基于小波变换和人眼视觉特性的图像压缩新方法
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摘要
本文着重对基于小波变换算法及人眼视觉特性的图像压缩及其计算机实现进行了研究。包含的内容主要有以下几方面：
论文首先介绍了课题的研究背景和图像压缩方面的有关情况，包括图像压缩的基本原理和常用方法。通过进行分析比较，选择了目前用得最多、效果也较好的二维离散小波变换方法，并以图像压缩的小波变换结合人眼视觉特性的计算机实现及其应用作为本课题的研究内容；在考虑人人眼视觉特性时，着重考虑了将图像边缘提取出来，作为一个重要的对象进行单独处理。
接下来阐明了为什么要选用小波变换用于图像压缩以及为什么要进行边缘提取，并论证了这种方法的可行性。小波变换以其良好的时－频局部化特性引起了人们的广泛关注，在图像压缩领域中也做出了一定的贡献。本文就是以小波变换的时－频局部化特性和与人眼视觉特性的一致性为入手点，来研究小波变换用于图像压缩的具有普遍性的编码方法。
在进行小波变换的图像压缩中，根据小波的时－频局部化特性以及能量集中特性，来选取适合图像压缩的小波基，并以此确定出进行变换的最佳级数；同时，还根据这两个特性来进行了量化阈值的选取和量化方案的确定，以及小波系数的组织。另外，考虑到高频部分子图像包含较多的边缘信息，它们对人眼视觉特性敏感性大，采用小波方法进行边缘检测，以进一步保护图像的有用信息，增强图像的主观质量。
本论文以具有“数学显微镜”美称的小波变换为理论基础，结合图像的统计特性和人眼视觉特性，实现了小波变换结合人眼视觉特性的图像压缩，得到很好的实验结果：图像质量高、计算不复杂、计算量小、编解码时间短、算法具有普遍性。
最后本文对图像压缩编码方法的发展趋势和图像压缩编码方法本身及小波变换方法本身所存在的问题进行了讨论，并提出了改进意见，为后续工作的开展奠定了坚实的基础。
The paper focuses on the image compression and coding scheme based on wavelet
transform and human visual system(HVS)and its realization by programming．The
contents of the paper covers as follows：
First，the paper introduces the research background of the subj ect and the relevant
things of image compression，including the basic theories and methods in common use
of image compression．By analyzing and comparing，the image coding scheme based on
two—dimension(2一D)discrete wavelet transform(DWT)was chose which was used
much more and could lead to better results，then the contents of research was
determined as the image compression and coding based on wavelet transform combined
with human visual system．
Then it clarified the reasons why DWT was chose as the image compression
scheme and why edge detection was made，and reasoned the feasibility of the image
scheme．Because of its time—frequency localized properties，wavelet transform catches
people’S eyes and makes its contribution in the field of image compression．Starting
with the time—frequency localized properties of wavelet transform and its coherence
with human visual system，the paper aims at researching an image compression scheme
with universality based on wavelet transform．
During the image compression based on wavelet transform，according to the
time—frequency localized properties and concentricity of energy distribution of wavelet．
transform，we chose wavelet bases adapt to image compression，and determined the
levels that image should be transformed，and determined the threshold for quantification
and schemes of quantification and regrouping coefficients．In addition，considering that
sub-images of high frequency contains much information of edges and human visual
system is sensitive to the edges，SO we detect edges with the wavelet method to reserve
useful information of image and enhance the quality of the reconstructed image．
The paper takes the theoretic base of wavelet transform which was highly praised
as“mathematic microscope”，and make full use of statistical properties of image and
human visual system，implements the image compression，finally good experimental
results were achieved，such as high quality of image，low complexities of computation，
small quantity of computation，short time of coding and decoding and provided with
universality．
In the end，it discusses the developmental tendency of image compression and
some existing problems of the methods of image compression and the wavelet
transform，which would establish strong bases for the future work．
论文首先介绍了课题的研究背景和图像压缩方面的有关情况，包括图像压缩的基本原理和常用方法。通过进行分析比较，选择了目前用得最多、效果也较好的二维离散小波变换方法，并以图像压缩的小波变换结合人眼视觉特性的计算机实现及其应用作为本课题的研究内容；在考虑人人眼视觉特性时，着重考虑了将图像边缘提取出来，作为一个重要的对象进行单独处理。
接下来阐明了为什么要选用小波变换用于图像压缩以及为什么要进行边缘提取，并论证了这种方法的可行性。小波变换以其良好的时－频局部化特性引起了人们的广泛关注，在图像压缩领域中也做出了一定的贡献。本文就是以小波变换的时－频局部化特性和与人眼视觉特性的一致性为入手点，来研究小波变换用于图像压缩的具有普遍性的编码方法。
