基于小波理论的图像去噪和增强技术研究
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摘要
小波分析在图像处理中有非常重要的应用。本文研究方向是在其图像去噪和图像增强中的应用。小波分析是傅立叶分析思想方法的发展与延拓。二维小波分析用于图像去噪和图像增强是小波分析应用的一个重要方面。小波分析用于图像去噪和增强具有明显的优点。基于小波分析的图像去噪方法有很多,比较成功的有小波阈值法,空域相关法,模极大值重构法,投影法等。而基于小波的图像增强方法也比传统图像增强方法更有效。主要工作包括:
本文详细阐述了小波基本理论在图像处理中的应用,介绍了连续小波变换和离散小波变换,给出离散二进小波变换的快速分解与重构算法,最后研究了小波基的函数及其特性,分析了它们对实际应用的影响和作用。
在对目前小波理论、小波图像去噪的相关文献进行研究的基础上,介绍了小波变换在图像去噪领域的应用;其次,对目前常用的几类小波去噪方法进行了分别阐述,着重分析了阈值收缩法并分析了其存在的不足;最后,提出了新的阈值选取方法和阈值函数改进方法。本文采用Matlab进行仿真实验,分别对含噪图像使用改进的阈值,改进的阈值函数进行去噪处理,新函数是现有软、硬阈值函数的推广,通过调整参数,克服了硬阈值函数不连续和软阈值函数有偏差的缺点,改善了图像的视觉效果和客观指标,对图像进行仿真实验得到了较好的结果。
研究了基于小波变换的图像增强,先分析了图像增强的基本方法,然后将图像增强放入小波域中去研究,并提出了一种新的小波变换自适应图像增强算法,在Matlab环境中验证了该算法的可行性和优越性。
本文主要研究了基于小波的图像去噪与增强技术的理论基础,提出了新的基于小波变换的图像去噪和增强方法,以Matlab为平台实现图像去噪和增强算法过程,并对相应的图像处理结果进行了分析和比较,验证了其可行性和高效性。
Wavelet analysis in the image processing applications are very important. In this paper, the direction of its image noise reduction and image enhancement are researched in the application. Wavelet analysis is the development of Fourier analysis of the way of thinking and extension. Two-dimensional images of wavelet analysis for noise reduction and image enhancement application of wavelet analysis is an important aspect. Wavelet analysis for noise reduction and enhance the image has obvious advantages. Based on wavelet analysis of the image means a lot of noise, the more successful a wavelet threshold method, air-related laws, modulus maximum reconstruction, projection and so on. And the wavelet-based image enhancement methods than the traditional image enhancement methods more effective.
The fundamental theories of wavelet analysis are discussed in detail. Continuous wavelet transform, discrete wavelet transfonn and dyadic wavelet transform are introduced. The fast algorithm of discrete dyadic wavelet transform is given. Finally, an analysis is made on the influence of the wavelet bases on practical applications by studying their mathematical properties.
Based on the profound comprehension and generalization of a lot of existing literature on wavelet de-noising, the applications in the image de-noising are described; second, the wavelet image de-noising methods are classified and introduced, moreover, the shortcomings of threshold de-noising method are specially analyzed; in the end, after analyzing and comparing the classical threshold de-noising methods, a new threshold selecting method and a new threshold function are proposed. Simulation experiments are implemented by Matlab wavelet tool box. And experiment results show that the new methods usually obtain better performance than classical threshold de-noising methods.
Image enhancement based on wavelet transform are studied in the thesis. Firstly, the concept of wavelet transform is described, and the characters after wavelet transform are analyzed; secondly, an adaptive local threshold scheme is proposed namely by threshold of the wavelet transform; At last, the way that wavelet cooperate with image enhancement realize the arithmetic, which balance de-noising and image enhancement. The Matlab simulation experiment indicates the new adaptive image enhancement is effective and excellent.
This paper elaborated on the wavelet-based image noise reduction and enhancement of the theoretical basis to Matlab as a platform for noise reduction and image enhancement algorithm to achieve process and the corresponding image processing results were analyzed and compared in order to arrive at a comprehensive performance distinctions based on wavelet of the noise reduction and image enhancement algorithm program.
