空域自适应滤波方法及其在斜模式遥感图像复原中的应用
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摘要
计算机技术推动着滚滚的历史车轮驶入了富有挑战的信息时代。随着这一时代的发展,科学研究与实际应用对信号质量的要求与日俱增,为此,先进的数字信号处理技术受到了广泛关注。滤波是数字信号处理中一项重要的研究课题,一方面其能有效地抑制噪声;另一方面滤波方法在理论上与正则化方法以及图像建模理论有着紧密的联系,对滤波方法的研究还能促进其它信号复原问题的解决。
论文着重于空域自适应滤波的理论方法及其应用研究。在理论方法方面,分别开展了总变差(Total Variation,TV)自适应保真权系数的构造方法,张量驱动的曲率保持偏微分方程(Partial Differential Equation,PDE)滤波方法,基于预选择的非局部平均滤波方法,基于各向异性扩散PDE的结构张量平滑方法的研究;在方法应用方面,分别开展了斜模式遥感图像复原框架及去模糊方法的研究。论文取得的主要成果与创新理论如下:
1)提出了结合局部结构信息的TV自适应保真权系数的构造方法。研究分析了已有的保真权系数构造方法,指出了这些方法本质上在寻求局部结构描述子。讨论了局部结构描述子应满足的2个基本条件,即鲁棒性与高精度性,指出了非线性结构张量是一种优良的局部结构描述子,利用非线性结构张量构造了TV自适应保真权系数。实验结果表明,引入了本文自适应保真权系数的TV滤波方法不仅能很好地去除噪声还能较好地保持图像中目标的几何结构,同时滤波速度较快。
2)提出了加权型曲率保持PDE滤波方法。深入分析了目前流行的张量驱动PDE滤波方法,指出了张量驱动的曲率保持PDE滤波方法未考虑各积分曲线可能经历不同的图像结构,如此影响了其对图像边缘的保持能力。在此基础上,利用局部图像方向信息为不同积分曲线设计了相应的权重,得到了一种张量驱动的加权型曲率保持PDE滤波方法。实验结果显示本文方法在滤波的同时能较好地保持图像中边缘与曲率结构,且对图像具有一定的增强能力。
3)深入研究了基于预选择的非局部平均滤波方法,指出了目前已提出的方法在提取图像片特征方面存有的不足。利用二维主成分分析(Two-dimensional PrincipalComponent Analysis,2DPCA)提出了一种有效的非局部平均滤波方法。该方法对基于预选择的非局部平均滤波方法的贡献有:(1)用于提取各图像片特征向量的面向图像片的2DPCA;(2)基于相似距离直方图的相似集自动选取方法;(3)相似距离权重参数自适应选取方法。实验结果表明,本文方法对弱梯度、人脸、以及纹理图像均能取得良好的滤波效果。
4)提出了基于加权型曲率保持PDE的结构张量平滑方法。分析了已有的基于各向异性扩散的结构张量平滑方法,指出了这些方法在平滑张量场时容易破坏结构张量数据中的重要信息,如此造成了所得非线性结构张量不能较好地提取图像中的2维结构信息。将第3章提出的加权型曲率保持PDE图像滤波方法扩展到张量场得到了一种加权型曲率保持PDE张量场平滑方法,继而用该方法平滑结构张量得到了新的非线性结构张量。实验结果表明,本文方法生成的非线性结构张量能较好地提取图像局部2维结构信息。
5)基于图像链优化设计理论,提出了斜模式遥感图像地面复原框架。重点论述了2维采样定理与倒易晶胞理论,用此分析了遥感图像中混叠的起因。利用有效分辨率模型与自适应倒易晶胞研究了斜模式图像获取系统的系统传递函数、混叠、噪声的分布,指出了在欠采样条件下,斜模式采样系统所获图像中存在有用的错位频谱。进一步提出了可通过提高系统截止频率得到上述错位频谱,并以此提高斜模式遥感图像有效分辨率的新观点。在此观点下给出了斜模式遥感图像复原框架,该框架依次由如下4步组成:(1)生成自适应倒易晶胞,(2)提取有效频谱,(3)上采样,(4)去模糊。
6)提出了两种斜模式遥感图像去模糊方法。首先将TV模型中的数据保真项定义在斜模式自适应倒易晶胞上,建立了一种基于自适应倒易晶胞的TV正则化模型,并用第1章提出的方法构造了自适应权系数。进一步地,为使上述模型具备更好的图像复原能力,将梯度保真项引入到该模型得到了一种改进的基于斜模式自适应倒易晶胞的TV正则化模型,并分析指出了梯度保真项具有高频信息补偿能力。实验结果显示本章提出的两种TV正则化模型去模糊效果良好。两种方法中,改进的基于自适应倒易晶胞的TV模型得到的斜模式遥感图像复原结果视觉更清晰,信噪比值更高。
Computer technologies have moved the wheel of history into the ambitious information age. With the developments of the age, the needs of scientific researches and practical applications for high quality signals are becoming more evident. Thus, advanced digital signal technologies have gained wide interests. In the field of digital processing, filtering is a most important research subject, on the one hand, it can be able to suppress noise effectively, and on the other hand, the study of filtering can promote solution of other signal restoration problems due to that filtering is very closely associated with regularization method and image modeling theory in the terms of theory.
