小波零树编码在图像压缩及其去噪中的应用研究
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摘要
图像压缩编码技术是多媒体通信技术中的关键技术，近年来各种压缩标准应运而生(例如JPEG2000和MPEG-4)，这两个标准都推荐使用小波变换技术来编码。本文主要研究了小波零树编码在图像压缩及其去噪中的应用，提出了一些改进算法；最后对各种基于小波零树思想的压缩编码方法进行比较和总结。
本文首先阐述了各种图像压缩方法和视频图像压缩标准，用于图像压缩的小波变换基本理论；其次介绍了基于小波零树编码思想的两种成功的图像编码算法嵌入式零树编码算法EZW和多层次零树编码算法SPIHT。本文提出了两种改进算法，算法一：DPCM、零树和游程相结合的改进算法；算法二：DPCM、零树和矢量量化相结合的改进算法；仿真结果表明这两种改进算法无论从客观信噪比还是从主观质量都取得了很好的效果，从而证明改进方案是有实际意义的；然后是含噪图像的小波零树编码去噪研究，软门限去噪以后采用第一种改进算法对图像进一步压缩，解压后的仿真结果显示噪声得到了很好的去除；最后是对基于零树编码思想的各种编码方法进行总结、分析和比较。
Image compression coding plays a very important role in the multimedia communication technology.Various compression standards,such as JPEG2000 and MPEG-4, have appeared.Wavelet transform technology is used both in JPEG2000 and MPEG-4.In this paper,firstly,I mainly discuss the problem about wavelet zerotree in image coding and two improved algorithms are proposed.Secondly,we compress image combined with deleting noise by wavelet zerotree algorithm.Lastly,several compessing methods based on wavelet zerotree idea are compared and summarized.
Firstly,all kinds of image compressing methods and image coding standards are reviewed. Furthermore I introduce the elementary wavelet theory. Secondly,two classical wavelet image coding algorithm based wavelet zerotree idea are introduced and two improved algorithms are proposed.The first algorithm is that we combine runlength coding and zerotree coding in which LL band coefficients are coded lonely with DPCM.The second algorithm is the zerotree algorithm with vector quantization is combined with LL band coefficients alone coding with DPCM.The simulating results show they can get better performance both in PSNR and subjective quality.Thirdly, we make research on how to compress image combined with deleting noise by zerotree algorithm.First we use soft-threshold method to denoise image with noise,and then the first improved zerotree algorithm is used to compress image.Simulating results show that the subjective quality of the decoded image is good.Lastly,we compare,analyse and summarize all kinds of compress
ing methods based on wavelet zerotree idea.
本文首先阐述了各种图像压缩方法和视频图像压缩标准，用于图像压缩的小波变换基本理论；其次介绍了基于小波零树编码思想的两种成功的图像编码算法嵌入式零树编码算法EZW和多层次零树编码算法SPIHT。本文提出了两种改进算法，算法一：DPCM、零树和游程相结合的改进算法；算法二：DPCM、零树和矢量量化相结合的改进算法；仿真结果表明这两种改进算法无论从客观信噪比还是从主观质量都取得了很好的效果，从而证明改进方案是有实际意义的；然后是含噪图像的小波零树编码去噪研究，软门限去噪以后采用第一种改进算法对图像进一步压缩，解压后的仿真结果显示噪声得到了很好的去除；最后是对基于零树编码思想的各种编码方法进行总结、分析和比较。
Image compression coding plays a very important role in the multimedia communication technology.Various compression standards,such as JPEG2000 and MPEG-4, have appeared.Wavelet transform technology is used both in JPEG2000 and MPEG-4.In this paper,firstly,I mainly discuss the problem about wavelet zerotree in image coding and two improved algorithms are proposed.Secondly,we compress image combined with deleting noise by wavelet zerotree algorithm.Lastly,several compessing methods based on wavelet zerotree idea are compared and summarized.
