中变换与编码同步实现的角度出发，提出了一种基于分块变换一融合的改进EZW算法。在上述理论工作的基础上，通过VC编程实现了该算法。实验结果表明，使用本算法，解码图像保持了与EZW算法相似的客观性能，但通过使用变换阶段的副产品一带峰值，可以简化零树扫描步骤，在一定程度上降低了算法执行时间，同时可实现真正意义上的子图像编码。
With the extension of image application,some new image compression and coding techniques which can not only achive high compression ratio and definition but also meet such demands by Progressive Transmission,and other applications are needed. Therebefore, compression and coding technique in image and video becomes a hot point in image research field.
In this paper, the digital image compression techniques based on wavelet transform are analyzed and summarized, the current state of the techniques is introduced and several directions of development are proposed. Some important problems such as the arichitecture of wavelet coder, the coding step and how to choose wavelet basis are discussed, some simulations with matlab wavelet toolbox is made to demonstrate. A conclusion that the difference in performance between orthnorgal wavelets and biorthnorgal wavelets were not as largr as we desired when they have familiar mathematical properties is also made.
This paper proposes an improved EZW algorithm based on Partition-transform-Merge computation. Stronger coupling and pipelining between the transform and the coding stages is made possible. The algorithm computes the sub_band_max for each sub-band as a by-product of the Partition-transform-Merge computation to improve the zero-tree checking process and reduce the computing complexities.
An extensive research on static image compression is presented in this paper. On the basis theoretical above, programming achieves corresponding algorithm, experimental results show that our new algorithm actually improves the execution time .
本文在对图像压缩编码理论与实际应用技术的的现状和发展趋势进行简要分析的基础上，从一定理论深度较为详细阐述了基于小波变换的静止图像压缩编码技术，重点探讨了编码器结构、编码步骤、小波基的选取以及影响压缩编码性能因素等几个关键问题。对基于图像压缩性能的小波特性进行了分析与仿真，通过仿真比较了具有相似小波特性的正交与双正交小波的压缩性能。
在基于小波变换的图像压缩方案中，嵌入式零树小波(EZW)编码能够很好地利用小波系数的特性使得输出的码流具有嵌入特性。论文在深入分析了EZW算法的原理、步骤、实现过程和优缺点的基础上，针对EZW算法计算复杂度高的缺陷，从探求算法中变换与编码同步实现的角度出发，提出了一种基于分块变换一融合的改进EZW算法。在上述理论工作的基础上，通过VC编程实现了该算法。实验结果表明，使用本算法，解码图像保持了与EZW算法相似的客观性能，但通过使用变换阶段的副产品一带峰值，可以简化零树扫描步骤，在一定程度上降低了算法执行时间，同时可实现真正意义上的子图像编码。
With the extension of image application,some new image compression and coding techniques which can not only achive high compression ratio and definition but also meet such demands by Progressive Transmission,and other applications are needed. Therebefore, compression and coding technique in image and video becomes a hot point in image research field.
In this paper, the digital image compression techniques based on wavelet transform are analyzed and summarized, the current state of the techniques is introduced and several directions of development are proposed. Some important problems such as the arichitecture of wavelet coder, the coding step and how to choose wavelet basis are discussed, some simulations with matlab wavelet toolbox is made to demonstrate. A conclusion that the difference in performance between orthnorgal wavelets and biorthnorgal wavelets were not as largr as we desired when they have familiar mathematical properties is also made.
This paper proposes an improved EZW algorithm based on Partition-transform-Merge computation. Stronger coupling and pipelining between the transform and the coding stages is made possible. The algorithm computes the sub_band_max for each sub-band as a by-product of the Partition-transform-Merge computation to improve the zero-tree checking process and reduce the computing complexities.
An extensive research on static image compression is presented in this paper. On the basis theoretical above, programming achieves corresponding algorithm, experimental results show that our new algorithm actually improves the execution time .