This paper mainly focuses on the studies of the spatial adaptive filtering theoretic methods and theirs applications. In the terms of theoretic methods, we have respectively studied methods of designing adaptive fidelity coefficients, tensor-driven curvature preserving PDE based image filtering methods, preselection based non-local means image filtering methods and anisotropic diffusion PDE based structure tensor smoothing methods; In the terms of applications, we have respectively studied restoration framework and deblurring methods for tilting mode satellite image. Main innovation theory and research results have been proposed as following:
1) A local structure information based method for designing the adaptive fidelity coefficients in TV model is proposed. At first, informed methods for computing the adaptive fidelity coefficients are systematically discussed and pointed out that they were trying to search local structure descriptors in essence. Then we present two requirements of local structure descriptors, which are robustness and high accuracy, and indicate that nonlinear structure tensor is an excellent local structure descriptor. After this the adaptive fidelity coefficients are constructed by nonlinear structure tensor. Experimental results show that the TV filtering method with our new adaptive fidelity coefficients is capable of sufficiently preserving geometric information such as edges and corners in addition to its effectiveness for image filtering meanwhile the speed of filtering is fast.
2) A weighted curvature-preserving PDE based filtering method is proposed. At first, informed tensor-driven PDE based filtering methods are systematically analyzed. Then, the tensor-driven curvature-preserving PDE filtering method is pointed out that it can not preserve image edge very well due to that the method did not take into account the differences between integral curves. Based on this, we employ local image directional information to design weight coefficients for different integral curve, and present a new tensor-driven curvature-preserving PDE. Experimental results indicate that new method shows superior performance on preserving image edge and curvature geometric structure, meanwhile the method has some image enhancement ability.
3) The informed preselection based nonlocal means filters are analyzed intensively, and pointed out that they all had defects in terms of feature extraction from image patch. We employ 2DPCA to extract feature from image patch and propose an efficient nonlocal means filter. Mainly, our contributions to the preselection based nonlocal means filter are: (l)patch-oriented 2DPCA for extracting features from image patches; (2)automatic selection of the similar sets based on the histogram of similarity distance.(3)adaptive determination of the similar weight coefficient parameter. Experimental results show that our method can achieve better filtering results in a variety of images, such as weak gradient image, face image and texture image.
4) A structure tensor smoothing method based on the weighted curvature-preserving PDE is proposed. At first, informed anisotropic diffusion based structure tensor smoothing methods are analyzed and pointed out that the smoothing methods can not preserve 2D structure information in structure tensor data leading to that corresponding nonlinear structure tensor are deficient in extracting 2D structure information form image. Then, the image filtering method proposed in the third chapter of this thesis is extended to tensor field, and yield a weighted curvature-preserving PDE based tensor field filtering method. At last, structure tensor is smoothed by the new filtering method and produces a new nonlinear structure tensor. Experimental results indicate that new nonlinear structure tensor can be able to extract local 2D structure information from image well.
5) A restoration framework for tilting mode satellite image based on the theory of theory of optimum design for image chain is proposed. At first, 2D sampling theorem and reciprocal cell theory are discussed especially, and employed to analyze the cause of aliasing in satellite image. Then, the distribution of the systemic modulation transfer function, noise and aliasing of acquisition system of tilting mode satellite image, is studied by using efficient resolution model and adaptive reciprocal cell, and we point out that there could be available malposed frequency spectrum in the tilting mode satellite image, in the context of undersampling. Based on this, a viewpoint that the malposed frequency spectrum can be acquired by increasing systemic cut-off frequency in tilting mode imaging system is proposed. At last, under such condition, we present a restoration framework consisting of four successive steps of generating adaptive reciprocal cell, extracting efficient frequency spectrum, upsampling and deblurring.
6) Two deblurring methods are proposed for titling mode satellite image. At first, the data-fitting term of TV model is rewrite in the fourier domain and defined on the titling mode adaptive reciprocal cell, thus a adaptive reciprocal cell based TV regularization model(ARCTV) is constructed, which also employs the method presented in chapter1 in this thesis to compute the adaptive weight coefficients. Then, in order to improve the deblurring capacity of the ARCTV model, a gradient-fitting term is introduced into it and yields a modification. Future, the gradient-fitting is analyzed and pointed out that it has the ability of compensating high frequency information. Experimental results show that the two proposed methods can achieve good deblured results and the deblurred results by the modified ARCTV method are better, both in visual effect and SNR values.
