多分辨率分析及其在图像处理中的应用研究
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摘要
多分辨率分析是局部化时频分析,它用时域和频域的联合来表示信号,是分析非平稳信号的有力工具。它通过基函数的伸缩、平移等运算对信号进行多尺度细化分析,能有效地从信号中提取信息,是一种灵活、快速、有效的高维信号处理算法。二维多分辨率分析中的Ridgelet,Curvelet和Contourlet代表了一类具有多分辨率、时频局域性、方向各异性基函数的变换工具。多分辨率分析是目前国际公认的信号与信息处理领域的高新技术,是信号处理的前沿课题和研究热点。它在信号滤波、图像去噪、图像融合、图像边缘检测等领域的应用越来越多地受到人们的重视。
本论文主要研究多分辨率分析及其在图像处理中的应用。主要在图像去噪、图像融合以及图像边缘检测三个方面进行了研究。
首先,分析了基于多分辨变换图像处理技术的原理,介绍了Wavelet变换、Ridgelet变换、Curvelet变换、Contourlet变换、Steerable Pyramid变换特点以及各变换的系数分布规律。
其次,在分析基于Ridgelet变换去噪的基础上,提出了三种基于Ridgelet变换的图像去噪算法。他们分别为:基于FRIT自适应循环抽样去噪算法、自适应单尺度Ridgelet去噪以及紧缩能量分层有限Ridgelet去噪。另外,为了同时削弱Wavelet的伪吉布斯现象以及Contourlet的划痕效果。根据多分辨率分析原理,在Wavelet域与Contourlet域建立统一的隐马尔可夫树(HMT)去噪模型,实现了对图像的有效去噪与细节增强。这些方法具有多向性,图像信息并行处理,信息利用率高,多频率图像融合增强等特点。并且通过仿真实验,验证了这些去噪方法的有效性和优越性。
再次,针对小波变换在图像融合中,分解方向数目有限的不足。提出两种融合算法,这两种算法分别为基于非亚采样Contourlet变换的图像融合算法和基于Steerable Pyramid融合算法。这两种方法分别在高、低频域采用不同的融合策略,能够对不同分辨率不同方向上的信息进行有效地提取及融合。它们都具有多分辨率分析和多方向滤波等特点,提高了融合后图像中的信息量和清晰度,克服了传统小波融合算法中方向数目受限的不足。通过仿真实验效果及评价质量参数,对所提出的融合算法性能做了综合比较。实验结果表明,文中提到的两种融合方法,均能够对图像进行有效地融合,并且能够在融合过程对细节进行增强。
最后,针对现有基于多分辨率方法在图像边缘检测方面的问题,通过研究多分辨率域图像边缘检测原理,实现了利用Wavelet以及Contourlet对图像高频边缘的有效提取。另外,论文提出一种无缠绕有限Ridgelet定义方式,从根本上解决了有限Ridgelet的“缠绕”问题,并利用àtrous小波代替Mallat小波算法对改进的Radon变换进行检测。提高了奇异点的检测精度。基于该方法的边缘检测能够对线段进行筛选与连接,并能有效检测目标的方向、端点、长度及宽度。实验结果表明,在具有一定噪声干扰的情况下,该算法能够较精确地实现机场跑道及港口边缘的检测,克服了传统有限Ridgelet变换无法定位线段端点的不足。
综上所述,本文研究了基于多分辨率方法在图像处理中的应用,并针对目前该领域中存在的不足,设计相应算法进行改进。仿真实验证实,本文所应用的算法和提出的改进方案,均能够获得很好的效果。
Multi-resolution analysis is local analysis in the time domain and frequency domain,and which represents the signal property using combination of the time domain and frequency domain.It is a useful tool to analyze the Non-stationary signals that implements multi-scale analysis to the signal by the translation and dilation of the mother function.It can effectively extract information from signal.
Multi-resolution analysis is a booming hot research topic in recent years, which aims to obtain flexible,fast and effective signal processing algorithms through efficient approximation and characterization for the inherent geometric structures of high-dimensional data.Ridgelet,Curvelet and Contourlet,as their two-dimensional cases,represent a new type of harmonic transforms with multiresolution,locality,directionality,anisotropy and fixed basis elements.At present,Multi-resolution analysis is international acknowledged advanced technology in the domain of information and signal processing.Meanwhile it is the front question for discuss and study hotspot attached more and more importance to people in the domain such as signal filtering,image denoising, image edge detecting,image fusing etc.