在进行小波变换的图像压缩中，根据小波的时－频局部化特性以及能量集中特性，来选取适合图像压缩的小波基，并以此确定出进行变换的最佳级数；同时，还根据这两个特性来进行了量化阈值的选取和量化方案的确定，以及小波系数的组织。另外，考虑到高频部分子图像包含较多的边缘信息，它们对人眼视觉特性敏感性大，采用小波方法进行边缘检测，以进一步保护图像的有用信息，增强图像的主观质量。
本论文以具有“数学显微镜”美称的小波变换为理论基础，结合图像的统计特性和人眼视觉特性，实现了小波变换结合人眼视觉特性的图像压缩，得到很好的实验结果：图像质量高、计算不复杂、计算量小、编解码时间短、算法具有普遍性。
最后本文对图像压缩编码方法的发展趋势和图像压缩编码方法本身及小波变换方法本身所存在的问题进行了讨论，并提出了改进意见，为后续工作的开展奠定了坚实的基础。
The paper focuses on the image compression and coding scheme based on wavelet
transform and human visual system(HVS)and its realization by programming．The
contents of the paper covers as follows：
First，the paper introduces the research background of the subj ect and the relevant
things of image compression，including the basic theories and methods in common use
of image compression．By analyzing and comparing，the image coding scheme based on
two—dimension(2一D)discrete wavelet transform(DWT)was chose which was used
much more and could lead to better results，then the contents of research was
determined as the image compression and coding based on wavelet transform combined
with human visual system．
Then it clarified the reasons why DWT was chose as the image compression
scheme and why edge detection was made，and reasoned the feasibility of the image
scheme．Because of its time—frequency localized properties，wavelet transform catches
people’S eyes and makes its contribution in the field of image compression．Starting
with the time—frequency localized properties of wavelet transform and its coherence
with human visual system，the paper aims at researching an image compression scheme
with universality based on wavelet transform．
During the image compression based on wavelet transform，according to the
time—frequency localized properties and concentricity of energy distribution of wavelet．
transform，we chose wavelet bases adapt to image compression，and determined the
levels that image should be transformed，and determined the threshold for quantification
and schemes of quantification and regrouping coefficients．In addition，considering that
sub-images of high frequency contains much information of edges and human visual
system is sensitive to the edges，SO we detect edges with the wavelet method to reserve
useful information of image and enhance the quality of the reconstructed image．
The paper takes the theoretic base of wavelet transform which was highly praised
as“mathematic microscope”，and make full use of statistical properties of image and
human visual system，implements the image compression，finally good experimental
results were achieved，such as high quality of image，low complexities of computation，
small quantity of computation，short time of coding and decoding and provided with
universality．
In the end，it discusses the developmental tendency of image compression and
some existing problems of the methods of image compression and the wavelet
transform，which would establish strong bases for the future work．
引文
[1] 周新伦, 柳建, 刘华志. 数字图像处理. 国防工业出版社
[2] 侯自强. 数字视频技术进展. 中国图像图形学报, 1996, 1(1):58-63
[3] 李建平. 小波分析与信号处理——理论、应用及软件实现. 重庆:重庆出版社, 1997
[4] 高西奇, 甘露, 邹采荣. 多小波变换的理论及其在图像处理中的应用[J]. 通信学报, 1999, 20(11): 55-60
[5] 秦前清, 杨宗凯. 实用小波分析. 西安: 西安电子科技大学出版社, 1995
[6] 赵荣春, 赵忠明, 崔苏生. 数字图像处理. 西北工业大学出版社
[7] 钟玉琢,冼伟铨,沈洪. 多媒体技术基础及应用. 清华大学出版社, 2000
[8] 王汇源. 数字图像通信原理与技术. 北京:国防工业出版社，2000
[9] 何梦林,王莉艾. 图像通信中的信息压缩技术[J]. 数字通信, 1996,16(1), 27-29
[10] 李春华, 张雨生, 戚银城等. 小波变换在图像压缩研究中的现状和趋势[J]. 华北电力大学学报. 2001.4., 28(2):87～91
[11] Castleman K R. Digital Image Processing. Prentice Hall, 1996
[12] Jacquin A E. Fractal Image Coding: A Review. Proc. IEEE, 1993, 81(10):1451-1465
[13] 李杰,付萍. 分形及分形图像编码. 长春大学学报. 1999, 9(4): 5-8
[14] 沙济彰, 冯忠义, 曹宁. 分形图像编码的IFS方法及其发展. 2000, 20(14): 27-29
[15] 刘贵忠,邸双亮. 小波变换及其应用.西安电子科技大学出版社
[16] 程正兴. 小波分析算法与应用[M]. 西安：西安交通大学出版社,1997.
