基于小波的方向变换及其在图像压缩中的应用
|
摘要
近十几年来数字图像的数据量飞速增长，为数据的存储和传输带来了一定的困难。因此对图像进行压缩，降低数据量是十分必要的。在图像压缩中，重要的是如何在最大程度上恢复原始图象，尤其是图像纹理、轮廓这些细节信息的恢复。但是传统算法包括目前使用最广泛的基于小波的图像压缩编码算法，并不能十分有效的保留具有方向特征的纹理细节信息。近几年发展起来的的多尺度几何分析(multiresolution geometry analysis，MGA)方法是最优的稀疏信号表示方法，对高维空间中具有直线或曲线奇异性信号具有良好的检测性能，它充分利用了图像的几何特征，为图像压缩提供了新的途径。
本文首先从分析目前较有效的MGA工具Contourlet变换入手，探讨了Contourlet变换的实现过程，Contourlet变换结合了Laplacian Pyramid滤波器的多尺度分解功能和方向滤波器组(directional filter banks，DFB)的多方向分解功能。通过实验验证Contourlet变换具有良好的非线性逼近性能，但是其冗余度不利于图像压缩。基于这种情况，本文重点以方向滤波器组为纽带，结合小波分析提出了两种基于小波的方向变换的图像压缩编码方法。针对Contourlet变换的冗余主要产生于Laplacian Pyramid滤波器的这种情况，提出了基于WBCT的SPITH压缩编码方法，它首先以小波做为多尺度分解工具并对其高频系数用DFB进行方向分解形成WBCT，再采用SPITH编码作为变换系数的压缩编码算法。实验结果表明将其应用于图像压缩可以更好的识别图像的方向特征，保留更多的纹理。由于WBCT会在平滑区域引入瑕玷，因此对其进一步优化，实现了基于小波的均衡方向变换(WUDFB)，该变换以性能更良好的均衡方向滤波器组代替方向滤波器组，有效抑制了瑕玷的产生，对变换后系数进行SPECK编码，将其用于压缩后恢复图像较WBCT编码恢复的图像在平滑区域的视觉效果有一定的改善。
Recently, the amount of image data increase quickly, this brings some problems for data storage and transport. Thus it's very necessary to compress the image in order to decrease the data amount. In image compression, we focus on how to reconstruct the original image with least distortion, especially on the retain of textures and contours. But the traditional algorithms include the most popular image coding algorithms based on wavelet can not restore the detailed texture information which has distinct directional property very effectively. The multiresolution geometry analysis (MGA) developed in recent years is the best sparse signal expression method, it has a good detect ability for the lines and curves in high dimensional space. It takes advantage of the image's geometry property, and provides new ways for image compression.
This paper first starts with the popular MGA tools-contourlet transform, its
construct procedure will be discussed. Contourlet transform combines the multiresolution decomposition function of laplacian filters and the multidirection decomposition function of directional filter banks. The experiment results show that contourlet transform has good nonlinear approach ability, but its redundancy is a block for image compression. Thus takes the DFB as a tie and combines with the wavelet transform theory, this paper proposes two kind of compression encode methods for wavelet based directional transform. To overcome the redundancy of contourlet, we discard the laplacian pyramid filter banks which could induce redundancy. By using the wavelet for multiresolution decomposition and then add DFB to high frequency subbands for directional decomposition, the wavelet based contourlet transform (WBCT) is implemented. Accordingly the WBCT-based SPITH compression coding method is proposed, the experiment results prove that the method can identify the image directional character much better, and restore more textures. Since WBCT can bring artifacts to the smooth area of an image, it is optimized by
本文首先从分析目前较有效的MGA工具Contourlet变换入手，探讨了Contourlet变换的实现过程，Contourlet变换结合了Laplacian Pyramid滤波器的多尺度分解功能和方向滤波器组(directional filter banks，DFB)的多方向分解功能。通过实验验证Contourlet变换具有良好的非线性逼近性能，但是其冗余度不利于图像压缩。基于这种情况，本文重点以方向滤波器组为纽带，结合小波分析提出了两种基于小波的方向变换的图像压缩编码方法。针对Contourlet变换的冗余主要产生于Laplacian Pyramid滤波器的这种情况，提出了基于WBCT的SPITH压缩编码方法，它首先以小波做为多尺度分解工具并对其高频系数用DFB进行方向分解形成WBCT，再采用SPITH编码作为变换系数的压缩编码算法。实验结果表明将其应用于图像压缩可以更好的识别图像的方向特征，保留更多的纹理。由于WBCT会在平滑区域引入瑕玷，因此对其进一步优化，实现了基于小波的均衡方向变换(WUDFB)，该变换以性能更良好的均衡方向滤波器组代替方向滤波器组，有效抑制了瑕玷的产生，对变换后系数进行SPECK编码，将其用于压缩后恢复图像较WBCT编码恢复的图像在平滑区域的视觉效果有一定的改善。