引文
[1] 胡栋．静止图像编码的基本方法与国际标准[M]．北京：北京邮电大学出版社，2003
[2] 刘政凯等．数字图像恢复与重建[M]．合肥：中国科技大学出版社，1989
[3] 沈兰荪．图像编码与异步传输[M]．北京：人民邮电出版社，1998
[4] Kunt, Murat, Ikonomopoulos, Athanassios. SECOND-GENERATION IMAGE-CODING TECHNIQUES. Proceedings of the IEEE, 1985, 73(4): 549-574
[5] J. M. Shapiro. Embedded image coding using zerotrees of wavelets coefficients. IEEE Trans. Signal Processing, Vol.41, No.12, pp.3445-2462, Dec. 1993
[6] A. Said and W. A. Pearlman. Anew, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Trans. Circuits and System for Video Technology, VOL. 6, No. 3, pp. 243-249, June 1996
[7] Pennebaker，William B．，Mitchell，Joan L．JPEG静止图像数据压缩标准．黎洪松等译．北京：学苑出版社，1996
[8] Wang Yao，Ostermann，Zhang Ya-Qin．视频处理与通信．候正信等译．北京：电子工业出版社，2003
[9] 杨品，钟玉琢译．MPEG运动图像压缩编码标准．北京：机械工业出版社，1995
[10] 何小海．图像通信[M]．西安：西安电子科技大学出版社，2005
[11] 戴善荣．数据压缩[M]．西安：西安电子科技大学出版社，2005
[12] 胡栋．二值图像编码的基本方法与国际标准[M]．北京：北京邮电大学出版社，2003
[13] 智艾娣．在JPEG压缩算法中选择量化表的尝试[J]，小型微型计算机系统，1997．9
[14] 蔡世杰，岳华，刘小燕．静止图像的压缩与编码JPEG[M]，南京大学出版社，1995
[15] 黄佳庆，翁默颖．一种基于子波变换德改进型零树量化编码算法[J]，华东师范大学学报，1999．9
[16] 唐朝京，雷箐．信息论与编码基础．长沙：国防科技大学出版社，2003
[17] 飞思科技产品研发中心．小波分析理论与MATLAB7实现．北京：电子工业出 版社，2005
[18] [美]崔锦泰著，程正兴译．小波分析导论．西安：西安交通大学出版社，1995
[19] 刘贵中，邸双亮．小波分析及其应用．西安：西安电子科技大学出版社，1992
[20] Mallat. S. A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Analysis and machine Intelligence, 1989, Vol. 11, pp. 674-693.
[15] Daubechies. I. Pro IEEE, 1996. 84, Where do wavelet come from?, IEEE, 1996. 84
[21] Mallat. S. A theory of multifrequency Channel Decompositionof image and wavelet Models, IEEE Trans. on ASSP, 1989. 37(12), 2091-2110
[22] Daubechies. I. Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied mathematics, 1988, Vol. 41, No. 11, pp. 909-996
[23] Cohen. A, Daubechies, I. and Feanvean, J., Bi-orthogonal bases of compactly supported wavelets. Comm.. Pure Appl. Math., 1992, Vol. 45, pp. 485-560.
[24] Marc Antonini, Michel Barlaud. Image Coding Using Wavelet Transform. IEEE Trans. On Image processing, 1992, 1(2):205-220
[25] 高文．多媒体数据压缩技术，北京：电子工业出版社，1994。
[26] Unser, M. Approximation power of bi-orthogonal wavelet expansions, IEEE Trans. on signal Processing, 1996, Vol. 44, pp. 519-527.
[27] Rioul. O. Regular wavelets: a discrete-time approach, IEEE Trans. on Signal processing, 1993, Vol. 41, pp. 3572-3579.
[28] Antonini. M. et. al., Image coding using wavelet transform, IEEE Trans. Image Proc., 1992, Vol. 1, pp. 205-220.
[29] Vetterli. M. and Herley, C. Wavelets and filter banks: Theory and design, IEEE Trans. Acoust. Speech signal proc., 1992, Vol. 40, No. 9, pp. 2207-2232.
[30] Villasenor. J. Belzer, B., Liao, J., Wavelet Filter Evaluation for Image Compression, IEEE Transactions on Image Processing, 1995, Vol. 2, pp. 1053-1060.
[31] Tay. D. B. H, Marusic. S, Palaniswami. M, Guang Deng; Mathematical properties of the two-parameter family of 9/7 biorthogonal filters, Circuits and Systems, 2004. ISCAS'04. Proceedings of the 2004 International Symposium on Volume 3, 23-26 May 2004 Page(s): Ⅲ- 569-72 Vol. 3
[32] Unser. M, Blu. T. Mathematical properties of the JPEG2000 wavelet filters, IEEE Transactions on Image Processing, 2003, Vol2. 9, pp. 1080-1090.
[33] 胡春玲．图像编码时小波基的选择，中国图像图形学报，1998．10
[34] Shapiro J M. Embedded image coding using zerotree of wavelet coefficients. IEEE Trans. Signal Processing, 1993, 41(12): 3445～3462.
[35] A. Said and W. A. Pearlman. Anew, fast, and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. VideoTechnol, vol. 6, pp. 243-250, June 1996.