论文着重于空域自适应滤波的理论方法及其应用研究。在理论方法方面,分别开展了总变差(Total Variation,TV)自适应保真权系数的构造方法,张量驱动的曲率保持偏微分方程(Partial Differential Equation,PDE)滤波方法,基于预选择的非局部平均滤波方法,基于各向异性扩散PDE的结构张量平滑方法的研究;在方法应用方面,分别开展了斜模式遥感图像复原框架及去模糊方法的研究。论文取得的主要成果与创新理论如下:
1)提出了结合局部结构信息的TV自适应保真权系数的构造方法。研究分析了已有的保真权系数构造方法,指出了这些方法本质上在寻求局部结构描述子。讨论了局部结构描述子应满足的2个基本条件,即鲁棒性与高精度性,指出了非线性结构张量是一种优良的局部结构描述子,利用非线性结构张量构造了TV自适应保真权系数。实验结果表明,引入了本文自适应保真权系数的TV滤波方法不仅能很好地去除噪声还能较好地保持图像中目标的几何结构,同时滤波速度较快。
2)提出了加权型曲率保持PDE滤波方法。深入分析了目前流行的张量驱动PDE滤波方法,指出了张量驱动的曲率保持PDE滤波方法未考虑各积分曲线可能经历不同的图像结构,如此影响了其对图像边缘的保持能力。在此基础上,利用局部图像方向信息为不同积分曲线设计了相应的权重,得到了一种张量驱动的加权型曲率保持PDE滤波方法。实验结果显示本文方法在滤波的同时能较好地保持图像中边缘与曲率结构,且对图像具有一定的增强能力。
3)深入研究了基于预选择的非局部平均滤波方法,指出了目前已提出的方法在提取图像片特征方面存有的不足。利用二维主成分分析(Two-dimensional PrincipalComponent Analysis,2DPCA)提出了一种有效的非局部平均滤波方法。该方法对基于预选择的非局部平均滤波方法的贡献有:(1)用于提取各图像片特征向量的面向图像片的2DPCA;(2)基于相似距离直方图的相似集自动选取方法;(3)相似距离权重参数自适应选取方法。实验结果表明,本文方法对弱梯度、人脸、以及纹理图像均能取得良好的滤波效果。
4)提出了基于加权型曲率保持PDE的结构张量平滑方法。分析了已有的基于各向异性扩散的结构张量平滑方法,指出了这些方法在平滑张量场时容易破坏结构张量数据中的重要信息,如此造成了所得非线性结构张量不能较好地提取图像中的2维结构信息。将第3章提出的加权型曲率保持PDE图像滤波方法扩展到张量场得到了一种加权型曲率保持PDE张量场平滑方法,继而用该方法平滑结构张量得到了新的非线性结构张量。实验结果表明,本文方法生成的非线性结构张量能较好地提取图像局部2维结构信息。
5)基于图像链优化设计理论,提出了斜模式遥感图像地面复原框架。重点论述了2维采样定理与倒易晶胞理论,用此分析了遥感图像中混叠的起因。利用有效分辨率模型与自适应倒易晶胞研究了斜模式图像获取系统的系统传递函数、混叠、噪声的分布,指出了在欠采样条件下,斜模式采样系统所获图像中存在有用的错位频谱。进一步提出了可通过提高系统截止频率得到上述错位频谱,并以此提高斜模式遥感图像有效分辨率的新观点。在此观点下给出了斜模式遥感图像复原框架,该框架依次由如下4步组成:(1)生成自适应倒易晶胞,(2)提取有效频谱,(3)上采样,(4)去模糊。
6)提出了两种斜模式遥感图像去模糊方法。首先将TV模型中的数据保真项定义在斜模式自适应倒易晶胞上,建立了一种基于自适应倒易晶胞的TV正则化模型,并用第1章提出的方法构造了自适应权系数。进一步地,为使上述模型具备更好的图像复原能力,将梯度保真项引入到该模型得到了一种改进的基于斜模式自适应倒易晶胞的TV正则化模型,并分析指出了梯度保真项具有高频信息补偿能力。实验结果显示本章提出的两种TV正则化模型去模糊效果良好。两种方法中,改进的基于自适应倒易晶胞的TV模型得到的斜模式遥感图像复原结果视觉更清晰,信噪比值更高。
Computer technologies have moved the wheel of history into the ambitious information age. With the developments of the age, the needs of scientific researches and practical applications for high quality signals are becoming more evident. Thus, advanced digital signal technologies have gained wide interests. In the field of digital processing, filtering is a most important research subject, on the one hand, it can be able to suppress noise effectively, and on the other hand, the study of filtering can promote solution of other signal restoration problems due to that filtering is very closely associated with regularization method and image modeling theory in the terms of theory.
This paper mainly focuses on the studies of the spatial adaptive filtering theoretic methods and theirs applications. In the terms of theoretic methods, we have respectively studied methods of designing adaptive fidelity coefficients, tensor-driven curvature preserving PDE based image filtering methods, preselection based non-local means image filtering methods and anisotropic diffusion PDE based structure tensor smoothing methods; In the terms of applications, we have respectively studied restoration framework and deblurring methods for tilting mode satellite image. Main innovation theory and research results have been proposed as following:
1) A local structure information based method for designing the adaptive fidelity coefficients in TV model is proposed. At first, informed methods for computing the adaptive fidelity coefficients are systematically discussed and pointed out that they were trying to search local structure descriptors in essence. Then we present two requirements of local structure descriptors, which are robustness and high accuracy, and indicate that nonlinear structure tensor is an excellent local structure descriptor. After this the adaptive fidelity coefficients are constructed by nonlinear structure tensor. Experimental results show that the TV filtering method with our new adaptive fidelity coefficients is capable of sufficiently preserving geometric information such as edges and corners in addition to its effectiveness for image filtering meanwhile the speed of filtering is fast.
2) A weighted curvature-preserving PDE based filtering method is proposed. At first, informed tensor-driven PDE based filtering methods are systematically analyzed. Then, the tensor-driven curvature-preserving PDE filtering method is pointed out that it can not preserve image edge very well due to that the method did not take into account the differences between integral curves. Based on this, we employ local image directional information to design weight coefficients for different integral curve, and present a new tensor-driven curvature-preserving PDE. Experimental results indicate that new method shows superior performance on preserving image edge and curvature geometric structure, meanwhile the method has some image enhancement ability.
3) The informed preselection based nonlocal means filters are analyzed intensively, and pointed out that they all had defects in terms of feature extraction from image patch. We employ 2DPCA to extract feature from image patch and propose an efficient nonlocal means filter. Mainly, our contributions to the preselection based nonlocal means filter are: (l)patch-oriented 2DPCA for extracting features from image patches; (2)automatic selection of the similar sets based on the histogram of similarity distance.(3)adaptive determination of the similar weight coefficient parameter. Experimental results show that our method can achieve better filtering results in a variety of images, such as weak gradient image, face image and texture image.
4) A structure tensor smoothing method based on the weighted curvature-preserving PDE is proposed. At first, informed anisotropic diffusion based structure tensor smoothing methods are analyzed and pointed out that the smoothing methods can not preserve 2D structure information in structure tensor data leading to that corresponding nonlinear structure tensor are deficient in extracting 2D structure information form image. Then, the image filtering method proposed in the third chapter of this thesis is extended to tensor field, and yield a weighted curvature-preserving PDE based tensor field filtering method. At last, structure tensor is smoothed by the new filtering method and produces a new nonlinear structure tensor. Experimental results indicate that new nonlinear structure tensor can be able to extract local 2D structure information from image well.
