基于小波多分辨分析的图像增强及其应用研究
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摘要
在一个图像系统中，从图像的获取，到图像的发送、传输、接收、输出(显示)、复制等等，每一个环节都会产生干扰，都会使图像质量降低。如何对这些“降质”图像进行处理，满足实际需要，是图像处理的基本要求。图像增强是图像处理主要内容之一。现有的图像增强方法有很多种，但它们在增强图像的同时，往往会带来了比较严重的负效应。小波多分辨分析由于它能多尺度多角度提取信号特征，往往可在不同尺度上将噪声和信号明显地区分开来，所以它在图像去噪和增强方面有很大优势。本文主要研究了基于小波多分辨分析的图像去噪和增强，主要工作如下：
1 将反锐化掩模与基于小波多分辨分析的图像增强进行了对比分析，指出它们之间存在着内在的联系，即两者都是对与图像边缘细节对应的高频实行增强，而且指出前者只不过是后者的一个特例，因为小波分解后，多级尺度多个高频通道可得到增，而反锐化掩模仅增强了一个高频通道。
2 将小波去噪、边缘检测和图像增强有机结合起来，同时实现了图像去噪和增强。由于图像进行小波分解后，其边缘细节与噪声都存在于高频部分，因此，在高频段利用现有的小波去噪方法去掉噪声，增强图像中的边缘细节，从而达到同时实现去噪和增强的目的。利用增益函数将去噪和增强联系起来，通过调节增益函数的参数从而实现特定图像的去噪和增强。
3 对图像增强中的增益函数进行了比较深入的分析与研究，将它们分成两类：线性和非线性增益函数。分析了两类函数的优缺点，并对非线性增益函数中参数的选择提出了参考意见。
4 对小波基的选择作了初步研究，采用几组常用的小波基作了处理，给出了处理结果，并把处理结果作了比较，提出了图像增强时候选小波基应注意的几个方面，包括正交性、支撑集、对称性、规则性和消失矩阶数。并与现有的增强方法作了比较。
An image system consists of acquisition, transmission, reception and display, every part of which can be disturbed, so that the image equality can be degraded. Elementary requirement of image enhancement is how to deal with these degraded images to meet our need. One of main contents of image processing is image enhancement. Now, there are many methods of image enhancement, but they will more or less bring bad effects when enhancing images. Wavelet analysis has predominant advantages in image de-noising and image enhancement, due to its extracting multi-resolution characters of signal and making the difference between noise and signal very clear. Image de-noising and image enhancement based on wavelet multi-resolution are studied in the thesis. The main works are as follows:
Firstly, we compare image enhancement in wavelet domain with that based on unsharp masking and indicate that there is intrinsic relation between them, namely they both enhance images by enhancing the high frequency coefficients. Because after an image is decomposed in wavelet domain, every high frequency can be enhanced. However, if unshrap masking is used, only one high frequency channel is enhanced. So unsharp masking is a special case of image enhancement based on wavelet multi-resolution.
Secondly, wavelet de-noising and edge detection are merged into image enhancement, that is, the image de-noising and enhancement are accomplished at the same time. After an image is decomposed, its edges, details and noise will exist in high frequency. Noise can be removed by wavelet de-noising, and edges and details can be enhanced in high frequency, hence the goal of enhancing and de-noising at the same time can be attained. The de-noising and enhancement are linked by enhancement function. An image can be de-noised and enhanced by adjusting the parameters of enhancement function.
Thirdly, the enhancement functions are studied in detail. There are two classes of the enhancement functions: linear and nonlinear. Their merits and shortcomings are analyzed. A new method to choose the parameters of these functions is brought forward.
Finally, we have studied how to select wavelet bases. Several typical wavelet bases are adopted, and the simulation results are analyzed. Some advices selecting wavelet bases are put forward. The results are compared with those of other methods, too.