[36] 严敬文，孙辉，张圣华．小波树结构快速矢量量化编码方法，中国图像图形学报，1997．8
[37] 郭田德，高自友．改进的静态图像零树编码算法，计算机学报，1997．7
[38] 杜笑平．一种新的零树图像编码，电讯技术，1997．10
[39] 夏勇，田杰，戴汝为．一种改进的零树小波图像压缩算法，软件学报，1999．6
[40] A. Zandi, J. Allen, E. Schwartz, and M. Boliek. CREW: Compression with reversible embedded wavelets, IEEE Data Compression Conference, Snowbird, UT, pp. 212-221, March 1995.
[41] L. D. Villasenor., B. Belzer, and J. Liao. "Wavelet filter evaluation for image compression", IEEE Trans. Image Processing, vol. 4. pp. 1053-1060, Aug. 1995.
[42] A. Said and W. A. Pearman. "An image multiresolution representation for lossless and lossy compression", IEEE Trans. Image Processing, vol, 5, pp. 1303-1310, Sept, 1996.
[43] M. J. Gormish, E. L. Schwartz, A. F. Keith, M. P. Boliek, and A. Zandi, "Lossless and nearly lossless compression of high-quality images", Proc. SPIE, vol. 3025, pp. 62-70, Mar. 1997.
[44] A. R. Calderbank, I. Daubechies, W. Swedens, andB. L. Yeo. "Wavelet transforms hat map integers to inte, Appl. Comput. Harmon. Anal, vol. 5, pp. 332-369, July 1998.
[45] M. D. Adams and F. Kossentini. "Low-complexity reversible integer-to-integer wavelet transforms for image coding" in Proc. IEEE Pacific Rim Conf. Communication, Computers, Signal Processing, Victoria, B. C. Canada, Aug. 1999, pp177-180.
[46] M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies. "Image coding using wavelet tranform," IEEE Trans. ImagProcessing, vol.1, no. 2, pp. 205-220, Apr. 1992.
[47] 张正阳．高性能图像编码研究[博士论文]．西安：西安电子科技大．1999
[2] 刘政凯等．数字图像恢复与重建[M]．合肥：中国科技大学出版社，1989
[3] 沈兰荪．图像编码与异步传输[M]．北京：人民邮电出版社，1998
[4] Kunt, Murat, Ikonomopoulos, Athanassios. SECOND-GENERATION IMAGE-CODING TECHNIQUES. Proceedings of the IEEE, 1985, 73(4): 549-574
[5] J. M. Shapiro. Embedded image coding using zerotrees of wavelets coefficients. IEEE Trans. Signal Processing, Vol.41, No.12, pp.3445-2462, Dec. 1993
[6] A. Said and W. A. Pearlman. Anew, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Trans. Circuits and System for Video Technology, VOL. 6, No. 3, pp. 243-249, June 1996
[7] Pennebaker，William B．，Mitchell，Joan L．JPEG静止图像数据压缩标准．黎洪松等译．北京：学苑出版社，1996
[8] Wang Yao，Ostermann，Zhang Ya-Qin．视频处理与通信．候正信等译．北京：电子工业出版社，2003
[9] 杨品，钟玉琢译．MPEG运动图像压缩编码标准．北京：机械工业出版社，1995
[10] 何小海．图像通信[M]．西安：西安电子科技大学出版社，2005
[11] 戴善荣．数据压缩[M]．西安：西安电子科技大学出版社，2005
[12] 胡栋．二值图像编码的基本方法与国际标准[M]．北京：北京邮电大学出版社，2003
[13] 智艾娣．在JPEG压缩算法中选择量化表的尝试[J]，小型微型计算机系统，1997．9
[14] 蔡世杰，岳华，刘小燕．静止图像的压缩与编码JPEG[M]，南京大学出版社，1995
[15] 黄佳庆，翁默颖．一种基于子波变换德改进型零树量化编码算法[J]，华东师范大学学报，1999．9
[16] 唐朝京，雷箐．信息论与编码基础．长沙：国防科技大学出版社，2003
[17] 飞思科技产品研发中心．小波分析理论与MATLAB7实现．北京：电子工业出 版社，2005
[18] [美]崔锦泰著，程正兴译．小波分析导论．西安：西安交通大学出版社，1995
[19] 刘贵中，邸双亮．小波分析及其应用．西安：西安电子科技大学出版社，1992
[20] Mallat. S. A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Analysis and machine Intelligence, 1989, Vol. 11, pp. 674-693.