5) A restoration framework for tilting mode satellite image based on the theory of theory of optimum design for image chain is proposed. At first, 2D sampling theorem and reciprocal cell theory are discussed especially, and employed to analyze the cause of aliasing in satellite image. Then, the distribution of the systemic modulation transfer function, noise and aliasing of acquisition system of tilting mode satellite image, is studied by using efficient resolution model and adaptive reciprocal cell, and we point out that there could be available malposed frequency spectrum in the tilting mode satellite image, in the context of undersampling. Based on this, a viewpoint that the malposed frequency spectrum can be acquired by increasing systemic cut-off frequency in tilting mode imaging system is proposed. At last, under such condition, we present a restoration framework consisting of four successive steps of generating adaptive reciprocal cell, extracting efficient frequency spectrum, upsampling and deblurring.
6) Two deblurring methods are proposed for titling mode satellite image. At first, the data-fitting term of TV model is rewrite in the fourier domain and defined on the titling mode adaptive reciprocal cell, thus a adaptive reciprocal cell based TV regularization model(ARCTV) is constructed, which also employs the method presented in chapter1 in this thesis to compute the adaptive weight coefficients. Then, in order to improve the deblurring capacity of the ARCTV model, a gradient-fitting term is introduced into it and yields a modification. Future, the gradient-fitting is analyzed and pointed out that it has the ability of compensating high frequency information. Experimental results show that the two proposed methods can achieve good deblured results and the deblurred results by the modified ARCTV method are better, both in visual effect and SNR values.
引文
[1]Rob Callan著.黄宽厚,田胜丰等译.人工智能[M].北京:电子工业出版社,2004.
[2]L.G.Shapiro,G.C.Stockma著.赵清杰,钱芳,蔡利栋译.计算机视觉[M].北京:电子工业出版社,2005.
[3]史林,赵树杰.数字信号处理[M].北京:科学出版社,2007.
[4]李芳华.数字信号处理[M].保定:河北大学出版社,2003.
[5]G.A.Wright.Magnetic resonance imaging[J].IEEE Signal Processing Magazine,1997,14(1):56-66.
[6]赵喜平.磁共振成像[M].北京:科学出版社,2004.
[7]张直中.机载和星载合成孔径雷达导论[M].北京:电子工业出版社,2004.
[8]张永生,巩丹超等著.高分辨率遥感图像应用:成像模型、处理算法及应用技术[M].北京:科学出版社,2004.
[9]梁顺林著.范闻捷译.定量遥感[M].北京:科学出版社,2009.
[10]吴斌,吴亚东,张红英.基于变分偏微分方程的图像复原技术[M].北京:北京大学出版社,2008.
[11]肖亮.基于变分PDE和多重分形的图像建模理论、算法与应用[D].南京:南京理工大学,2003。
[12]邵文泽.基于图像建模理论的多幅图像正则化超分辨率重建算法研究[D].南京:南京理工大学,2008。
[13]何友,王国宏,彭应宁.多传感器信息融合及应用[M].北京,电子工业出版社,2000.
[14]吴显金.自适应正则化图像复原方法研究[D].长沙:国防科学技术大学,2006.
[15]W.R.Wu,A.Kundu.Image estimation using fast modified reduced update kalman filter[J].IEEE Tranactions On Signal Processing,1992,40(4):915-926.
[16]S.Citrin,M.R.Azimi-Sadjadi.A full-plane block kalman filter for image restoration[J].IEEE Transactions on Image Processing,1992,1(4):488-195.
[17]R.Molina,J.Numez,F.J.Cortijo,et al.Image restorationin astronomy:a Bayesian perspective[J].IEEE signal processing magazine,2001,18(2):11-29.
[18]严佩敏,刘泓等.基于马尔科夫随机场和遗传算法的图像恢复[J].上海大学学报,2000,6(4):355-358.
[19]M.Sigelle.A cumulant expansion technique for simultaneous markov random field image restoration and hyperparameter estimation[J].International Journal of Computer Vision,2000,37(3):275-293.
[20]M.Beige,M.E.Kilmer,E.L.Miller.Wavelet domain image restoration with adaptive edge-preserving regularization[J].IEEE Transactions on Image Processing,2000,9(4):597-608.
[21]R.Molina,J.Mateos,A.K.Katsaggelos,et al.Bayesian multichannel image restoration using compound gauss-markov random fields[J].IEEE Transactions on Image process,2003,12(12):1642-1654.
[22]汪雪林,赵书斌,彭思龙.基于小波域隐马儿可夫树模型的图像复原[J].计算机学报,2005,28(6):1006-1012.
[23]Willis M,Jeffs B.D,Long D.G.Maximum entropy image restoration revisited[C].Proceedings of IEEE International Conference on Image Processing,2000,1:89-92.
[24]陈春涛,黄步根等.最大熵图像及其新进展[J].光学技术,2004,30(1):36-39.
[25]T.Poggio,V.Torre,C.Koch.Computational vision and regularization theory[J].Nature,1985,317(26):314-319.
[26]A.K.Katsaggelos.Digital image restoration[M].Berlin,Germany:Spriner Verlag,1991.
[27]W.Wang,J.Zhang,G.W.Pan.Solution of inverse problems in image processing by wavelet expansion[J].IEEE Transactions on Image processing,1995,4(5):579-593.