1 将反锐化掩模与基于小波多分辨分析的图像增强进行了对比分析，指出它们之间存在着内在的联系，即两者都是对与图像边缘细节对应的高频实行增强，而且指出前者只不过是后者的一个特例，因为小波分解后，多级尺度多个高频通道可得到增，而反锐化掩模仅增强了一个高频通道。
2 将小波去噪、边缘检测和图像增强有机结合起来，同时实现了图像去噪和增强。由于图像进行小波分解后，其边缘细节与噪声都存在于高频部分，因此，在高频段利用现有的小波去噪方法去掉噪声，增强图像中的边缘细节，从而达到同时实现去噪和增强的目的。利用增益函数将去噪和增强联系起来，通过调节增益函数的参数从而实现特定图像的去噪和增强。
3 对图像增强中的增益函数进行了比较深入的分析与研究，将它们分成两类：线性和非线性增益函数。分析了两类函数的优缺点，并对非线性增益函数中参数的选择提出了参考意见。
4 对小波基的选择作了初步研究，采用几组常用的小波基作了处理，给出了处理结果，并把处理结果作了比较，提出了图像增强时候选小波基应注意的几个方面，包括正交性、支撑集、对称性、规则性和消失矩阶数。并与现有的增强方法作了比较。
An image system consists of acquisition, transmission, reception and display, every part of which can be disturbed, so that the image equality can be degraded. Elementary requirement of image enhancement is how to deal with these degraded images to meet our need. One of main contents of image processing is image enhancement. Now, there are many methods of image enhancement, but they will more or less bring bad effects when enhancing images. Wavelet analysis has predominant advantages in image de-noising and image enhancement, due to its extracting multi-resolution characters of signal and making the difference between noise and signal very clear. Image de-noising and image enhancement based on wavelet multi-resolution are studied in the thesis. The main works are as follows:
Firstly, we compare image enhancement in wavelet domain with that based on unsharp masking and indicate that there is intrinsic relation between them, namely they both enhance images by enhancing the high frequency coefficients. Because after an image is decomposed in wavelet domain, every high frequency can be enhanced. However, if unshrap masking is used, only one high frequency channel is enhanced. So unsharp masking is a special case of image enhancement based on wavelet multi-resolution.
Secondly, wavelet de-noising and edge detection are merged into image enhancement, that is, the image de-noising and enhancement are accomplished at the same time. After an image is decomposed, its edges, details and noise will exist in high frequency. Noise can be removed by wavelet de-noising, and edges and details can be enhanced in high frequency, hence the goal of enhancing and de-noising at the same time can be attained. The de-noising and enhancement are linked by enhancement function. An image can be de-noised and enhanced by adjusting the parameters of enhancement function.
Thirdly, the enhancement functions are studied in detail. There are two classes of the enhancement functions: linear and nonlinear. Their merits and shortcomings are analyzed. A new method to choose the parameters of these functions is brought forward.
Finally, we have studied how to select wavelet bases. Several typical wavelet bases are adopted, and the simulation results are analyzed. Some advices selecting wavelet bases are put forward. The results are compared with those of other methods, too.
引文
[1] 赵荣椿，“数字图像处理导论，”西北工业大学出版社，1995．
[2] 阮秋琦，“数字图像处理学，”电子工业出版社，2001．
[3] 胡广书，“数字信号处理，”清华大学出版社，1997．
[4] 容观澳，“计算机图像处理，”清华大学出版社，2000．
[5] K．R．Castleman著，朱志刚等译，“数字图像处理，”电子工业出版社，1998．
[6] 陈少卿，吴朝霞，程敬之 骨肿瘤X光片的多分辨特征增强 西安交通大学校报 1999．
[7] 董汉丽，基于小波变换的图像增强方法研究 郑州纺织工学院学报 1999．
[8] 王博，数字图象处理方法与应用研究博士论文，1998．
[9] 张日华，黄彦明，小波变换及其在图象处理中的特性分析，中国图象图形学报，Vol．2(7)，1997．
[10] Jian Lu, Contrast Enhancement of Medical Images Using Multiscale Edge Representation Optical Engineering Special Issue on Adaptive Wavelet Transform.