Firstly,all kinds of image compressing methods and image coding standards are reviewed. Furthermore I introduce the elementary wavelet theory. Secondly,two classical wavelet image coding algorithm based wavelet zerotree idea are introduced and two improved algorithms are proposed.The first algorithm is that we combine runlength coding and zerotree coding in which LL band coefficients are coded lonely with DPCM.The second algorithm is the zerotree algorithm with vector quantization is combined with LL band coefficients alone coding with DPCM.The simulating results show they can get better performance both in PSNR and subjective quality.Thirdly, we make research on how to compress image combined with deleting noise by zerotree algorithm.First we use soft-threshold method to denoise image with noise,and then the first improved zerotree algorithm is used to compress image.Simulating results show that the subjective quality of the decoded image is good.Lastly,we compare,analyse and summarize all kinds of compress
ing methods based on wavelet zerotree idea.
引文
[1] 夏良正．数字图像处理．东南大学出版社，1999
[2] 任明武，杨静宇著．数字图像压缩编码讲义．南京理工大学出版社，2002
[3] 彭玉华．小波变换与工程应用．科学出版社，1999
[4] 秦前清，杨宗凯．实用小波分析．西安电子科技大学出版社，1994
[5] 冉启文．小波分析方法及其应用．哈尔滨工业大学出版社，1995
[6] Kenneth. R. Castleman．数字图像处理．电子科技大学出版社，1998
[7] 吴乐南．数据压缩的原理及应用．电子工业出版社，1996
[8] Jerome M. Shapiro, "Embedded Image Coding Using Zerotrees of Wavelet Coefficients", IEEE Trans. On Signal Processing, 1993, 41(12): 3445-3462
[9] Amir Said, William A. Pearlman, "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(3): 243-250
[10] Zixiang Xiong, Kannan Ramchandran, Michael T. Orchard, "Space-Frequency Quantization for Wavelet Image Coding", IEEE Trans. On Image Processing, 1997, 6(5): 677-693
[11] Zixiang Xiong, Kannan Ramchandran, Michael T. Orchard, "Wavelet Packet Image Coding Using Space-Frequency Quantization", IEEE Trans. On Image Processing, 1998, 7(6): 892-898
[12] Francois G. Meyer, Amir Z. Averbuch, Jan-Olov Stromberg, "Fast Adaptive Wavelet Packet Image Compression", IEEE Trans. On Image Processing, 2000, 9(5): 792-780
[13] N. M. Rajpoot, E G. Meyer, R. G. Wilson, R. R. Coifman, "On Zerotree Quantization for Embedded Wavelet Packet Image Coding", IEEE Trans. On Image Processing, 1999, 9(8): 283-287
[14] Witten H, Neal R, Cleary J G, "Arithmetic coding for Data Comopressing", Comm. ACM, 1987, 30(6): 520-540
[15] J. H. Conway, N. J. A. Sloane, "Fast Quantizing and Decoding Algorithms for Lattice Quantizers and Codes", IEEE Information Theory, 1982, 28(2): 227-232
[16] Donoho D L, "De-noising via soft-thresholding", IEEE Trans. Information Theory, 1995, Vol. 41, No. 3: 613-627