本文详细阐述了小波基本理论在图像处理中的应用,介绍了连续小波变换和离散小波变换,给出离散二进小波变换的快速分解与重构算法,最后研究了小波基的函数及其特性,分析了它们对实际应用的影响和作用。
在对目前小波理论、小波图像去噪的相关文献进行研究的基础上,介绍了小波变换在图像去噪领域的应用;其次,对目前常用的几类小波去噪方法进行了分别阐述,着重分析了阈值收缩法并分析了其存在的不足;最后,提出了新的阈值选取方法和阈值函数改进方法。本文采用Matlab进行仿真实验,分别对含噪图像使用改进的阈值,改进的阈值函数进行去噪处理,新函数是现有软、硬阈值函数的推广,通过调整参数,克服了硬阈值函数不连续和软阈值函数有偏差的缺点,改善了图像的视觉效果和客观指标,对图像进行仿真实验得到了较好的结果。
研究了基于小波变换的图像增强,先分析了图像增强的基本方法,然后将图像增强放入小波域中去研究,并提出了一种新的小波变换自适应图像增强算法,在Matlab环境中验证了该算法的可行性和优越性。
本文主要研究了基于小波的图像去噪与增强技术的理论基础,提出了新的基于小波变换的图像去噪和增强方法,以Matlab为平台实现图像去噪和增强算法过程,并对相应的图像处理结果进行了分析和比较,验证了其可行性和高效性。
Wavelet analysis in the image processing applications are very important. In this paper, the direction of its image noise reduction and image enhancement are researched in the application. Wavelet analysis is the development of Fourier analysis of the way of thinking and extension. Two-dimensional images of wavelet analysis for noise reduction and image enhancement application of wavelet analysis is an important aspect. Wavelet analysis for noise reduction and enhance the image has obvious advantages. Based on wavelet analysis of the image means a lot of noise, the more successful a wavelet threshold method, air-related laws, modulus maximum reconstruction, projection and so on. And the wavelet-based image enhancement methods than the traditional image enhancement methods more effective.
The fundamental theories of wavelet analysis are discussed in detail. Continuous wavelet transform, discrete wavelet transfonn and dyadic wavelet transform are introduced. The fast algorithm of discrete dyadic wavelet transform is given. Finally, an analysis is made on the influence of the wavelet bases on practical applications by studying their mathematical properties.
Based on the profound comprehension and generalization of a lot of existing literature on wavelet de-noising, the applications in the image de-noising are described; second, the wavelet image de-noising methods are classified and introduced, moreover, the shortcomings of threshold de-noising method are specially analyzed; in the end, after analyzing and comparing the classical threshold de-noising methods, a new threshold selecting method and a new threshold function are proposed. Simulation experiments are implemented by Matlab wavelet tool box. And experiment results show that the new methods usually obtain better performance than classical threshold de-noising methods.
Image enhancement based on wavelet transform are studied in the thesis. Firstly, the concept of wavelet transform is described, and the characters after wavelet transform are analyzed; secondly, an adaptive local threshold scheme is proposed namely by threshold of the wavelet transform; At last, the way that wavelet cooperate with image enhancement realize the arithmetic, which balance de-noising and image enhancement. The Matlab simulation experiment indicates the new adaptive image enhancement is effective and excellent.
This paper elaborated on the wavelet-based image noise reduction and enhancement of the theoretical basis to Matlab as a platform for noise reduction and image enhancement algorithm to achieve process and the corresponding image processing results were analyzed and compared in order to arrive at a comprehensive performance distinctions based on wavelet of the noise reduction and image enhancement algorithm program.