[11] Hayit Greenspan, Charles H. Anderson, and Sofia Akber Image Enhancement By Nonlinear Extrapolation IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 9, NO. 6, JUNE 2000.
[12] Andrew Laine, Jian Fan and Wuhai Yang Wavelet for Contrast Enhancement of Digital Mammography the Special Issue of EMBS Magazine entitled "Wavelets in Machine".
[13] Donoho D. L. De-noising by soft-thresholding. IEEE Transactions on Information Theory, vol. 41, pp. 613-627, 1995.
[14] Donoho D. L. and Johnstone I. M. Neo-classical minimax theorems, thresholding, and adaptation. Technical report, Department of Statistics, Stanford University, 1992.
[15] D. L. Donoho and I. M. Johnstone. Ideal spatial adaption by wavelet shrinkage. Biometrika, 81: 425-455, 1994.
[16] D. L. Donoho and I. M. Johnstone. Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association, 90: 1200-1224, 1995.
[17] D. L. Donoho and I. M. Johnstone. Minimax estimation via wavelet shrinkage. Ann. Statist. 26, 879-921.
[18] 王国宇，王宁，基于小波变换的多尺度边缘检测，中国图象图形学报，Vol．2(10)，1997：717-720．
[19] 解梅，顾得仁，使用小波的图像边缘检测算法，电子科学学刊，Vol．19(2)，1997：173-182．
[20] 张天序，一种新的边缘检测计算模型和算法，自动化学报，Vol．20(4)，1994：435-443．
[21] 王磊，莫玉龙，基于Canny理论的边缘检测算法，中国图象图形学报，No．3，1996：191-195．
[22] 崔锦泰，“小波分析导论，”西安交通大学出版社，1995．
[23] 赵松年，熊小芸，“子波变换与子波分析，”电子工业出版社，1997．
[24] 程正兴，“小波分析算法与应用，”西安交通大学出版社，1998．
[25] 彭玉华，“小波变换与工程应用，”科学出版社，2000．
[26] 杨福生，小波变换的工程分析与应用，科学出版社，2000
[27] 胡昌华，张军波，夏军，张伟，“基于Matlab的系统分析与设计——小波分析，”西安电子科技大学出版社，2000．
[28] Wim Sweldens The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions Wavelet Applications in Signal and Image Processing Ⅲ, pp. 68-79, Proco SPIE 2569, 1995.
[29] S. Mallat A Theory of Multiresolution Signal Decomposition IEEE TRANSACTIONS ON PAMI-11(7) 1989.
[30] S. Mallat Multiresolution Approximation and Wavelet Orthogonal bases of L2 Trans. Amer. Math. Soc., 315 69-87, 1989.
[31] S. Mallat, Wavelet for vision, Proc. IEEE, 84(4), 605-614, 1996.
[32] S. Mallat, et al., Characterization of signals from multiscale edges IEEE TRANSACTIONS ON PAMI-14(7)710-732, 1992
[33] I. Daubechies, "Orthonormal Bases of Compactly Supported Wavelets," Comm. Pure and Appl. Math., vol. 41, pp. 909-996, 1988.
[34] S. Mallat, "A Theory for Multiresolution Signal Decomposition: the Wavelet Representation-on," IEEE Trans. PAMI, vol. 11, pp. 674-693, 1989.
[35] S. Mallat, "Multiresolution Approximation and Wavelet Orthonormal Bases of L~2(R)," Trans. Amer. Math. Soc., vol. 315, pp. 69-87, 1989.