[28]E.Belgeand,M.E.Kilmer,E.L.Miller.Wavelet domain image restoration with adaptive edge-preserving regularization[J].IEEE Transactions on Image processing,2000,9(4):597-608.
[29]周祚峰,水鹏郎.交替使用小波去噪和全变差正则化的盲图像恢复算法[J].电子与信息学报,2008,30(12),2912-1615.
[30]刘晨华,颜兵.基于小波变换和偏微分方程的图像去噪方法[J].山东理工大学学报(自然科学版),2007,21(3):94-100.
[31]袁修贵,王琛.一种基于小波分析的各向异性图像去噪方法[J].数学理论与应用,2007,27(1),121-124.
[32]傅红笋,韩波.偏微分方程参数反演的小波多尺度:正则化方法[J].黑龙江大学自然科学学报,2003,20(2),26-27.
[33]J.Bioucas-Dias,M.Figueiredo.A new TWIST:two-step iterative shrinkage/threshilding algorithms for image restoration[J].IEEE Transactions on Image processing,2007,16(12):2992-3004.
[34]M.Elad.Why simple shrinkage is till relevant for redundant representations[J].IEEE Transactions on Information Theory, 2006, 52(12): 5559-5569.
[35] H.Yang, Y D. Wang. An improved method of wavelets basis image denoising using besov norm regularization[J]. Proceeding of the 4~(th) International Conference on Image and Graphics, 2007, 81-85.
[36] J. J. Koenderink. The structures of images[J]. Biological Cybernetics, 1984, 50(5): 363-370.
[37] A. P. Witkin. Scale-space filtering[C]. Proceedings of International Joint Con-ference on Artificial Intelligence, 1983,1019-1022.
[38] L. Alvarez, F. Guichard, P. L. Lions, J. M. Morel. Axioms and fundamental equations of image processing[J]. Archive Rational Mechanics and Analysis. 1993, 123(3): 199-257.
[39] P. Perona, J. Malik. Scale-space and edge detection using anisotropic diffusion[J]. IEEE Transactions on Pattern Recognition and Machine Intelligence, 1990, 12(7): 629-639.
[40] F. Carte, T. Coll, P. Lions, J. M. Morel. Image selective smoothing and edge detection by nonlinear diffusion[J]. SI AM Journal on Numerical Analysis, 1992, 29: 182-193.
[41] M. J. Black, G. Sapiro, D. H. Marimont, et al. Robust anisotropic diffusion[J]. IEEE Transactions on Image Processing, 1998, 7(3):421-432.
[42] G. Gilboa, Y. Y. Zeevi, N. Sochen. Complex diffusion processes for image filtering[C]. Proceedings of the 3~(rd) International Conference on Scale-Space and Morphology in Computer Vision, 2001, 299-307.
[43] J. Weickert. A review of nonlinear diffusion filtering[C]. Proceedings of the 1~(st) International Conference on Scale-Space Theory in Computer Vision, 1997, 1252: 3-28.
[44] G. W. Wei. Generalized perona-malik equation for image restoration[J]. IEEE Signal Processing Letters, 1999, 6(7):165-167.
[45] S. Esedoglu. Stability properties of perona-malik scheme[J]. SIAM Journal on Numerical Analysis, 2006,44(3): 1297-1313.
[46] J. Weickert. Multiscale Texture enhancement[C]. Proceedings of the 6~(th) International Conference on Computer Analysis of Images and Patterns, 1995, 970: 230-237.
[47] J. Weickert, C. Schnorr. A theoretical framework for convex regularizers in PDE-based computation of image motion[J]. International Journal of Computer Vision, 2001,45(3): 245-264.
[48] J. Weickert. Theoretical foundations of anisotropic diffusion in image processing[C]. Proceedings of the 7~(th) conference on Theoretical Foundations of Computer Vision,1994,221-236.
[49]D.Tschumperle,R.Deriche.Vector-valued image regularization with PDE's:a common framework for different applications[J].IEEE Transactions on Pattern Recognition and Machine Intelligence.2005,27(4):506-517.
[50]D.Tschumperle.PDE's based regularization of multivalued images and applications[D].France:University of Nice-Sophia Antipolis,2002.
[51]D.Tschumperle.Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE's[J].International Journal of Computer Vision,2006,68(1),65-82.
[52]石澄贤.几何图像模型及其在医学图像处理中的应用研究[D].南京理工大学博士论文,2005.
[53]L.Rudin,S.Osher,E.Fatemi.Nonlinear total variation based noise removal algorithms[J].Physica D.1992,60(1-4):259-268.
[54]A.Chambolle,P.-L.Lions.Image recovery via total variation minimization and related problems[J].Numerische Mathematik.,1997,76(2):167-188.
[55]T.F.Chan,G.H.Golub,and P.Mulet,A nonlinear primal-dual method for total variation-based image restoration[J].SIAM Journal on Scientific Computing,1999,20(6):1964-1977.
[56]C.Vogel,M.Oman.Iterative methods for total variation denoising[J].SIAM Journal on Scientific Computing,1996,14(1-4):227-238.
[57]C.Vogel.Computational methods for inverse problems[M].Philadelphia:Society for Industrial and Applied Mathematics,2002.
[58]A.Chambolle.An algorithm for total variation minimization and applications[J].Journal of Mathematical Imaging and Vision,2004,20(1-2):89-97.
[59]H.Fu,M.K.Ng,M.Nikolova,and J.L.Barlow.Efficient minimization methods of mixed L2-L1 and L1-L1 norms for image restoration[J].SIAM Journal on Scientific Computing,2006,27(6):1881-1902.
[60]P.Rodriguez,B.Wohlberg.Efficient minimization method for a generalized total variation functional[J].IEEE Transactions on image processing,2009,18(2):322-332.
