SAR幅值图像相干斑抑制的变分PDE模型与算法研究
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摘要
合成孔径雷达(SAR)是深空探测、对地遥感和成像探测的重要手段,在军事和民用等众多领域具有广阔的应用前景。SAR图像的分辨率包括空间分辨率和辐射分辨率,对SAR图像的理解、分析与模式识别非常重要。其中SAR幅值图像的乘性相干斑噪声严重影响了图像的辐射分辨率。因此,如何抑制SAR相干斑噪声是目前研究的一个热点问题。
本文从SAR成像机理出发,以变分偏微分方程图像处理模型为研究主线,结合贝叶斯理论和正则化方法,对SAR图像的相干斑噪声抑制进行理论探索和算法设计。论文主要工作和创新点包括:
首先研究了经典的SAR滤波算法,介绍了Lee滤波、Kuan滤波,Frost滤波,Sigma滤波和精致gamma MAP滤波等5个基于SAR图像局域统计特性估计的滤波算法,分析了经典滤波法的优缺点,进行了实验分析。
第二,研究并实现了基于Aujol和Aubert的图像恢复模型及Huang的快速算法,分析了两个模型在保持图像细节上的不足。基于非局部正则化理论,提出了一个基于非局部正则化与纹理保真的SAR恢复模型。该模型主要在正则化部分进行了改进,得到了一种新的正则化先验模型。研究了像素间的几何距离和相似度的关系后,给出了三种不同的权重函数,分析了不同权重函数引导的正则化先验模型对相干斑噪声抑制的性能。实验证明:新模型因为结合了AA和非局部正则化的优点,可以有效去除图像噪声,并提高了图像细节保持能力。
第三,耦合双树复小波软阈值与Aujol和Aubert的正则化方法,提出了一个双树复小波-全变差驱动的非线性扩散算法。实验证明:双树复小波-全变差驱动的非线性扩散算法具有较好的去噪效果。经与AA算法以及快速算法进行对比分析,验证了本文提出算法的有效性。
Since the emergence of the SAR (Synthetic Aperture Radar), it has been widely applied in military, civilian and other fields, for example: deep space exploration, earth remote sensing and imaging to detect. The Image resolution of the SAR includes spatial resolution and radiometric, which is important for understanding, analysis and pattern recognition about SAR image. The speckle about SAR exerts severe impact on the image quality. Thus, how to curb the speckle has always been a hot spot of research.
This paper starts from the SAR imaging mechanism, focuses on the model of variational partial differential equations, and combines Bayesian method and Regularization method. The aim is for researching theory and algorithm for removing the noise of image effectively. The main job and the great achievements it has made are as follows:
Firstly, it makes the research on classic filtering algorithm of SAR, about local statistical properties of algorithm based SAR (Lee filter, Kuan filter, Frost filter, Sigma filter and exquisite gamma map filter). Also experiments have been done in order to analyze the merits and demerits of classic filtering algorithm.
Secondly, it researches and achieves Aujol and Aubert's image restoration model and Huang's fast algorithm. Also it has discovered the details of maintaining image concerning these two patterns. Based on the theory of non-local regularizing, this thesis has proposed a refreshed SAR pattern based on non-local regularizing and texture fidelity. This pattern has made improvements in the part of regularizing and a new and regularizing priori model has been put forward. Since regularizing priori model has respect to the weighting function, three different weighting functions have been advanced after the research of relations between the geometric distance of pixels and the similarity. Also it researches effect of removing the noise of image using three different weighting functions. For the new pattern integrates AA and the ideas of non-local regularizing, it can retain the details of image better while remove the noise of image effectively. And experiments have verified the above point.
Thirdly, it has proposed a new algorithm: nonlinear diffusion algorithm of dual-tree Complex wavelet - TV, coupling Soft-threshold method of dual-tree complex wavelet and Aujol and Aubert's regularizing method. The new algorithm can remove the noise of image effectively using experiments. The merit of this algorithm can be confirmed by juxtaposing Aujol and Aubert's image restoration model and Huang's fast algorithm.