[36] A. Kirac and P. R Vaidyanathan, "Theory and Design of Signal-adapted FIR
Paraunitary Filter Banks," IEEE Trans. Signal Processing, vol. 46, pp. 920-929, 1992．
[37] A. Cohen and I. Daubechies, "Bi-orthogonal Bases of Compactly Supported Wavelets," Comm. Pure and Appl. Math., vol. 45, pp. 485-560, 1992．
[38] I. Daubechies, "Ten Lectures on Wavelets," CBMS-NSF Series in Appl. Math. , SIAM, 1992．
[39] S. Mallat and S.Zhong, "Characterization of Signals from Multiscale Edges," IEEE Trans. PAMI, vol. 14, pp. 710-732, 1992．
[40] W.Sweldens, The lifting scheme: A custom-design construction of biorthogonal wavelets. Journal of Appl. And Comput. Harmonic Analysis, 3(2) : 186-200, 1996．
[41] R.Calderbank, I.Daubechies, W.Sweldens, and B.-L.Yeo. Wavelet transforms that map integers to integers. Appl. Comput. Harmon. Anal.,5(3) :332-369,1998．
[42] I. Daubechies, Wim Sweldens. Factoring wavelet transforms into lifting steps. J. Fourier Anal., 1998．
[43] S. Mallat and W. L. Hwang, "Singularity Detection and Processing with Wavelets," IEEE Trans. Information Theory, vol. 38, pp. 617-643, 1992．
[44] S. Mallat et al, "Matching Pursuits with Time Frequency Dictionaries," IEEE Trans. Signal Processing, vol. 41, pp. 3397-3451, 1993．
[45] M. V. Wickerhauser, "Adapted Wavelet Analysis from Theory to Software," AK Peters, Wellesey, 1994．
[46] G. Battle. A block spin construction of ondelettes, Part I: Lemarie function. Commun. Math. Phys., 1987, 110(3) : 601-615．
[47] Yansun Xu and et al. Wavelet transform domain filters: a spatially selective noise filtration technique, IEEE Trans, on Image Processing, vol. 3, pp. 747-758, 1994．
[48] Y.Lu,C.J.Ramesh, Reasoning About Edges in Scale Space,IEEE Trans.on PAMI,Vol. 14(4) , 1992:450-468
[49] Pan Quan,Wang Bo,Zhang Hongcai and Dai Guanzhong:Image Denoising and Edge Detection with Fuzzy Model Distinguishing,第二届全球华人智能控制与自动化大会 (CWCICIA' 97) 论文集，西安 , 1997
[50] R.P.Johnson, Contrast Based Edge Detection, Pattern Recognition, No23,1990．
[51] R.M.Haralick,J.S.Lee, Context Detection and Evaluation, IEEE on Pattern Recognition, No.23．
[52] J. Canny, A Computation Approach to Edge Detection,IEEE Trans, on
PAMI, Vol. 8(6), 1986.
[53] 薛晓辉，高文，“正交小波的零误差边界延拓算法，”电子科学，vol．25，pp．11-13，1997．
[54] 张磊，潘泉，张洪才，戴冠中，“小波域滤波闽值参数c的选取，”电子学报，vol．29，pp．400-402，2001．
[55] 潘泉，张洪才，戴冠中：基于阈值决策的子波域滤波算法研究，电子学报，Vol．26(1)，1998．
[56] 周德龙，张洪才，“基于模糊的图像处理技术，”硕士论文，1997．
[57] 宁冬子，基于自适应下拨变换的静态图像编码压缩，西北工业大学硕士论文，2002
[58] 李强，王正治，基于小波理论的遥感图像高保真压缩方法研究，DownLoad from Internet http://yq8031. home. sohu. com/xjsyd. html
[2] 阮秋琦，“数字图像处理学，”电子工业出版社，2001．
[3] 胡广书，“数字信号处理，”清华大学出版社，1997．
[4] 容观澳，“计算机图像处理，”清华大学出版社，2000．
[5] K．R．Castleman著，朱志刚等译，“数字图像处理，”电子工业出版社，1998．
[6] 陈少卿，吴朝霞，程敬之 骨肿瘤X光片的多分辨特征增强 西安交通大学校报 1999．
[7] 董汉丽，基于小波变换的图像增强方法研究 郑州纺织工学院学报 1999．
[8] 王博，数字图象处理方法与应用研究博士论文，1998．
[9] 张日华，黄彦明，小波变换及其在图象处理中的特性分析，中国图象图形学报，Vol．2(7)，1997．
[10] Jian Lu, Contrast Enhancement of Medical Images Using Multiscale Edge Representation Optical Engineering Special Issue on Adaptive Wavelet Transform.