引文
[1]李弼强,罗建书小波分析及其应用.电子工业出版社,2003
[2]林堪贤,宋国乡,薛文.图像的几种小波去噪方法的比较与改进.西安电子科技大学学报(自然科学版),2004.8:626-629
[3]Keita Alpha,彭嘉雄.基于小波门限化的图像去噪方法.华中科技大学学报,2001.29(6):13-15
[4]韦凤梅,李翠华.基于自适应模糊阈值小波的图像去噪.厦门大学学报,2005.44(2):185-188
[5]查宇飞,毕笃彦.基于小波变换的自适应多阈值图像去噪.中国图像图形学报,2005.10(5):567-570
[6]S.Mallat.A wavelet Tour of signal proeessing.China Machine press,2002.9(1)
[7]S.Mallat.A theory for multi-resolution signal decomposition:The wavelet representation.[J]EEE Trans.Pattern.Anal.Machine Intell,1989.21(7):674-633
[8]Donoho D L,Johnstone J M.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994.81:425-455
[9]Mallat S G.A theory of multiresolution signal decomposition:the wavelet representation.IEEE Trans on PAMI,1989.11(7):674-693
[10]陈贺新.非线形滤波器与数字图像处理.北京:国防工业出版社,2005
[11]Cohen A.Wavelets and multiscale signal processing.Chapman and Hall,1995
[12]Chui,C.K.An introduction to wavelets.Academic Press,2002
[13]Daubechies I.Ten lectures on wavelets.SLAM,2002
[14]Antoniadis,Pham DT[J].Wavelets regression for random or irregular design.Comp.Stat.and Data Analysis,2004
[15]毕为民,唐炬,姚陈果.基于熵阈值的小波包变换抑制局部放电窄带干扰的研究.中国电机工程学报,2003.23(5):128-131
[16]Unser M.Texture classification and segmentation using wavelet frames.IEEE Trans.on IP,1995.4(11):1549-1560
[17]王玲.多小波理论及其在图像处理中的应用研究.西安:西安电子科技大学,2000
[18]孔祥茜,吴继伟,岳继光.地震信号小波变换的去噪方法.计算机辅助工程,200514(3):52-56
[19]郭艳芬,张红梅,曲智林,马晓剑.一种基于小波的并行算法及其在大型数值计算中的应用.东北林业大学学报,2005.33(4):15-116
[20]何坤等.非平稳环境下基于小波变换的图像去噪.中国图像图形学报,2005.10(10):567-570
[21]张宗平,刘贵忠,董恩清.基于二进小波变换的信号去噪.电子与信息学报,2001.23(11):1083-1090
[22]任震,何建军,黄雯莹.基于小波包算法的电机故障信号的压缩和重构.中国电机工程学报,2001.21(1):25-29
[23]李杏梅,陈亮.小波阈值去噪在图像去噪中的应用.现代计算机,2006.10
[24]骆正虎,杨敬安,吴刚.基于小波变换的图像的多分辨率分解与重构的实现.计算机科学,2001,28(10):69-71
[25]C.S.Lu,P.C.Chung,C.R Chen.Unsupervised texture segmentation via wavelet transform,Pattern Recognition,vol.30,no.5,pp.729-742
[26]Donoho D.L.De-noising by soft thresholding.IEEE Trans.on IT.,1995.41(3):613-627
[27]Wang Z,Guerriero A,Sario M De.Comparison of several approaches for the segmentation of texture images.Pattern Recognition Letters,1996.17:509-521
[28]Chang T,Kuo C C J.Texture analysis and classification with tree-structure wavelet transform.IEEE Trans.on IP,1993.2(4):429-441
[29]崔华,宋国乡.基于小波阈值去噪方法的一种改进方案.现代电子技术,2005.1:8-9
[30]Kenneth R,Castleman.数字图像处理.朱志刚,林学闾,石定机译.北京:电子工业出版社,1988
[31]郭敏,马远良,朱霆.基于小波变换的医学超声图像去噪及增强方法.中国医学影像技术,2006.22(9):1435-1437
[32]包振华.基于Matlab的灰度级线性变换图像增强.工程技术,2006.5(3):54-56
[33]张光年.多尺度小波梯度图像增强方法.首都师范大学学报(自然科学版),2006.7(2):16-19
[34]周旋,周树道,黄峰,周小滔.基于小波变换的图像新增强算法.计算机应用,2005.25(3):606-608
[35]Gopinath R A,Lang M,Guo H,et al.Enhancement of decompressed images at low bit rates.SPIE Math Imaging:Wavelet Applications in Signal and Image Processing.San Diego,1994.15(2):366-377