[17] Mallat S. A Theory for multiresolution Signal Decomposition: the Wavelet Representation[J]. IEEE Trans PAMI., 1989,11(7): 674-693
[18] 郁晓红, 姚敏. 小波变换及图像压缩编码时小波基选择[J]. 计算机应用, 2001, 21(7): 20-23
[19] 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[J]. 2000, 23(2): 73-74
[20] C.Mariantonia, L.Damiana, L. B. Montefusco. Image Compression Through Embedded Multiwavelet Transform Coding[M]. IEEE Trans. Image Processing, 2000, 9(2): 184-189
[21] B. M. Machael, A. E. Bell, New Image Compression Techniques Using Multiwavelets and Multiwavelet Packets[M]. IEEE Trans. Image Compression, 2001, 10(4): 500-510
[22] J. M. Shapiro. Embedded Image Coding Using Zerotrees of Wavelets Coefficients. IEEE Trans. on Signal Processing. 1993, 41(12): 3445-3462
[23] M.Antonini. Image Coding Using Wavelet Transform. IEEE Trans. on IP, 1992, 1(2): 205-220
[24] 吴谨. 图像编码与小波变换图像编码[J]. 武汉科技大学学报, 2000, 23(3): 289-292
[25] 袁杰辉. 一种实用小波零树图像编码方法[J]. 计算机工程与应用, 1998, 21(5): 21-23
[26] 黄鹰, 吴国平, 岳锐. 用于图像传输的超低位速率图像压缩方法[J]. 计算机软件, 2000, 20(8): 21-23
[27] M.Barland. Pyramidal Lattice Vector Quantization for Multiscale Coding[M]. IEEE Trans. on IP, 1994, 43(15): 367-380
[28] W.B.Robert, Image Compression via Joint Statistical Characterization in the wavelet Domain[M]. IEEE Trans. IP, 1999, 8(12): 1688-1701
[29] Gray R M. Vector Quantization. IEEE ASSP Magazine, 1984, 6(4):4-29
[30] R. Rinaldo, G. Calvagno. Image Coding by Block Prediction of Multiresolution Subimages[M]. IEEE Trans. Image Processing, 1995, 4(7): 909-920
[31] 周建鹏, 杨义先. 基于小波分析的静止图像分层编码方法[J]. 电子学报, 1998, 26(1): 6-8
[32] G. M. Davis. A Wavelet-based Analysis of Fractal Image Compression[M]. IEEE Trans. Image Processing, 1998, 7(9): 141-154
[33] 张颖, 余英林, 布礼文. 结合分形和小波变换的自适应混合图像编码[J]. 电子学报. 26(10): 70-74
[34] Canny. A Computational approach to edge detection. IEEE Trans on PAMI, 1986, 8(6): 670-698
[35] I.Daubechies . Wavelet Transform, Time-frequency Localization and Signal Analysis[J]. IEEE Trans. IT., 1990, 36(5): 961-1005
[36] S.G.Mallat , Zhang S.. Characterization of signals from multiscale edges. IEEE Trans on PAMI, 1992, 14(6): 710-731
[37] S.G.Mallat, Hwang WL. Singularity detection and processing with wavelet. IEEE Trans on Information Theory. 1992, 38(2): 617-643
[38] 夏勇,田捷等.静止图像的小波压缩研究进展.电子学报, 1999,27(1): 34-37
[39] Battle G A. Block spin construction of ondelettes, Part 1: Lemarie function. Commun. Math.Phys, 1987,110（3）:745-767
[40] 马维桢. 利用小波变换的图像压缩编码技术. 信号处理, 1995, 11(3): 129～137
[41] Wong PW. Space-Frequency Localized Image Compression. IEEE Trans on Image Processing, 1994, 3(3): 523-536
[42] 黎洪松. 数字图像压缩编码技术及其C语言程序范例. 北京:学苑出版社, 1994
[2] 侯自强. 数字视频技术进展. 中国图像图形学报, 1996, 1(1):58-63
[3] 李建平. 小波分析与信号处理——理论、应用及软件实现. 重庆:重庆出版社, 1997
[4] 高西奇, 甘露, 邹采荣. 多小波变换的理论及其在图像处理中的应用[J]. 通信学报, 1999, 20(11): 55-60
[5] 秦前清, 杨宗凯. 实用小波分析. 西安: 西安电子科技大学出版社, 1995
[6] 赵荣春, 赵忠明, 崔苏生. 数字图像处理. 西北工业大学出版社
[7] 钟玉琢,冼伟铨,沈洪. 多媒体技术基础及应用. 清华大学出版社, 2000
[8] 王汇源. 数字图像通信原理与技术. 北京:国防工业出版社，2000
[9] 何梦林,王莉艾. 图像通信中的信息压缩技术[J]. 数字通信, 1996,16(1), 27-29
[10] 李春华, 张雨生, 戚银城等. 小波变换在图像压缩研究中的现状和趋势[J]. 华北电力大学学报. 2001.4., 28(2):87～91
[11] Castleman K R. Digital Image Processing. Prentice Hall, 1996
[12] Jacquin A E. Fractal Image Coding: A Review. Proc. IEEE, 1993, 81(10):1451-1465
[13] 李杰,付萍. 分形及分形图像编码. 长春大学学报. 1999, 9(4): 5-8
[14] 沙济彰, 冯忠义, 曹宁. 分形图像编码的IFS方法及其发展. 2000, 20(14): 27-29
[15] 刘贵忠,邸双亮. 小波变换及其应用.西安电子科技大学出版社
[16] 程正兴. 小波分析算法与应用[M]. 西安：西安交通大学出版社,1997.