本文从SAR成像机理出发,以变分偏微分方程图像处理模型为研究主线,结合贝叶斯理论和正则化方法,对SAR图像的相干斑噪声抑制进行理论探索和算法设计。论文主要工作和创新点包括:
首先研究了经典的SAR滤波算法,介绍了Lee滤波、Kuan滤波,Frost滤波,Sigma滤波和精致gamma MAP滤波等5个基于SAR图像局域统计特性估计的滤波算法,分析了经典滤波法的优缺点,进行了实验分析。
第二,研究并实现了基于Aujol和Aubert的图像恢复模型及Huang的快速算法,分析了两个模型在保持图像细节上的不足。基于非局部正则化理论,提出了一个基于非局部正则化与纹理保真的SAR恢复模型。该模型主要在正则化部分进行了改进,得到了一种新的正则化先验模型。研究了像素间的几何距离和相似度的关系后,给出了三种不同的权重函数,分析了不同权重函数引导的正则化先验模型对相干斑噪声抑制的性能。实验证明:新模型因为结合了AA和非局部正则化的优点,可以有效去除图像噪声,并提高了图像细节保持能力。
第三,耦合双树复小波软阈值与Aujol和Aubert的正则化方法,提出了一个双树复小波-全变差驱动的非线性扩散算法。实验证明:双树复小波-全变差驱动的非线性扩散算法具有较好的去噪效果。经与AA算法以及快速算法进行对比分析,验证了本文提出算法的有效性。
Since the emergence of the SAR (Synthetic Aperture Radar), it has been widely applied in military, civilian and other fields, for example: deep space exploration, earth remote sensing and imaging to detect. The Image resolution of the SAR includes spatial resolution and radiometric, which is important for understanding, analysis and pattern recognition about SAR image. The speckle about SAR exerts severe impact on the image quality. Thus, how to curb the speckle has always been a hot spot of research.
This paper starts from the SAR imaging mechanism, focuses on the model of variational partial differential equations, and combines Bayesian method and Regularization method. The aim is for researching theory and algorithm for removing the noise of image effectively. The main job and the great achievements it has made are as follows:
Firstly, it makes the research on classic filtering algorithm of SAR, about local statistical properties of algorithm based SAR (Lee filter, Kuan filter, Frost filter, Sigma filter and exquisite gamma map filter). Also experiments have been done in order to analyze the merits and demerits of classic filtering algorithm.
Secondly, it researches and achieves Aujol and Aubert's image restoration model and Huang's fast algorithm. Also it has discovered the details of maintaining image concerning these two patterns. Based on the theory of non-local regularizing, this thesis has proposed a refreshed SAR pattern based on non-local regularizing and texture fidelity. This pattern has made improvements in the part of regularizing and a new and regularizing priori model has been put forward. Since regularizing priori model has respect to the weighting function, three different weighting functions have been advanced after the research of relations between the geometric distance of pixels and the similarity. Also it researches effect of removing the noise of image using three different weighting functions. For the new pattern integrates AA and the ideas of non-local regularizing, it can retain the details of image better while remove the noise of image effectively. And experiments have verified the above point.
Thirdly, it has proposed a new algorithm: nonlinear diffusion algorithm of dual-tree Complex wavelet - TV, coupling Soft-threshold method of dual-tree complex wavelet and Aujol and Aubert's regularizing method. The new algorithm can remove the noise of image effectively using experiments. The merit of this algorithm can be confirmed by juxtaposing Aujol and Aubert's image restoration model and Huang's fast algorithm.