[61]T.F.Chan,S.Esedoglu.Aspects of total variation regularized L1 function approximation[J].SIAM Journal Applied Mathematics,2005,65(5):1817-1837.
[62]P.Mrazek,M.Navara.Selection of optimal stopping time for nonlinear diffusion filtering[J].International Journal of Computer Vision,2003,52(2/3):189-203.
[63]Y.Meyer.Osillating patterns in image processing and nonlinear evolution equation[M]Providence:American Mathematical Society,2001.
[64]G.Gilboa,N.Sochen,Y.Y.Zeevi.Variational denoising of partly textured images by spatially varying constraints[J].IEEE Transactions on image processing,2006,15(8):2281-2289.
[65]朱立新,王平安,夏德深.非线性扩散图像去噪中的耦合自适应保真项研究[J].计算机辅助设计与图形学报,2006,18(10):1519-1524.
[66]Y.Chan,A.Marquina,P.Mulet.High-order total variation-based image restoration[J].SIAM Journal on Scientific Computing,2000,22(2):503-516.
[67]S.Didas,S.Setzer,G.Steidl.Combined l_2 data and gradient fitting in conjunction with l_1 regularization[J].Advances in Computational Mathematics,2009,30(1):79-99.
[68]L.X.Zhu,D.S.Xia.Staircase effect alleviation by couping gradient fidelity term[J].Image and Vision Computing,2008,26(8):1163-1170.
[69]D.Mumford,J.Shah.Optimal approximation by piecewise smooth functions and associated variational problems[J].Communication on Pure and Applied Mathematics,1989,42(5):577-685.
[70]E.Giorgi,De,M.Carriero,A.Leac.Existence theorem for a minimum problem with free discontinuity set[J].Archive for Rational Mechanics and Analysis.1989,108(3):195-218.
[71]G.Sapiro.Geometric partial differential equations and image analysis[M].Cambridge:Cambridge University Press,2001.
[72]R.Malladi,J.A.Sethian.Image processing:flows under min/max curvatureand mean curvature[J].Graphical models and image processing,1996,58(2):127-141.
[73]N.Sochen,R.Kimmel,R.Malladi.A general framework for low level vision[J].IEEE Transactions on Image Processing,1998,7(3):310-318.
[74]Suk-Ho Lee,Jin Keun Seo.Noise removal with gauss curvature-driven diffusion[J].IEEE Transactions on Image Processing.2005,14(7):904-909.
[75]C.Tomasi,R.Manduchi.Bilateral filtering for gray and color images[C].Processings of IEEE International Conference on Computer Vision,1998:839-846.
[76]A.Buades,B.Coil,J.M.Morel.A review of image denoising algorithms,with a new one[J].SIAM Multiscale Modeling and Simulation,2005,4(2):490-530.
[77]A.Buades,B.Coll,J.M.Morel.The staircasing effect in neighborhood filters and its solution[J].IEEE Transactions Image Processing,2006,15(6):1499-1505.
[78] A. Buades, B. Coll, J. M. Morel. A non-local algorithm for image denoising[C]. Prococessings of IEEE International Conference on Computer Vision and Pattern Recognition, 2005, 60-65.
[79] C. Kervrann, J. Boulanger, P.Coupe. Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[M]. Lecture Notes in Computer Science. Heigelbeg: Springer-Verlag, 2007, 4485: 520-532.
[80] G. Gilboa, J. Darbon, S. Osher, T. Chan. Nonlocal convex functionals for image regularization[R]. UCLA, CAM, Report, 06-57, 2006.
[81] D. Zhou, B. Scholkopf. Regularization on discrete spaces[C]. Processings of German Pattern Recognition Symposium, 2005, 361-368.
[82] A. Elmoataz, O.Lezoray, S. Bougleus. Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing[J]. IEEE Transactions Image Processing, 2008, 17(7): 1047-1060.
[83] G. Peyre, S.Bougleux, L. Cohen. Non-local regularization of inverse problem[C]. Proceedngs of the 10~(th) European Conference on Computer Vision, 2008, 7-68.
[84] D. Tschumperle, L. Brun. Defining some variational methods on the space of patches: applications to multi-valued image denoising and registration[R]. Les cahiers du GREYC, Report, 06-01, 2008.
[85] O. Kleinschmidt, T. Brox, D. Cremers. Nonlocal texture filtering with efficient tree structures and invariant patch similarity measures [C]. International Workshop on local and nonlocal Approximation, Invited paper, 2008.
[86] M. Mahmoudi, G. Sapiro. Fast image and video denoising via nonlocal means of similar neighborhoods [J]. IEEE Signal Processing letters, 2005, 12(12): 839-842.
[87] T. Brox, O. Kleinschmidt, D.Cremers. Efficient nonlocal means for denoising of textural Patterns[J]. IEEE Transactions on Image Processing, 2008, 17(7): 1083-1092.
[88] P. Coupe, P. Yger, S. Prima, et al. An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images[J]. IEEE Transactions on Medical Imaging, 2008, 27(4): 425-440.
[89] S. K. Nath, K. Palaniappan. Adaptive robust structure tensors for orientation estimation and image segmentation[M]. Lecture Notes in Computer Science. Heigelbeg: Springer-Verlag, 2005, 3804: 445-453.
[90] J. Bigun, G. H. Granlund, J. Wiklund. Multidimensional orientation estimation with applications to texture analysis and optical flow[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(8): 775-790.
[91]T.Brox,J.Weickert,B.Burgeth.et al.Nonlinear structure tensors[J].Image and Vision Computing,2006,24(1):41-55.