[36]Laine A,Fan J,Yang W.Wavelets for contrast enhancement of digital mammography.IEEE Engineering in Medicine and Biology Magazine,1995.14(5):536-550
[37]徐皓,范铁生.一种采用分段线性函数的图像增强方法.辽宁大学学报(自然科学版),2006.65(4):362-364
[38]陈会羽.图像对比度增强的小波变换法.计算机工程与应用,2006.5(25):66-68
[39]Xu Y,Weaver J B,Healy D M,et al.Wavelet transform domain filters:A spatially selective noise filtration technique.IEEE Transactions on Image Processing,1994.3(6):747-758
[40]Zong X,Laine A.F,Geiser E.A.et al.De-noising and contrast enhancement via wavelet shrinkage and non-linear adaptive gain[C].WaveletApplications3:Proceeding of SPIE,Orlando,1996:566-574
[41]吴颖谦,施鹏飞.基于小波变换的低对比度图像增强.红外与激光工程,2003.32(1):4-7
[42]Donoho D L.Nonlinear wavelet methods for recovery of signals,densities,and spectra from indirect and noisy data[A].Proc Symposia Applied Math[C].Rhode Island:American Mathematical Society,1993:173-205
[43]YAN Jingwen,QIAN shen-en.The theory model analysis and evolution for non-Gaussian noise[A].Zhang Jia-jie.Proceedings of Wational Symposium on Developments of Microwave Compatibility,1996:38-44
[44]粘永键.基于三维小波变换的视频图像消噪研究.第四界全国虚拟现实与可视化学术论文集.大连:大连海事大学出版社,2004:424-429
[45]Jawerth B D,Hiton M L,Huntsberger T L.Local enhancement of compressed images.Mathematical Imaging and Vision,1993.3(1):39-49
[46]杜世培,沈敏.分割式图像频域增强及其改进方法.贵州工业大学学报(自然科学版),2000.29(5):95-97
[47]Conzalez R C,Woods R E.Digital image processing.2nd ed.[S.l.]:Publishing House of Electronics Industry,2003
[2]林堪贤,宋国乡,薛文.图像的几种小波去噪方法的比较与改进.西安电子科技大学学报(自然科学版),2004.8:626-629
[3]Keita Alpha,彭嘉雄.基于小波门限化的图像去噪方法.华中科技大学学报,2001.29(6):13-15
[4]韦凤梅,李翠华.基于自适应模糊阈值小波的图像去噪.厦门大学学报,2005.44(2):185-188
[5]查宇飞,毕笃彦.基于小波变换的自适应多阈值图像去噪.中国图像图形学报,2005.10(5):567-570
[6]S.Mallat.A wavelet Tour of signal proeessing.China Machine press,2002.9(1)
[7]S.Mallat.A theory for multi-resolution signal decomposition:The wavelet representation.[J]EEE Trans.Pattern.Anal.Machine Intell,1989.21(7):674-633
[8]Donoho D L,Johnstone J M.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994.81:425-455
[9]Mallat S G.A theory of multiresolution signal decomposition:the wavelet representation.IEEE Trans on PAMI,1989.11(7):674-693
[10]陈贺新.非线形滤波器与数字图像处理.北京:国防工业出版社,2005
[11]Cohen A.Wavelets and multiscale signal processing.Chapman and Hall,1995
[12]Chui,C.K.An introduction to wavelets.Academic Press,2002
[13]Daubechies I.Ten lectures on wavelets.SLAM,2002
[14]Antoniadis,Pham DT[J].Wavelets regression for random or irregular design.Comp.Stat.and Data Analysis,2004
[15]毕为民,唐炬,姚陈果.基于熵阈值的小波包变换抑制局部放电窄带干扰的研究.中国电机工程学报,2003.23(5):128-131
[16]Unser M.Texture classification and segmentation using wavelet frames.IEEE Trans.on IP,1995.4(11):1549-1560
[17]王玲.多小波理论及其在图像处理中的应用研究.西安:西安电子科技大学,2000
[18]孔祥茜,吴继伟,岳继光.地震信号小波变换的去噪方法.计算机辅助工程,200514(3):52-56
[19]郭艳芬,张红梅,曲智林,马晓剑.一种基于小波的并行算法及其在大型数值计算中的应用.东北林业大学学报,2005.33(4):15-116