[17] 陆锦辉，王崇彦．信息论．南京理工大学出版社，1996
[18] 黄卓君，马争鸣．“一种零树与游程相结合的小波图像编码方法”．中国图像图形学报．2001，Vol．6(A)，No．11：1118-1124
[19] 刘九芬，黄达人．“基于零树、金字塔格型矢量量化的小波图像编码”．中国图像图形学报．2001，Vol．6(A)，No．4：329-332
[20] 刘九芬，黄达人．“基于金字塔格型矢量量化的多尺度图像编码”．浙江大学学报(理学版)，2000，27(2)：152-158
[21] 高西奇，连乃祥，邹采荣．“基于格型矢量量化的小波零树图像编码方法”．东南大学学报．1999，Vol．29，No．5：41-46
[22] 杨云峰，苏志勋，钟似分．“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, Vol．6(A)，No．6：542-545
[23] 乔世杰，智贵连．“一种快速的小波变换图像编码算法”．中国图像图形学报．2001，Vol．6(A)，No．5：434-438
[24] 王祥林，林行刚，吴国威．“采用格型矢量量化的小波图像编码方法”．清华大学学报(自然科学版)．1997，Vol(37)，No．10：69-71
[25] 王嘉，余松昱．“一种改进的基于零树集合的小波图像压缩算法”．数据采集与处理．2000，Vol．15，No．1：18-22
[26] 徐佩霞，孙功宪．小波分析与应用实例．中国科学技术大学出版社，1996
[27] 李弼程，胡宗云．“基于小波变换的图像矢量量化”．信号处理．2000，Vol．16．No．1：32-35
[28] 柳斌，田金文，柳健．“一种基于零树量化的小波图像压缩方法”．华中理工大学学报．2000，Vol．28，No．3：68-70
[29] 张哓娣，刘贵忠，曾召华，胡波．“新一代的静止图像压缩标准JPEG2000”．电信科学．2001，No．5：20-23
[30] 余越，薛永林，李凤亭，葛成辉．“基于软门限去噪的图像压缩编码研究”．中国国图像图形学报．2001，Vol．6，No．1：46-50
[31] 戴卫恒，姚峺峺．“带噪图像的小波零树压缩研究”．系统工程与电子技术．2001，Vol．23．No．7：21-23
[32] 薛哓辉，高文，冯英俊．“基于小波变换的静止图像压缩系统”．宇航学报．1997，Vol．18．No．1：67-75
[33] 冉启文，冯英俊．“小波和小波包算法与图像压缩”．数理统计与管理．1999，Vol．18．No．6：54-57
[34] 杜笑平．“一种新的小波变换零树图像编码”．电讯技术．1997、Vol．37，No．5：45-49
[35] 王向阳，杨红颜．“基于多阀值与嵌入零树小波的图像压缩算法”．通信学报．2001，Vol．22，No．12：88-93
[36] 李龙云．“利用小波包最优基进行图像数据压缩”．山东工业大学学报．2001，Vol．31．No．1：30-34
[37] 张素文，杭小庆，王天珍．“零树+游程的编码方法在数字摄影图像压缩中的应用”．测绘学报．2001，No．7：12-14
[38] 彭嘉维．“嵌入式图像编码的高效性与实现”．华中科技大学学报．2001，Vol．29，No．9：95-98
[39] 张素文，杭小庆，王天珍．“一种改进的零树编码方法”．武汉理工大学学报(信息与管理工程版)．2001，Vol．23，No．9：9-12
[40] 夏勇，田捷，戴汝为．“一种改进的零树小波图像压缩算法”．软件学报．1999，Vol．10．No．6：626-630
[41] 沈贵明，刘劲松．“应用小波变换技术的图像噪声消除新方法”．厦门大学学报(自然科学版)．2000，Vol．20，No．5：612-616
[42] 赵红诒．“基于小波变换阀值的信号去噪”．现代雷达．2001，No．4：37-39
[43] 沈敏，朱淼良，杜世陪．“基于小波变换的自适应算术编码方法”．1999，Vol．28，No．2：39-42
[44] Anotonini M, Barlaud M, Mathieu P, "Image coding using wavelet transform", IEEE Trans. On Image Processing, 1992, 1: 205-220
[45] M. Antonini, "Image Coding Using Vector Quantization in The Wavelet Transform Domain", Proc IEEE ICASSP, 1990: 2297-2300
[46] M. Effros, "Zerotree design for image compression: Toward weighted universal zerotree coding", IEEE Intl. Conf. On Image Processing, November 1997
[47] F. G. Meyer, A. Z. Averbuch, J-O. Stromberg, R. R. Coifman, "Fast wavelet packet image compression, Data Compression Conferenee-DCC'98,1998
[48] N. M. Rajpoot, E G. Meyer, Coifman, "Wavelet packet image coding using compatible zerotree quantization, Technical Report, Dept. of Computer Science, Yale University, New Haven(1999)
[49] Rioul O, et al. "Wavelets and signal processing", IEEE SP Magazine, 1991, (10).