[92]W.F(o|¨)rstner,E.G(u|¨)lch.A fast operator for detection and precise location of distinct points,corners and centres of circular features[C].Proceedings of ISPRS Intercommission Workshop on Fast Processing of Photogrammetric Data,Interlaken,1987:281-305.
[93]U.K(o|¨)the.Edge and junction detection with an improved structure tensor[M].Lecture Notes in Computer Science.Heigelbeg:Springer-Verlag,2003,2781:25-32.
[94]J.Weickert.Coherence-enhancing diffusion of colour images[J].Image and Vision Computing,1999,17(3):201-212.
[95]J.Weickert.Anisotropic Diffusion in Image processing[M].Stuttgart:Teubner-Verlag,1998.
[96]M.Middendorf,H.-H.Nagel.Estimation and interpretation of discontinuities in optical flow fields[C].Proceedings of IEEE International Conference on Computer Vision,2001:178-183.
[97]H.-H.Nagel,A.Gehrke.Spatiotemporally adaptive estimation and segmentation of OF-fields[M].Lecture Notes in Computer Science.Heigelbeg:Springer-Verlag,1998,1407:86-102.
[98]J.Weijier,R.Boomgaard.Least squares and robust estimation of local image structure[J].International Journal of Computer Vision,2005,64(2/3):143-155.
[99]郑钰辉,潘渝,王平安等.基于迹的非线性结构张量[J].计算机辅助设计与图形学学报,2008,20(2):259-266.
[100]H.R.Sheikh,M.F.Sabir,A.C.Bovik.A statistical evaluation of Recent Full Reference Image Quality Assessment Algorithms[J].IEEE Transactions on image processing,2006,15(11):3441-3452.
[101]R.Y.Tasiand,T.S.Huang.Multiframe image restoration and registration[J].Advances in computer vision and Image Processing,1984,1(2):317-339.
[102]A.M.Tekalp,M.K.Ozkan,M.L.Sezan.High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration[C].Proceedings of IEEE International Conference on Acoustics,Speech and Signal Processing.1992,3:169-172.
[103]S.P.Kim,N.K.Bose,H.M.Valenzuela.Recursive reconstruction of high-resolution image from noisy undersampled frames[J].IEEE Transaction on Acoustics,Speech and Signal.Processing,1990,38(6):1013-1027.
[104]Z.Zhang and R.S.Blum.Region-based image fusion scheme for concealed weapon detection[C].Proceedings of the 31~(th) Annual Conference on Information Sciences and Systems,1997,168-173.
[105]P.E.Eren,M.I.Sezan,A.M.Tekalp.Robust,object-based high-resolution image reconstruction from low-resolution video[J].IEEE Transactions Image Processing,1997,6(10):1446-1451.
[106]J.G.Nagy,D.P.O'leary.Image restoration through subimages and confidence images[J].Electronic Transaction Numerical Analysis,2002,13(1):22-37.
[107]Weerasinghe C,Ji L and Yan H.ROI extraction from motion affected MRI images based on fuzzy and active contour models[C].Proceedings of IEEE International Conference on Acoustics,Speech and Signal Processing.1999,6:3405-3408.
[108]S.Baker,T.Kanade.Limits on super-resolution and how to break them[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(9):1167-1183.
[109]S.Baker,Y.Kanade.Hallucinating Faces[C].Proceedings.of 4~(th) International Conferece on Automatic Face and Gesture Recognition.2000,83-88.
[110]W.T.Freeman,T.R.Jones,E.C.Pasztor.Example-based super-resolution[J].IEEE Computer Graphics and Applications,2002,22(2):56-65.
[111]W.Freeman,E.Pasztor,O.T.Carmichael.Learning low-level vision[J].International Journal of Computer Vision,2000,40(1):25-47.
[112]F.M.Candocia,J.C.Principe.Super-resolution of images based on local correlations[J].IEEE Transcation on Neural Networks,1999,10(2):372-380
[113]S.Borman,R.L.Stevenson.Super-resolution from image sequences-A review[C].Proceedings of 1998 Midwest Symposium on Circuits and Systems.1998,374-378.
[114]H.Ur,D.Gross.Improved resolution from subpixel shifted pictures[J].Graphical Models and Image Processing,1992,54(2):181-186.
[115]T.Komatsu,T.Igarashi,K.AIZAWA.Very high resolution imaging scheme with mutiple difference aperture cameras[J].Signal Processing Image Communication,1993,5(5-6):511-526
[116]N.Nguyen,P.A Milanfar.A Wavelet-Based interpolation-restoration method for superresolution[J].Circuits,Systems,and Signal Processing,Special issue on advanced signal and image reconstruction,2000,19(4):321-338.
[117]S.Lertrattanapanich,H.K.Bose.High resolution image formation from low resolution frames using delaunay triangulation[J].IEEE Transations on Image Processing,2002,11(12):1427-1441.
[118] M. Irani, S, Peleg. Motion analysis for image enhancement: Resolution, occlusion and transparency[J]. Jouranl of Visual Communications and Image Representation, 1993,4(4): 324-335.
[119] R. R. Schultz, R. L Stevenson. Extraction of high resolution frames from video sequences[J]. IEEE Transactions Image Processing, 1996, 5(6): 996-1011
[120] P. Cheeseman, B. Kanefsky, R.Kraft, et al. Super-resolved surface reconstruction from multiple images[M]. G. R. Heidbreder. Maximum Entropy and Bayesian Methods, Santa Barbarra: Kluwer, 1996,293-308.
[121] R. C. Hardie, K. J. Barnard and Armstrong E E. Joint MAP registration and high-resolution image estimation using a sequences of undersampled images [J]. IEEE Transations Image Processing, 1997, 6(12): 1621-1633.