Recently, the amount of image data increase quickly, this brings some problems for data storage and transport. Thus it's very necessary to compress the image in order to decrease the data amount. In image compression, we focus on how to reconstruct the original image with least distortion, especially on the retain of textures and contours. But the traditional algorithms include the most popular image coding algorithms based on wavelet can not restore the detailed texture information which has distinct directional property very effectively. The multiresolution geometry analysis (MGA) developed in recent years is the best sparse signal expression method, it has a good detect ability for the lines and curves in high dimensional space. It takes advantage of the image's geometry property, and provides new ways for image compression.
This paper first starts with the popular MGA tools-contourlet transform, its
construct procedure will be discussed. Contourlet transform combines the multiresolution decomposition function of laplacian filters and the multidirection decomposition function of directional filter banks. The experiment results show that contourlet transform has good nonlinear approach ability, but its redundancy is a block for image compression. Thus takes the DFB as a tie and combines with the wavelet transform theory, this paper proposes two kind of compression encode methods for wavelet based directional transform. To overcome the redundancy of contourlet, we discard the laplacian pyramid filter banks which could induce redundancy. By using the wavelet for multiresolution decomposition and then add DFB to high frequency subbands for directional decomposition, the wavelet based contourlet transform (WBCT) is implemented. Accordingly the WBCT-based SPITH compression coding method is proposed, the experiment results prove that the method can identify the image directional character much better, and restore more textures. Since WBCT can bring artifacts to the smooth area of an image, it is optimized by
引文
[1] David Salomon著，吴乐南译．数据压缩原理与应用(第二版)．电子工业出版社，2003年9月第1版．
[2] 张旭东，卢国栋，冯健编著．图像编码基础和小波压缩技术——算法原理与标准．清华大学出版社，2004年3月第1版．
[3] 赵荣椿，赵忠明等编著．数字图像处理导论．西北工业大学出版社，2000年8月第1版．
[4] 余成波编．信息论与编码．重庆大学出版社，2002年6月第1版．
[5] 朱雪龙编著．应用信息论基础．清华大学出版社，2001年3月．
[6] 彭玉华．小波变换与工程应用．科学出版社，2002年2月．
[7] [美]崔锦泰著，程正兴译．小波分析导论．西安交通大学出版社，1995年1月．
[8] Wallace G. K. The JEPG: still picture compression standard. Communi. Of the ACM, 1991, 34(4): 30～44.
[9] Majid Rabbani and Rajan Joshi. An overview of the JPEG2000 still image compression standard. Signal Processing: Image Communication, 2002, 17(1): 3～48.
[10] S. Mallat. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal. Machine Intell. 1989, 11(7): 674～693.
[11] J. M. Shapiro. Embedded image coding using zerotrees of wavelet coefficient, IEEE Trans. On Signal Processing, 1993, 41(12): 3445～3462.
[12] A. Said and W. Pearlman. A new, fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees. IEEE Trans. Ciucuits Syst. Vedio Technol, 1996, 6(3): 243～250.