[15] Daubechies. I. Pro IEEE, 1996. 84, Where do wavelet come from?, IEEE, 1996. 84
[21] Mallat. S. A theory of multifrequency Channel Decompositionof image and wavelet Models, IEEE Trans. on ASSP, 1989. 37(12), 2091-2110
[22] Daubechies. I. Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied mathematics, 1988, Vol. 41, No. 11, pp. 909-996
[23] Cohen. A, Daubechies, I. and Feanvean, J., Bi-orthogonal bases of compactly supported wavelets. Comm.. Pure Appl. Math., 1992, Vol. 45, pp. 485-560.
[24] Marc Antonini, Michel Barlaud. Image Coding Using Wavelet Transform. IEEE Trans. On Image processing, 1992, 1(2):205-220
[25] 高文．多媒体数据压缩技术，北京：电子工业出版社，1994。
[26] Unser, M. Approximation power of bi-orthogonal wavelet expansions, IEEE Trans. on signal Processing, 1996, Vol. 44, pp. 519-527.
[27] Rioul. O. Regular wavelets: a discrete-time approach, IEEE Trans. on Signal processing, 1993, Vol. 41, pp. 3572-3579.
[28] Antonini. M. et. al., Image coding using wavelet transform, IEEE Trans. Image Proc., 1992, Vol. 1, pp. 205-220.
[29] Vetterli. M. and Herley, C. Wavelets and filter banks: Theory and design, IEEE Trans. Acoust. Speech signal proc., 1992, Vol. 40, No. 9, pp. 2207-2232.
[30] Villasenor. J. Belzer, B., Liao, J., Wavelet Filter Evaluation for Image Compression, IEEE Transactions on Image Processing, 1995, Vol. 2, pp. 1053-1060.
[31] Tay. D. B. H, Marusic. S, Palaniswami. M, Guang Deng; Mathematical properties of the two-parameter family of 9/7 biorthogonal filters, Circuits and Systems, 2004. ISCAS'04. Proceedings of the 2004 International Symposium on Volume 3, 23-26 May 2004 Page(s): Ⅲ- 569-72 Vol. 3
[32] Unser. M, Blu. T. Mathematical properties of the JPEG2000 wavelet filters, IEEE Transactions on Image Processing, 2003, Vol2. 9, pp. 1080-1090.
[33] 胡春玲．图像编码时小波基的选择，中国图像图形学报，1998．10
[34] Shapiro J M. Embedded image coding using zerotree of wavelet coefficients. IEEE Trans. Signal Processing, 1993, 41(12): 3445～3462.
[35] A. Said and W. A. Pearlman. Anew, fast, and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. VideoTechnol, vol. 6, pp. 243-250, June 1996.
[36] 严敬文，孙辉，张圣华．小波树结构快速矢量量化编码方法，中国图像图形学报，1997．8
[37] 郭田德，高自友．改进的静态图像零树编码算法，计算机学报，1997．7
[38] 杜笑平．一种新的零树图像编码，电讯技术，1997．10
[39] 夏勇，田杰，戴汝为．一种改进的零树小波图像压缩算法，软件学报，1999．6
[40] A. Zandi, J. Allen, E. Schwartz, and M. Boliek. CREW: Compression with reversible embedded wavelets, IEEE Data Compression Conference, Snowbird, UT, pp. 212-221, March 1995.
[41] L. D. Villasenor., B. Belzer, and J. Liao. "Wavelet filter evaluation for image compression", IEEE Trans. Image Processing, vol. 4. pp. 1053-1060, Aug. 1995.
[42] A. Said and W. A. Pearman. "An image multiresolution representation for lossless and lossy compression", IEEE Trans. Image Processing, vol, 5, pp. 1303-1310, Sept, 1996.
[43] M. J. Gormish, E. L. Schwartz, A. F. Keith, M. P. Boliek, and A. Zandi, "Lossless and nearly lossless compression of high-quality images", Proc. SPIE, vol. 3025, pp. 62-70, Mar. 1997.
[44] A. R. Calderbank, I. Daubechies, W. Swedens, andB. L. Yeo. "Wavelet transforms hat map integers to inte, Appl. Comput. Harmon. Anal, vol. 5, pp. 332-369, July 1998.
[45] M. D. Adams and F. Kossentini. "Low-complexity reversible integer-to-integer wavelet transforms for image coding" in Proc. IEEE Pacific Rim Conf. Communication, Computers, Signal Processing, Victoria, B. C. Canada, Aug. 1999, pp177-180.
[46] M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies. "Image coding using wavelet tranform," IEEE Trans. ImagProcessing, vol.1, no. 2, pp. 205-220, Apr. 1992.
[47] 张正阳．高性能图像编码研究[博士论文]．西安：西安电子科技大．1999