[50] S. A. Martucci et al. "A Zerotree wavelet video coder", IEEE Trans. On Circuits and Systems ffor video Technology. 1997, FEB. 7(1): 109-118
[51] Thomas Sikora, "The Mpeg-4 video standard vertification model", IEEE Trans. On Circuits and Systems for Video Technology, 1997, Vol. 7, No. 1
[52] K. Clinkler, "Very low bit-rate wavelet video coding", IEEE Journal on Areas in Comm, 1998, Vol. 16, No. 1
[53] I. Daubechies, "Orthonormal bases of compactly supported wavelets", Comm. On Pure and Appl. Math., 1988, 11: 674-693
[54] Jon K. Rogers and Pamela C. Cosman, "Wavelet Zerotree Image Compression with Packetization", IEEE Trans. On Signal Processing letters, 1998, Vol. 5, No. 5: 105-107
[55] David Taubman, "High Performance Scalable Image Compression with EBCOT", IEEE Trans. On Image Processing, 2000, Vol. 9, No. 7: 1158-1170
[56] Christos Chrysafis, Antonio Ortega, "Line-Based, Reduced Memory, Wavelet Image. Compression", IEEE Trans. 2000, Vol. 9, No. 3: 378-388
[57] Niranjan Damera-Venkata, Thomas D. Kite, Kite Wilson S. Geisler, Brian L. Evans, Alan C. Bovik, "Image Quality Assessment Based on a Degradation Model", IEEE Trans. On Image Processing, Vol. 9, No. 4: 636-649
[2] 任明武，杨静宇著．数字图像压缩编码讲义．南京理工大学出版社，2002
[3] 彭玉华．小波变换与工程应用．科学出版社，1999
[4] 秦前清，杨宗凯．实用小波分析．西安电子科技大学出版社，1994
[5] 冉启文．小波分析方法及其应用．哈尔滨工业大学出版社，1995
[6] Kenneth. R. Castleman．数字图像处理．电子科技大学出版社，1998
[7] 吴乐南．数据压缩的原理及应用．电子工业出版社，1996
[8] Jerome M. Shapiro, "Embedded Image Coding Using Zerotrees of Wavelet Coefficients", IEEE Trans. On Signal Processing, 1993, 41(12): 3445-3462
[9] Amir Said, William A. Pearlman, "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(3): 243-250
[10] Zixiang Xiong, Kannan Ramchandran, Michael T. Orchard, "Space-Frequency Quantization for Wavelet Image Coding", IEEE Trans. On Image Processing, 1997, 6(5): 677-693
[11] Zixiang Xiong, Kannan Ramchandran, Michael T. Orchard, "Wavelet Packet Image Coding Using Space-Frequency Quantization", IEEE Trans. On Image Processing, 1998, 7(6): 892-898
[12] Francois G. Meyer, Amir Z. Averbuch, Jan-Olov Stromberg, "Fast Adaptive Wavelet Packet Image Compression", IEEE Trans. On Image Processing, 2000, 9(5): 792-780
[13] N. M. Rajpoot, E G. Meyer, R. G. Wilson, R. R. Coifman, "On Zerotree Quantization for Embedded Wavelet Packet Image Coding", IEEE Trans. On Image Processing, 1999, 9(8): 283-287
[14] Witten H, Neal R, Cleary J G, "Arithmetic coding for Data Comopressing", Comm. ACM, 1987, 30(6): 520-540
[15] J. H. Conway, N. J. A. Sloane, "Fast Quantizing and Decoding Algorithms for Lattice Quantizers and Codes", IEEE Information Theory, 1982, 28(2): 227-232
[16] Donoho D L, "De-noising via soft-thresholding", IEEE Trans. Information Theory, 1995, Vol. 41, No. 3: 613-627
[17] 陆锦辉，王崇彦．信息论．南京理工大学出版社，1996
[18] 黄卓君，马争鸣．“一种零树与游程相结合的小波图像编码方法”．中国图像图形学报．2001，Vol．6(A)，No．11：1118-1124
[19] 刘九芬，黄达人．“基于零树、金字塔格型矢量量化的小波图像编码”．中国图像图形学报．2001，Vol．6(A)，No．4：329-332