[11] Hayit Greenspan, Charles H. Anderson, and Sofia Akber Image Enhancement By Nonlinear Extrapolation IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 9, NO. 6, JUNE 2000.
[12] Andrew Laine, Jian Fan and Wuhai Yang Wavelet for Contrast Enhancement of Digital Mammography the Special Issue of EMBS Magazine entitled "Wavelets in Machine".
[13] Donoho D. L. De-noising by soft-thresholding. IEEE Transactions on Information Theory, vol. 41, pp. 613-627, 1995.
[14] Donoho D. L. and Johnstone I. M. Neo-classical minimax theorems, thresholding, and adaptation. Technical report, Department of Statistics, Stanford University, 1992.
[15] D. L. Donoho and I. M. Johnstone. Ideal spatial adaption by wavelet shrinkage. Biometrika, 81: 425-455, 1994.
[16] D. L. Donoho and I. M. Johnstone. Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association, 90: 1200-1224, 1995.
[17] D. L. Donoho and I. M. Johnstone. Minimax estimation via wavelet shrinkage. Ann. Statist. 26, 879-921.
[18] 王国宇，王宁，基于小波变换的多尺度边缘检测，中国图象图形学报，Vol．2(10)，1997：717-720．
[19] 解梅，顾得仁，使用小波的图像边缘检测算法，电子科学学刊，Vol．19(2)，1997：173-182．
[20] 张天序，一种新的边缘检测计算模型和算法，自动化学报，Vol．20(4)，1994：435-443．
[21] 王磊，莫玉龙，基于Canny理论的边缘检测算法，中国图象图形学报，No．3，1996：191-195．
[22] 崔锦泰，“小波分析导论，”西安交通大学出版社，1995．
[23] 赵松年，熊小芸，“子波变换与子波分析，”电子工业出版社，1997．
[24] 程正兴，“小波分析算法与应用，”西安交通大学出版社，1998．
[25] 彭玉华，“小波变换与工程应用，”科学出版社，2000．
[26] 杨福生，小波变换的工程分析与应用，科学出版社，2000
[27] 胡昌华，张军波，夏军，张伟，“基于Matlab的系统分析与设计——小波分析，”西安电子科技大学出版社，2000．
[28] Wim Sweldens The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions Wavelet Applications in Signal and Image Processing Ⅲ, pp. 68-79, Proco SPIE 2569, 1995.
[29] S. Mallat A Theory of Multiresolution Signal Decomposition IEEE TRANSACTIONS ON PAMI-11(7) 1989.
[30] S. Mallat Multiresolution Approximation and Wavelet Orthogonal bases of L2 Trans. Amer. Math. Soc., 315 69-87, 1989.
[31] S. Mallat, Wavelet for vision, Proc. IEEE, 84(4), 605-614, 1996.
[32] S. Mallat, et al., Characterization of signals from multiscale edges IEEE TRANSACTIONS ON PAMI-14(7)710-732, 1992
[33] I. Daubechies, "Orthonormal Bases of Compactly Supported Wavelets," Comm. Pure and Appl. Math., vol. 41, pp. 909-996, 1988.
[34] S. Mallat, "A Theory for Multiresolution Signal Decomposition: the Wavelet Representation-on," IEEE Trans. PAMI, vol. 11, pp. 674-693, 1989.