Multi-resolution analysis and its application in image processing are investigated in detail in this dissertation.The main work can be summarized on image denoising,image fusion,image edge detection.
Firstly,the basic principles of the Wavelet、Ridgelet、Contourlet、Steerable Pyramid and their coefficients characteristics are discussed in the dissertation.
Secondly,the finite Ridgelet transform and its application in image denoising are studied.Three denoising algorithms based on Finite Ridgelet Transform (FRIT) are proposed.They are adaptive denoising method based on cycle sample FRIT,block adaptive denoising method based on FRIT and the FRIT denoising method based on compact energy delaminating.To waken the Gibbs done by Wavelet and scratch by Contourlet,this paper theorizes uniform Hidden Markov Tree(HMT) denoising model both in Wavelet and Contourlet domain based on the multi-resolution principle.The method could both denoising and enhances the image efficiently.It is characterized by multi direction option,parallel information processing,high efficiency of information using,and fusing the enhanced on multi-resolution.By the simulation results,the effectiveness and superiority of the methods are proved.
Thirdly,aiming at the limited direction of the Wavelet in the image fusion, the image fusion method based on Contourlet and the method based on Steerable Pyramid are proposed.The two methods for image fusion based on multi-resolution transform extract the edge and detail coefficients and fuse the information in high and low resolutions efficiently.The multi-directional and multi-resolution method fully extracting the fusion information,improves the image definition and information quantity by using different fusion methods in different frequency and directions,which comes over the directional limitation of Wavelet.By simulation experiment and comparison with other arithmetic,the validity and superiority of the method are proved.
Finally,aiming at image fusion in the multi resolution domain,the edge detection methods based on Multi-resolution transform are carried out,which could extract the edge coefficients efficiently by Wavelet and Contourlet.A novel algorithm is presented for solving the "wrap" of the finite Ridgelet transform (FRIT) radically by the no wrap lines,and could advance the detection precision by using a trous Wavelet on the improved finite Radon transform instead of Mallat Wavelet.The method could choose and connect the lines,detect the points the length the width and the direction of the objects.The experimental results show that the method is precise to detect the edges of runways and harbor with the noise and comes over the FRIT defect.
In conclusion,on the base of multi resolution analysis,this paper had researched on multi resolution analysis and its application on the image processing.Aiming at the shortcoming of the transforms,the improved algorithms were proposed.Experimental results indicated that the adopted intelligent optimization algorithms and the proposed methods could attain good results.
本论文主要研究多分辨率分析及其在图像处理中的应用。主要在图像去噪、图像融合以及图像边缘检测三个方面进行了研究。
首先,分析了基于多分辨变换图像处理技术的原理,介绍了Wavelet变换、Ridgelet变换、Curvelet变换、Contourlet变换、Steerable Pyramid变换特点以及各变换的系数分布规律。
其次,在分析基于Ridgelet变换去噪的基础上,提出了三种基于Ridgelet变换的图像去噪算法。他们分别为:基于FRIT自适应循环抽样去噪算法、自适应单尺度Ridgelet去噪以及紧缩能量分层有限Ridgelet去噪。另外,为了同时削弱Wavelet的伪吉布斯现象以及Contourlet的划痕效果。根据多分辨率分析原理,在Wavelet域与Contourlet域建立统一的隐马尔可夫树(HMT)去噪模型,实现了对图像的有效去噪与细节增强。这些方法具有多向性,图像信息并行处理,信息利用率高,多频率图像融合增强等特点。并且通过仿真实验,验证了这些去噪方法的有效性和优越性。
再次,针对小波变换在图像融合中,分解方向数目有限的不足。提出两种融合算法,这两种算法分别为基于非亚采样Contourlet变换的图像融合算法和基于Steerable Pyramid融合算法。这两种方法分别在高、低频域采用不同的融合策略,能够对不同分辨率不同方向上的信息进行有效地提取及融合。它们都具有多分辨率分析和多方向滤波等特点,提高了融合后图像中的信息量和清晰度,克服了传统小波融合算法中方向数目受限的不足。通过仿真实验效果及评价质量参数,对所提出的融合算法性能做了综合比较。实验结果表明,文中提到的两种融合方法,均能够对图像进行有效地融合,并且能够在融合过程对细节进行增强。
最后,针对现有基于多分辨率方法在图像边缘检测方面的问题,通过研究多分辨率域图像边缘检测原理,实现了利用Wavelet以及Contourlet对图像高频边缘的有效提取。另外,论文提出一种无缠绕有限Ridgelet定义方式,从根本上解决了有限Ridgelet的“缠绕”问题,并利用àtrous小波代替Mallat小波算法对改进的Radon变换进行检测。提高了奇异点的检测精度。基于该方法的边缘检测能够对线段进行筛选与连接,并能有效检测目标的方向、端点、长度及宽度。实验结果表明,在具有一定噪声干扰的情况下,该算法能够较精确地实现机场跑道及港口边缘的检测,克服了传统有限Ridgelet变换无法定位线段端点的不足。
综上所述,本文研究了基于多分辨率方法在图像处理中的应用,并针对目前该领域中存在的不足,设计相应算法进行改进。仿真实验证实,本文所应用的算法和提出的改进方案,均能够获得很好的效果。
Multi-resolution analysis is local analysis in the time domain and frequency domain,and which represents the signal property using combination of the time domain and frequency domain.It is a useful tool to analyze the Non-stationary signals that implements multi-scale analysis to the signal by the translation and dilation of the mother function.It can effectively extract information from signal.