[20] 刘九芬，黄达人．“基于金字塔格型矢量量化的多尺度图像编码”．浙江大学学报(理学版)，2000，27(2)：152-158
[21] 高西奇，连乃祥，邹采荣．“基于格型矢量量化的小波零树图像编码方法”．东南大学学报．1999，Vol．29，No．5：41-46
[22] 杨云峰，苏志勋，钟似分．“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, Vol．6(A)，No．6：542-545
[23] 乔世杰，智贵连．“一种快速的小波变换图像编码算法”．中国图像图形学报．2001，Vol．6(A)，No．5：434-438
[24] 王祥林，林行刚，吴国威．“采用格型矢量量化的小波图像编码方法”．清华大学学报(自然科学版)．1997，Vol(37)，No．10：69-71
[25] 王嘉，余松昱．“一种改进的基于零树集合的小波图像压缩算法”．数据采集与处理．2000，Vol．15，No．1：18-22
[26] 徐佩霞，孙功宪．小波分析与应用实例．中国科学技术大学出版社，1996
[27] 李弼程，胡宗云．“基于小波变换的图像矢量量化”．信号处理．2000，Vol．16．No．1：32-35
[28] 柳斌，田金文，柳健．“一种基于零树量化的小波图像压缩方法”．华中理工大学学报．2000，Vol．28，No．3：68-70
[29] 张哓娣，刘贵忠，曾召华，胡波．“新一代的静止图像压缩标准JPEG2000”．电信科学．2001，No．5：20-23
[30] 余越，薛永林，李凤亭，葛成辉．“基于软门限去噪的图像压缩编码研究”．中国国图像图形学报．2001，Vol．6，No．1：46-50
[31] 戴卫恒，姚峺峺．“带噪图像的小波零树压缩研究”．系统工程与电子技术．2001，Vol．23．No．7：21-23
[32] 薛哓辉，高文，冯英俊．“基于小波变换的静止图像压缩系统”．宇航学报．1997，Vol．18．No．1：67-75
[33] 冉启文，冯英俊．“小波和小波包算法与图像压缩”．数理统计与管理．1999，Vol．18．No．6：54-57
[34] 杜笑平．“一种新的小波变换零树图像编码”．电讯技术．1997、Vol．37，No．5：45-49
[35] 王向阳，杨红颜．“基于多阀值与嵌入零树小波的图像压缩算法”．通信学报．2001，Vol．22，No．12：88-93
[36] 李龙云．“利用小波包最优基进行图像数据压缩”．山东工业大学学报．2001，Vol．31．No．1：30-34
[37] 张素文，杭小庆，王天珍．“零树+游程的编码方法在数字摄影图像压缩中的应用”．测绘学报．2001，No．7：12-14
[38] 彭嘉维．“嵌入式图像编码的高效性与实现”．华中科技大学学报．2001，Vol．29，No．9：95-98
[39] 张素文，杭小庆，王天珍．“一种改进的零树编码方法”．武汉理工大学学报(信息与管理工程版)．2001，Vol．23，No．9：9-12
[40] 夏勇，田捷，戴汝为．“一种改进的零树小波图像压缩算法”．软件学报．1999，Vol．10．No．6：626-630
[41] 沈贵明，刘劲松．“应用小波变换技术的图像噪声消除新方法”．厦门大学学报(自然科学版)．2000，Vol．20，No．5：612-616
[42] 赵红诒．“基于小波变换阀值的信号去噪”．现代雷达．2001，No．4：37-39
[43] 沈敏，朱淼良，杜世陪．“基于小波变换的自适应算术编码方法”．1999，Vol．28，No．2：39-42
[44] Anotonini M, Barlaud M, Mathieu P, "Image coding using wavelet transform", IEEE Trans. On Image Processing, 1992, 1: 205-220
[45] M. Antonini, "Image Coding Using Vector Quantization in The Wavelet Transform Domain", Proc IEEE ICASSP, 1990: 2297-2300
[46] M. Effros, "Zerotree design for image compression: Toward weighted universal zerotree coding", IEEE Intl. Conf. On Image Processing, November 1997
[47] F. G. Meyer, A. Z. Averbuch, J-O. Stromberg, R. R. Coifman, "Fast wavelet packet image compression, Data Compression Conferenee-DCC'98,1998
[48] N. M. Rajpoot, E G. Meyer, Coifman, "Wavelet packet image coding using compatible zerotree quantization, Technical Report, Dept. of Computer Science, Yale University, New Haven(1999)
[49] Rioul O, et al. "Wavelets and signal processing", IEEE SP Magazine, 1991, (10).
[50] S. A. Martucci et al. "A Zerotree wavelet video coder", IEEE Trans. On Circuits and Systems ffor video Technology. 1997, FEB. 7(1): 109-118
[51] Thomas Sikora, "The Mpeg-4 video standard vertification model", IEEE Trans. On Circuits and Systems for Video Technology, 1997, Vol. 7, No. 1
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[53] I. Daubechies, "Orthonormal bases of compactly supported wavelets", Comm. On Pure and Appl. Math., 1988, 11: 674-693
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