[35] S. Mallat, "Multiresolution Approximation and Wavelet Orthonormal Bases of L~2(R)," Trans. Amer. Math. Soc., vol. 315, pp. 69-87, 1989.
[36] A. Kirac and P. R Vaidyanathan, "Theory and Design of Signal-adapted FIR
Paraunitary Filter Banks," IEEE Trans. Signal Processing, vol. 46, pp. 920-929, 1992．
[37] A. Cohen and I. Daubechies, "Bi-orthogonal Bases of Compactly Supported Wavelets," Comm. Pure and Appl. Math., vol. 45, pp. 485-560, 1992．
[38] I. Daubechies, "Ten Lectures on Wavelets," CBMS-NSF Series in Appl. Math. , SIAM, 1992．
[39] S. Mallat and S.Zhong, "Characterization of Signals from Multiscale Edges," IEEE Trans. PAMI, vol. 14, pp. 710-732, 1992．
[40] W.Sweldens, The lifting scheme: A custom-design construction of biorthogonal wavelets. Journal of Appl. And Comput. Harmonic Analysis, 3(2) : 186-200, 1996．
[41] R.Calderbank, I.Daubechies, W.Sweldens, and B.-L.Yeo. Wavelet transforms that map integers to integers. Appl. Comput. Harmon. Anal.,5(3) :332-369,1998．
[42] I. Daubechies, Wim Sweldens. Factoring wavelet transforms into lifting steps. J. Fourier Anal., 1998．
[43] S. Mallat and W. L. Hwang, "Singularity Detection and Processing with Wavelets," IEEE Trans. Information Theory, vol. 38, pp. 617-643, 1992．
[44] S. Mallat et al, "Matching Pursuits with Time Frequency Dictionaries," IEEE Trans. Signal Processing, vol. 41, pp. 3397-3451, 1993．
[45] M. V. Wickerhauser, "Adapted Wavelet Analysis from Theory to Software," AK Peters, Wellesey, 1994．
[46] G. Battle. A block spin construction of ondelettes, Part I: Lemarie function. Commun. Math. Phys., 1987, 110(3) : 601-615．
[47] Yansun Xu and et al. Wavelet transform domain filters: a spatially selective noise filtration technique, IEEE Trans, on Image Processing, vol. 3, pp. 747-758, 1994．
[48] Y.Lu,C.J.Ramesh, Reasoning About Edges in Scale Space,IEEE Trans.on PAMI,Vol. 14(4) , 1992:450-468
[49] Pan Quan,Wang Bo,Zhang Hongcai and Dai Guanzhong:Image Denoising and Edge Detection with Fuzzy Model Distinguishing,第二届全球华人智能控制与自动化大会 (CWCICIA' 97) 论文集，西安 , 1997
[50] R.P.Johnson, Contrast Based Edge Detection, Pattern Recognition, No23,1990．
[51] R.M.Haralick,J.S.Lee, Context Detection and Evaluation, IEEE on Pattern Recognition, No.23．
[52] J. Canny, A Computation Approach to Edge Detection,IEEE Trans, on
PAMI, Vol. 8(6), 1986.
[53] 薛晓辉，高文，“正交小波的零误差边界延拓算法，”电子科学，vol．25，pp．11-13，1997．
[54] 张磊，潘泉，张洪才，戴冠中，“小波域滤波闽值参数c的选取，”电子学报，vol．29，pp．400-402，2001．
[55] 潘泉，张洪才，戴冠中：基于阈值决策的子波域滤波算法研究，电子学报，Vol．26(1)，1998．
[56] 周德龙，张洪才，“基于模糊的图像处理技术，”硕士论文，1997．
[57] 宁冬子，基于自适应下拨变换的静态图像编码压缩，西北工业大学硕士论文，2002
[58] 李强，王正治，基于小波理论的遥感图像高保真压缩方法研究，DownLoad from Internet http://yq8031. home. sohu. com/xjsyd. html
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