[13] David Taubman. High Performance Scalable Image Compression with EBCOT. IEEE Trans. on Image Processing, 2000, 9(7): 1158-1170.
[14] 焦李成，谭山．图像的多尺度几何分析：回顾和展望．电子学报，2003，31(12A)：1975～1981．
[15] Candes. E. J. Ridgelets: Theory and Applications. PhDThesis, Stanford University,1998.
[16] 隆刚，肖磊等．Curvelet变换在图像处理中的应用综述．计算机研究与发展，2005，42(8)，1331～1337．
[17] Donoho. D.L. Duncan M R. Digital curvelet transform: stategy, implementation and experiment. In: Proc of SPIE, 2000, 4056, 12～29.
[18] 倪伟，郭宝龙等．图像多尺度几何分析新进展：Contourlet．计算机科学，2006，33 (2), 234-236.
[19] DO. M.N. Directional multiresolution image representation. PhD Thesis, EPFL, Lausanne, Switzerland ,2001.
[20] DO. M. N, Vetterli.M. Contourlets: a new directional multiresolution image representation. Signal, Systems and Computers. 2002, 1: 497-501.
[21] Tsuhan Chen, P.P.Vaidyanathan. Recent Developments in Multidimensional Multirate Systems. IEEE Trans. Ciucuits Syst. Vedio Technol, 1993 , 3 (2): 116-136.
[22] D. B. H. Tay, N. G. Kingsbury. Flexible design of multidimentional perfect reconstruction FIR 2-band filter using transformations of variables. IEEE Trans. Image Proc. 1993, 2(4), 466-480.
[23] R. H. Bamberger, M. J. T. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Trans. Signal Proc . 1992, 40(4), 882-893.
[24] Sang-II Park, Mark. J. T. Smith. Improved structure of maximally decimated directional filter banks for spatial image analysis. IEEE Trans. Image Proc. 2004,13(11), 1424-1431.
[25] M. N. Do, M.Vetterli. Framing pyramids. IEEE Trans. Signal Proc. 2003, 51(9), 2329-2342.
[26] P. J. Burt, E. H. Adelson. The laplacian pyramid as a compact image code. IEEE Trans. Commun. 1983, 31(4), 532-5401.
[27] 胡广书编著。数学信号处理──理论、算法与实现。北京,清华大学出版社,1997.
[28] R. Eslami, H. Radha. Wavelet-Based contourlet transform and its application to image coding. Proc of IEEE International Conference on Image Processing, Singapore, 2004, 3189-3192
[29] Eslami. R, H. Radha. On low bit rate coding using the contourlet tansform. Signal Systems and Computers, 2003, 2,1524-1528.
[30] Truong. T. Nguyen, Soontorn Oraintara. Multiresolution direction filterbanks: theory, design and appliations. IEEE Trans. Signal Proc . 2005, 53(10), 3895-3905.
[31] Asad Islam, W. A. Pearman. An embedded and efficient low complexity hierarchical image code. Proc of SPIE on Visual Communications and Image Processing. 1999, 3635, 294-305.
[32] F. W. Wheeler, W. A. Pearlman. SPIHT Image Compression without Lists. IEEE Int. Conf, on Acoustics, Speech and Signal Processing (ICASSP 2000), Istanbul, Turkey. 2000, 5-9.
[2] 张旭东，卢国栋，冯健编著．图像编码基础和小波压缩技术——算法原理与标准．清华大学出版社，2004年3月第1版．
[3] 赵荣椿，赵忠明等编著．数字图像处理导论．西北工业大学出版社，2000年8月第1版．
[4] 余成波编．信息论与编码．重庆大学出版社，2002年6月第1版．
[5] 朱雪龙编著．应用信息论基础．清华大学出版社，2001年3月．
[6] 彭玉华．小波变换与工程应用．科学出版社，2002年2月．
[7] [美]崔锦泰著，程正兴译．小波分析导论．西安交通大学出版社，1995年1月．
[8] Wallace G. K. The JEPG: still picture compression standard. Communi. Of the ACM, 1991, 34(4): 30～44.