引文
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[13]Xin W.Lee filter for multiscale image denoising[A].International Conference on Signal Processing Proceedings[C].2006
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[16]Kin L,Benoit V,Kacem C.Processing multi-channel radar images by modified vector sigma filter for edge detection enhancement[A].IEEE International Conference on Acoustics[C].2006:833-836
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[18]Tommi M,Petri M.Fast NML computation for naive bayes models[J].Lecture Notes in Computer Science.2007:151-160
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[34]张红英,彭启琮.变分图像复原中PDE的推导及其数值实现[J].计算机工程与科学,2006,28(6):44-46
[35]Tur M,Chin K C,Goodman J W.When is speckle noise multiplicative[J].Applied Optics.1982,21(7):1157-1159
[36]Aubert G,Kornprobst P.Mathematical Problems in Image Processing[J].Applied Mathematical Sciences on Springer-Verlag.2002
[37]Anzellotti G.The Euler equation for functionals with linear growth[A].Transactions of the American Mathematical Society[C].1985,290(2):483-501
[38]Goodman J W.Statistical Properties of Laser Speckle Patterns[J].Applied Physics in Springer-Vedag.1984
[39]肖亮,吴慧中,韦志辉,汤淑春,刘扬.基于图的数字全变差模型及其带噪图像任意精度放大[J].计算机辅助设计与图形学学报,2004,16(1):51-56
[40]Aubert G,Aujol J F.A variational approach to remove multiplicative noise[J].SIAM Journal on Applied Mathematics.2008:925-946
[41]Lindenbaum M,Fischer M,Bruckstein A.On Gabor's contribution to image enhancement[J].Pattern Recognition.1994:1-8
[42]Krissian K,Vosburgh K,Kikinis R,Westin C F.A new total variation method for multiplicative noise removal[EB/OL].2008,http://www.math.hkbu.edu.hk
[43]Yaroslavsky L.Digital image Processing - an introduction[J].Springer Verlag,1985
[44]Ng M K,Qi L,Yang Y,Huang Y.On semismooth Newton's methods for total variation minimization[J].Journal of Mathematical Imaging and Vision.2007:265-276
[45]Chambolle A.An algorithm for total variation minimization and applications[J].Journal of Mathematical Imaging and Vision.2004,20:89-97
[46]Chambolle A.Total variation minimization and a class of binary MRF models[A].Lecture Notes in Computer Science[C].Springer:Berlin,2005,3757:136-152
[47]Buades A,Coll B,Morel J M.Neighborhood filters and PDE's[J].Numerische Mathematik.2006,105(10):1-34
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[49]Buades A,Coll B,Morel J M.A non-local algorithm for image denoising[A].IEEE Computer Society Conference on Computer Vision[C].2005
[50]Cecil T,Qian J,Osher S.Numerical methods for high dimensional Hamilton-Jacobi equations using radial bases functions[J].Journal of Computational Physics.2004,196:327-347
[51]Barash D.A fundamental relationship between bilateral filtering,adaptive smoothing,and the nonlinear diffusion equation[A].IEEE Transactions on Pattern Analysis and MachineIntelligence[C].2002,24(6):844-847
[52]Rudin L,Osher S,Fatemi E.Nonlinear total variation based noise removal algorithms[A],computational issues in nonlinear science[C].1992:259-268
[53]Chan T F,Osher S,Shen J.The digital TV filter and nonlinear denoising[A].IEEE Trans on Image Process[C].2001,10(2):231-241
[54]Barash D,Comaniciu D.A common framework for nonlinear diffusion,adaptive smoothing,bilateral filtering and mean shift[J].Image and Vision Computing.2004,22(1):73-81,
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[2]Wehner D R.High Resolution radar[J].Artech House.1987:273-340
[3]Aujol J F,Gilboa G,Chen T,Osher S.Structure-Texture Image Decomposition- Modeling,Algorithms,and Parameter Selection[J].International Journal of Computer Vision.2006,67(1):111-136
[4]郭华东.雷达对地观测理论与应用[M].第1版.北京:科学出版社.2000
[5]黄世奇,刘代志.星载SAR成像与SAR图像中一些不确定性因素分析[J].测绘学报,2007:1001-1595
[6]Moser G,Zerubia J,Serpico S B.SAR amplitude probability density function estimation based on a generalized Gaussian scattering model Trans[A].Image Process[C].2006:1429-1442
[7]Donoho D L,Elad M,Temlyakov V.Stable recovery of sparse overcomplete representations in the presence of noise[A].IEEE Trans on Information Theory [C].2006:6-18
[8]Goodman J W.Some fundamental properties of speckle[J].Journal of the optical society of America.American,1976:1145-1150
[9]Bruniquel J and Lopes A.Multi-variate optimal speckle reduction in SAR imagery[J].International Journal of Remote Sensing.1997,18(3):603-627.