[20]何坤等.非平稳环境下基于小波变换的图像去噪.中国图像图形学报,2005.10(10):567-570
[21]张宗平,刘贵忠,董恩清.基于二进小波变换的信号去噪.电子与信息学报,2001.23(11):1083-1090
[22]任震,何建军,黄雯莹.基于小波包算法的电机故障信号的压缩和重构.中国电机工程学报,2001.21(1):25-29
[23]李杏梅,陈亮.小波阈值去噪在图像去噪中的应用.现代计算机,2006.10
[24]骆正虎,杨敬安,吴刚.基于小波变换的图像的多分辨率分解与重构的实现.计算机科学,2001,28(10):69-71
[25]C.S.Lu,P.C.Chung,C.R Chen.Unsupervised texture segmentation via wavelet transform,Pattern Recognition,vol.30,no.5,pp.729-742
[26]Donoho D.L.De-noising by soft thresholding.IEEE Trans.on IT.,1995.41(3):613-627
[27]Wang Z,Guerriero A,Sario M De.Comparison of several approaches for the segmentation of texture images.Pattern Recognition Letters,1996.17:509-521
[28]Chang T,Kuo C C J.Texture analysis and classification with tree-structure wavelet transform.IEEE Trans.on IP,1993.2(4):429-441
[29]崔华,宋国乡.基于小波阈值去噪方法的一种改进方案.现代电子技术,2005.1:8-9
[30]Kenneth R,Castleman.数字图像处理.朱志刚,林学闾,石定机译.北京:电子工业出版社,1988
[31]郭敏,马远良,朱霆.基于小波变换的医学超声图像去噪及增强方法.中国医学影像技术,2006.22(9):1435-1437
[32]包振华.基于Matlab的灰度级线性变换图像增强.工程技术,2006.5(3):54-56
[33]张光年.多尺度小波梯度图像增强方法.首都师范大学学报(自然科学版),2006.7(2):16-19
[34]周旋,周树道,黄峰,周小滔.基于小波变换的图像新增强算法.计算机应用,2005.25(3):606-608
[35]Gopinath R A,Lang M,Guo H,et al.Enhancement of decompressed images at low bit rates.SPIE Math Imaging:Wavelet Applications in Signal and Image Processing.San Diego,1994.15(2):366-377
[36]Laine A,Fan J,Yang W.Wavelets for contrast enhancement of digital mammography.IEEE Engineering in Medicine and Biology Magazine,1995.14(5):536-550
[37]徐皓,范铁生.一种采用分段线性函数的图像增强方法.辽宁大学学报(自然科学版),2006.65(4):362-364
[38]陈会羽.图像对比度增强的小波变换法.计算机工程与应用,2006.5(25):66-68
[39]Xu Y,Weaver J B,Healy D M,et al.Wavelet transform domain filters:A spatially selective noise filtration technique.IEEE Transactions on Image Processing,1994.3(6):747-758
[40]Zong X,Laine A.F,Geiser E.A.et al.De-noising and contrast enhancement via wavelet shrinkage and non-linear adaptive gain[C].WaveletApplications3:Proceeding of SPIE,Orlando,1996:566-574
[41]吴颖谦,施鹏飞.基于小波变换的低对比度图像增强.红外与激光工程,2003.32(1):4-7
[42]Donoho D L.Nonlinear wavelet methods for recovery of signals,densities,and spectra from indirect and noisy data[A].Proc Symposia Applied Math[C].Rhode Island:American Mathematical Society,1993:173-205
[43]YAN Jingwen,QIAN shen-en.The theory model analysis and evolution for non-Gaussian noise[A].Zhang Jia-jie.Proceedings of Wational Symposium on Developments of Microwave Compatibility,1996:38-44
[44]粘永键.基于三维小波变换的视频图像消噪研究.第四界全国虚拟现实与可视化学术论文集.大连:大连海事大学出版社,2004:424-429
[45]Jawerth B D,Hiton M L,Huntsberger T L.Local enhancement of compressed images.Mathematical Imaging and Vision,1993.3(1):39-49
[46]杜世培,沈敏.分割式图像频域增强及其改进方法.贵州工业大学学报(自然科学版),2000.29(5):95-97
[47]Conzalez R C,Woods R E.Digital image processing.2nd ed.[S.l.]:Publishing House of Electronics Industry,2003