[9] Majid Rabbani and Rajan Joshi. An overview of the JPEG2000 still image compression standard. Signal Processing: Image Communication, 2002, 17(1): 3～48.
[10] S. Mallat. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal. Machine Intell. 1989, 11(7): 674～693.
[11] J. M. Shapiro. Embedded image coding using zerotrees of wavelet coefficient, IEEE Trans. On Signal Processing, 1993, 41(12): 3445～3462.
[12] A. Said and W. Pearlman. A new, fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees. IEEE Trans. Ciucuits Syst. Vedio Technol, 1996, 6(3): 243～250.
[13] David Taubman. High Performance Scalable Image Compression with EBCOT. IEEE Trans. on Image Processing, 2000, 9(7): 1158-1170.
[14] 焦李成，谭山．图像的多尺度几何分析：回顾和展望．电子学报，2003，31(12A)：1975～1981．
[15] Candes. E. J. Ridgelets: Theory and Applications. PhDThesis, Stanford University,1998.
[16] 隆刚，肖磊等．Curvelet变换在图像处理中的应用综述．计算机研究与发展，2005，42(8)，1331～1337．
[17] Donoho. D.L. Duncan M R. Digital curvelet transform: stategy, implementation and experiment. In: Proc of SPIE, 2000, 4056, 12～29.
[18] 倪伟，郭宝龙等．图像多尺度几何分析新进展：Contourlet．计算机科学，2006，33 (2), 234-236.
[19] DO. M.N. Directional multiresolution image representation. PhD Thesis, EPFL, Lausanne, Switzerland ,2001.
[20] DO. M. N, Vetterli.M. Contourlets: a new directional multiresolution image representation. Signal, Systems and Computers. 2002, 1: 497-501.
[21] Tsuhan Chen, P.P.Vaidyanathan. Recent Developments in Multidimensional Multirate Systems. IEEE Trans. Ciucuits Syst. Vedio Technol, 1993 , 3 (2): 116-136.
[22] D. B. H. Tay, N. G. Kingsbury. Flexible design of multidimentional perfect reconstruction FIR 2-band filter using transformations of variables. IEEE Trans. Image Proc. 1993, 2(4), 466-480.
[23] R. H. Bamberger, M. J. T. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Trans. Signal Proc . 1992, 40(4), 882-893.
[24] Sang-II Park, Mark. J. T. Smith. Improved structure of maximally decimated directional filter banks for spatial image analysis. IEEE Trans. Image Proc. 2004,13(11), 1424-1431.
[25] M. N. Do, M.Vetterli. Framing pyramids. IEEE Trans. Signal Proc. 2003, 51(9), 2329-2342.
[26] P. J. Burt, E. H. Adelson. The laplacian pyramid as a compact image code. IEEE Trans. Commun. 1983, 31(4), 532-5401.
[27] 胡广书编著。数学信号处理──理论、算法与实现。北京,清华大学出版社,1997.
[28] R. Eslami, H. Radha. Wavelet-Based contourlet transform and its application to image coding. Proc of IEEE International Conference on Image Processing, Singapore, 2004, 3189-3192
[29] Eslami. R, H. Radha. On low bit rate coding using the contourlet tansform. Signal Systems and Computers, 2003, 2,1524-1528.
[30] Truong. T. Nguyen, Soontorn Oraintara. Multiresolution direction filterbanks: theory, design and appliations. IEEE Trans. Signal Proc . 2005, 53(10), 3895-3905.
[31] Asad Islam, W. A. Pearman. An embedded and efficient low complexity hierarchical image code. Proc of SPIE on Visual Communications and Image Processing. 1999, 3635, 294-305.
[32] F. W. Wheeler, W. A. Pearlman. SPIHT Image Compression without Lists. IEEE Int. Conf, on Acoustics, Speech and Signal Processing (ICASSP 2000), Istanbul, Turkey. 2000, 5-9.