[10]Wang Y,Yin W,Zhang Y.A fast algorithm for image deblurring with total variation regularization[A].UCLACAM[C].2007:07-22
[11]Lee J S.Digital image enhancement and noise filtering by use of local statistics[A].IEEE Trans on Pattern Analysis and Machine[C].1980:165-168
[12]Tison C,Nicolas J M,Tupin F,Maitre H.A new statistical model for Markovian classification of urban areas in high-resolution SAR images[A].IEEE Trans on Geoscience and Remote Sensing[C].2004,42(10):2046-2057
[13]Xin W.Lee filter for multiscale image denoising[A].International Conference on Signal Processing Proceedings[C].2006
[14]Yu Y J,Acton S T.Speckle reducing anisotropic diffusion[A].IEEE Trans on Image Processing[C].2006:1480-1484
[15]Chen K H,Chiueh T D.A low-power digit-based reconfigurable FIR filter.IEEE Transactions on Circuits and Systems.2007,53(08):505-507
[16]Kin L,Benoit V,Kacem C.Processing multi-channel radar images by modified vector sigma filter for edge detection enhancement[A].IEEE International Conference on Acoustics[C].2006:833-836
[17]Fei Y,Yue S,Cheng H X.An information audit system based on Bayes algorithm[J].Lecture Notes in Computer Science.2006:869-876
[18]Tommi M,Petri M.Fast NML computation for naive bayes models[J].Lecture Notes in Computer Science.2007:151-160
[19]Migliaccio M,Tranfaglia M,Ermakov M.A physical approach for the observation of oil spills in SAR images[A].IEEE Journal of Oceanic Engineering[C].2005,30(3):495-507
[20]Lopes A,Touzi R,Nezry E.Adaptive speckle filters and scene heterogeneity[A].IEEE Transactions on Geoscience and Remote Sensing[C].1990,28(6):992-1000
[21]Davidson M W J,Steingieber R,Kuhbauch W.Assessing agricultural land use early during the growing season using multi-frequency and multi-polarization SIR-C backscatter features[A].European Conference on Synthetic Aperture Radar[C].1996:473-476
[22]Horstmann J,Schiller H,Schultz-Stellenfelth J,Lehner S.Global wind speed retrieval from SAR[A].IEEE Transactions on Geoscience and Remote Sensing[C].2003,41(10):2277-2286
[23]Walessa M,Datcu M.Model-based despeckling and information extraction from SAR images[A].IEEE Transactions on Geoscience and Remote Sensing[C].1992:568-577
[24]夏德深,傅德胜.计算机图像处理及应用[M].第1版.南京:东南大学出版社,1998
[25]章毓晋.图像工程[M].第2版.北京:清华大学出版社,2006
[26]王家文,曹宇.MATLAB 6.5图像图像处理[M].第1版.北京:北京国防工业出版社,2004
[27]Evans L C.Partial Differential Equations[J].Graduate Studies in Mathematics on American Mathematical Society.1991
[28]Rudin L,Lions P L,Osher S.Multiplicative denoising and deblurring:Theory and algorithms[J]Geometric level Set Methods in Imaging,Vision,and Graphics.2003:103-119
[29]Kornprobst P,Deriche R,Aubert G.Image sequence analysis via partial differential equations[J].Journal of Mathematical Imaging and Vision.1999,11(1):5-26
[30]Buades A,Coll B,Morel J M.A review of image denoising algorithms,with a new one[J].Multiscale Modeling and Simulation.2006,4(2):490-531
[31]Krissian K,Vosburgh K,Kikinis R,Westin C F.Anisotropic diffusion of ultrasound constrained by speckle noise model[EB/OL].2004,http://lmi.bwh.harvard.edu
[32]肖亮,吴慧中,韦志辉,汤淑春.基于总体变差模型的数字滤波器设计及其性能研究[J].信号处理,2003,19(3):247-251
[33]老大中.变分法基础[M].第1版.北京:北京国防工业出版社,2004.