Multi-resolution analysis is a booming hot research topic in recent years, which aims to obtain flexible,fast and effective signal processing algorithms through efficient approximation and characterization for the inherent geometric structures of high-dimensional data.Ridgelet,Curvelet and Contourlet,as their two-dimensional cases,represent a new type of harmonic transforms with multiresolution,locality,directionality,anisotropy and fixed basis elements.At present,Multi-resolution analysis is international acknowledged advanced technology in the domain of information and signal processing.Meanwhile it is the front question for discuss and study hotspot attached more and more importance to people in the domain such as signal filtering,image denoising, image edge detecting,image fusing etc.
Multi-resolution analysis and its application in image processing are investigated in detail in this dissertation.The main work can be summarized on image denoising,image fusion,image edge detection.
Firstly,the basic principles of the Wavelet、Ridgelet、Contourlet、Steerable Pyramid and their coefficients characteristics are discussed in the dissertation.
Secondly,the finite Ridgelet transform and its application in image denoising are studied.Three denoising algorithms based on Finite Ridgelet Transform (FRIT) are proposed.They are adaptive denoising method based on cycle sample FRIT,block adaptive denoising method based on FRIT and the FRIT denoising method based on compact energy delaminating.To waken the Gibbs done by Wavelet and scratch by Contourlet,this paper theorizes uniform Hidden Markov Tree(HMT) denoising model both in Wavelet and Contourlet domain based on the multi-resolution principle.The method could both denoising and enhances the image efficiently.It is characterized by multi direction option,parallel information processing,high efficiency of information using,and fusing the enhanced on multi-resolution.By the simulation results,the effectiveness and superiority of the methods are proved.
Thirdly,aiming at the limited direction of the Wavelet in the image fusion, the image fusion method based on Contourlet and the method based on Steerable Pyramid are proposed.The two methods for image fusion based on multi-resolution transform extract the edge and detail coefficients and fuse the information in high and low resolutions efficiently.The multi-directional and multi-resolution method fully extracting the fusion information,improves the image definition and information quantity by using different fusion methods in different frequency and directions,which comes over the directional limitation of Wavelet.By simulation experiment and comparison with other arithmetic,the validity and superiority of the method are proved.
Finally,aiming at image fusion in the multi resolution domain,the edge detection methods based on Multi-resolution transform are carried out,which could extract the edge coefficients efficiently by Wavelet and Contourlet.A novel algorithm is presented for solving the "wrap" of the finite Ridgelet transform (FRIT) radically by the no wrap lines,and could advance the detection precision by using a trous Wavelet on the improved finite Radon transform instead of Mallat Wavelet.The method could choose and connect the lines,detect the points the length the width and the direction of the objects.The experimental results show that the method is precise to detect the edges of runways and harbor with the noise and comes over the FRIT defect.
In conclusion,on the base of multi resolution analysis,this paper had researched on multi resolution analysis and its application on the image processing.Aiming at the shortcoming of the transforms,the improved algorithms were proposed.Experimental results indicated that the adopted intelligent optimization algorithms and the proposed methods could attain good results.
引文
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