[17] Mallat S. A Theory for multiresolution Signal Decomposition: the Wavelet Representation[J]. IEEE Trans PAMI., 1989,11(7): 674-693
[18] 郁晓红, 姚敏. 小波变换及图像压缩编码时小波基选择[J]. 计算机应用, 2001, 21(7): 20-23
[19] 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[J]. 2000, 23(2): 73-74
[20] C.Mariantonia, L.Damiana, L. B. Montefusco. Image Compression Through Embedded Multiwavelet Transform Coding[M]. IEEE Trans. Image Processing, 2000, 9(2): 184-189
[21] B. M. Machael, A. E. Bell, New Image Compression Techniques Using Multiwavelets and Multiwavelet Packets[M]. IEEE Trans. Image Compression, 2001, 10(4): 500-510
[22] J. M. Shapiro. Embedded Image Coding Using Zerotrees of Wavelets Coefficients. IEEE Trans. on Signal Processing. 1993, 41(12): 3445-3462
[23] M.Antonini. Image Coding Using Wavelet Transform. IEEE Trans. on IP, 1992, 1(2): 205-220
[24] 吴谨. 图像编码与小波变换图像编码[J]. 武汉科技大学学报, 2000, 23(3): 289-292
[25] 袁杰辉. 一种实用小波零树图像编码方法[J]. 计算机工程与应用, 1998, 21(5): 21-23
[26] 黄鹰, 吴国平, 岳锐. 用于图像传输的超低位速率图像压缩方法[J]. 计算机软件, 2000, 20(8): 21-23
[27] M.Barland. Pyramidal Lattice Vector Quantization for Multiscale Coding[M]. IEEE Trans. on IP, 1994, 43(15): 367-380
[28] W.B.Robert, Image Compression via Joint Statistical Characterization in the wavelet Domain[M]. IEEE Trans. IP, 1999, 8(12): 1688-1701
[29] Gray R M. Vector Quantization. IEEE ASSP Magazine, 1984, 6(4):4-29
[30] R. Rinaldo, G. Calvagno. Image Coding by Block Prediction of Multiresolution Subimages[M]. IEEE Trans. Image Processing, 1995, 4(7): 909-920
[31] 周建鹏, 杨义先. 基于小波分析的静止图像分层编码方法[J]. 电子学报, 1998, 26(1): 6-8
[32] G. M. Davis. A Wavelet-based Analysis of Fractal Image Compression[M]. IEEE Trans. Image Processing, 1998, 7(9): 141-154
[33] 张颖, 余英林, 布礼文. 结合分形和小波变换的自适应混合图像编码[J]. 电子学报. 26(10): 70-74
[34] Canny. A Computational approach to edge detection. IEEE Trans on PAMI, 1986, 8(6): 670-698
[35] I.Daubechies . Wavelet Transform, Time-frequency Localization and Signal Analysis[J]. IEEE Trans. IT., 1990, 36(5): 961-1005
[36] S.G.Mallat , Zhang S.. Characterization of signals from multiscale edges. IEEE Trans on PAMI, 1992, 14(6): 710-731
[37] S.G.Mallat, Hwang WL. Singularity detection and processing with wavelet. IEEE Trans on Information Theory. 1992, 38(2): 617-643
[38] 夏勇,田捷等.静止图像的小波压缩研究进展.电子学报, 1999,27(1): 34-37
[39] Battle G A. Block spin construction of ondelettes, Part 1: Lemarie function. Commun. Math.Phys, 1987,110（3）:745-767
[40] 马维桢. 利用小波变换的图像压缩编码技术. 信号处理, 1995, 11(3): 129～137
[41] Wong PW. Space-Frequency Localized Image Compression. IEEE Trans on Image Processing, 1994, 3(3): 523-536
[42] 黎洪松. 数字图像压缩编码技术及其C语言程序范例. 北京:学苑出版社, 1994
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