[34]张红英,彭启琮.变分图像复原中PDE的推导及其数值实现[J].计算机工程与科学,2006,28(6):44-46
[35]Tur M,Chin K C,Goodman J W.When is speckle noise multiplicative[J].Applied Optics.1982,21(7):1157-1159
[36]Aubert G,Kornprobst P.Mathematical Problems in Image Processing[J].Applied Mathematical Sciences on Springer-Verlag.2002
[37]Anzellotti G.The Euler equation for functionals with linear growth[A].Transactions of the American Mathematical Society[C].1985,290(2):483-501
[38]Goodman J W.Statistical Properties of Laser Speckle Patterns[J].Applied Physics in Springer-Vedag.1984
[39]肖亮,吴慧中,韦志辉,汤淑春,刘扬.基于图的数字全变差模型及其带噪图像任意精度放大[J].计算机辅助设计与图形学学报,2004,16(1):51-56
[40]Aubert G,Aujol J F.A variational approach to remove multiplicative noise[J].SIAM Journal on Applied Mathematics.2008:925-946
[41]Lindenbaum M,Fischer M,Bruckstein A.On Gabor's contribution to image enhancement[J].Pattern Recognition.1994:1-8
[42]Krissian K,Vosburgh K,Kikinis R,Westin C F.A new total variation method for multiplicative noise removal[EB/OL].2008,http://www.math.hkbu.edu.hk
[43]Yaroslavsky L.Digital image Processing - an introduction[J].Springer Verlag,1985
[44]Ng M K,Qi L,Yang Y,Huang Y.On semismooth Newton's methods for total variation minimization[J].Journal of Mathematical Imaging and Vision.2007:265-276
[45]Chambolle A.An algorithm for total variation minimization and applications[J].Journal of Mathematical Imaging and Vision.2004,20:89-97
[46]Chambolle A.Total variation minimization and a class of binary MRF models[A].Lecture Notes in Computer Science[C].Springer:Berlin,2005,3757:136-152
[47]Buades A,Coll B,Morel J M.Neighborhood filters and PDE's[J].Numerische Mathematik.2006,105(10):1-34
[48]Buades A,Coll B,Morel J M.On image denoising methods[A].SIAM Multiscale Modeling and Simulation[C].2005
[49]Buades A,Coll B,Morel J M.A non-local algorithm for image denoising[A].IEEE Computer Society Conference on Computer Vision[C].2005
[50]Cecil T,Qian J,Osher S.Numerical methods for high dimensional Hamilton-Jacobi equations using radial bases functions[J].Journal of Computational Physics.2004,196:327-347
[51]Barash D.A fundamental relationship between bilateral filtering,adaptive smoothing,and the nonlinear diffusion equation[A].IEEE Transactions on Pattern Analysis and MachineIntelligence[C].2002,24(6):844-847
[52]Rudin L,Osher S,Fatemi E.Nonlinear total variation based noise removal algorithms[A],computational issues in nonlinear science[C].1992:259-268
[53]Chan T F,Osher S,Shen J.The digital TV filter and nonlinear denoising[A].IEEE Trans on Image Process[C].2001,10(2):231-241
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