[122] D. Capel, A. Zisserman. Computer Vision Applied to Super Resolution[J]. IEEE Signal Processing, 2003, 20(3): 75-86.
[123] B.C. Tom, A.K. Katsaggelos. Reconstruction of a high resolution image from multiple degraded mis-registered low resolution images [C]. Proceedings of SPIE Conference on Visual Communications and Image Processing, 1994, 2308: 971-981.
[124] A.K. Patti, M.I. Sezan, A. M. Tekalp. Super resolution video reconstruction with arbitrary sampling lattices and nonzero aperture time[J]. IEEE Transacions on Image Processing, 1997,6(8): 1064-1076.
[125] T. F. Chan, C. K. Wong. Multichannel image deconvolution by total variation regularization[C]. Proceedings of SPIE Conference on Advanced Signal Processing: Algorithms, Architectures, and Implementations, 1997, 3162: 358-366.
[126] H. W. Kim, J. H. Jang, K. S. Hong. Edge-enhancing super-resolution using anisotropic diffusion[C]. Proceedings of IEEE International Conferrence on Image Process, 2001,130-133.
[127] M. C. Hong, M. G. Kang, A. K. Katsaggelos. A regularized multichannel restoration approach for globally optimal high resolution video sequence [C]. The International Society for Optical Engineering, 1997, 3024: 1306-1316.
[128] M. Ng, J. Koo, N.K.Bose. Constrained total least-squares computations for high-resolution image reconstruction with multisensors[J]. International Journal of Imaging Systems and Technology, 2002,12(1): 35-42.
[129] H. Y. Fu, J. Barlow. A regularized structured total least squares algorithm for high resolution image reconstruction [J]. Linear Algebra and its Applications, 2004, 391: 75-98.
[130]S.Farsiu,M.D.Robinson,M.Elad,et al.Fast and Robust multiframe Super-Resolution[J].IEEE Transaction on Image Processing,2004,13(10):1327-1344.
[131]周峰.提高采样式光学遥感器图像空间分辨率的方法研究[D].北京:中国空间技术研究院,2005.
[132]J.P.Gleyzes,A.Meygret,C.Fratter,et al.SPOT5:system overview and image ground segment[C].Proceedings of IEEE international Geoscience and Remote sensing symposium,2003,21-25.
[133]谭兵,邢帅,徐青等.SPOT5超模式数据处理技术研究[J].遥感技术与应用,2004,19(4):249-252
[134]郝云彩,纪强.提高线阵CCD相机MTF的细分采样理论与方法[J].航天返回与遥感,1999,20(2):27-31.
[135]钱霖,叶燕.一种提高CCD像元分辨率方法的初步探讨[J].光学技术,2002,28(4):374-375.
[136]周峰,王怀义,马文坡等.传输型光学遥感器斜模式采样新方法研究[J].航天返回与遥感,2005,26(3):47-51.
[137]周峰,王怀义,马文坡等.提高线阵采样式光学遥感器图像空间分辨率的新方法研究[J].宇航学报,2006,27(2):227-232.
[138]L.Alvarez,L.L.Pierre,J.M.Morel.Image selective smoothing and edge detection by nonlinear diffusion[J].SIAM Journal of Numerical Analysis,1992,29(3):845-866.
[139]C.Vogel,M.Oman.Fast,robust total variation-based reconstruction of noisy,blurred images[J].IEEE Transactions on image processing,1998,7(6):227-238.
[140]Y.Chan,C.-K.Wong.Total variation blind deconvolution[J].IEEE Transactions on image processing,1998,7(3):370-375.
[141]Y.Wang,W.Yin,Y Zhang.A Fast Algorithm for image deblurring with total variation regularization.Rice University Houstion Tx,tech.Report,2007.
[142]W.Guo,L.H.Qiao.Inpainting based on total variation[C].Proceedings of International Conference on Wavelet Analysis and Pattern Recognition,2007,2,939-943.
[143]T.F.Chan,J.Shen,H.M.Zhou.Total variation wavelet inpainting[J].Journal of Mathematical Imaging and Vision,2006,25(1):107-125.
[144]肖亮,吴慧中,韦志辉等.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.
[145]A.Chambolle.An algorithm for total variation minimization and applications[J].Journal of Mathematical Imaging and Vision,2004,20(1-2):89-97.
[146]袁小华.超分辨率图像恢复中的方法研究[D].南京:南京理工大学,2005.
[147]F.Malgouyres,F.Guichard.Edge direction preserving imag zooming:a mathematical and numerical analysis[J].SIAM Journal on numerical analysis,2001,39(1):1-37.
[148]朱立新.基于偏微分方程的图像去噪和增强研究[D].南京:南京理工大学,2007.
[149]C.F.Westin,S.E.Maier,B.Khidhir,et al.Image processing for diffusion tensor magnetic resonance imaging[C].Proceedings of the 2~(nd) International Conference on Medical Image Computing and Computer-Assisted Intervention,1999,441-452.
[150]M.Welk,J.Weichert,F.Becker et al.Median and related local filters for tensor-valued images[J].Signal Processing,2007,87(2).
[151]M.Welk,C.Feddern,B.Burgeth,et al,Tensor median filtering and M-smoothing[M].J.Weickert,H.Hagen.Visualization and Processing of Tensor Fields,Springer,Berlin,2006,345-356.
[152]J.Weickert,H.Hagen.visualization and processing of tensor fields[M].Berlin:Springer,2006.
[153]D.Tschumperl(?),R.Deriche.Tensor field visualization with PDE's and application to DT-MRI fiber visualization[M].Porceedings of IEEE Workshop on Variational and Level Set Methods,Nice,2003.
[154]J.Yang,D.Zhang,A.F.Frangi,et al.Two-dimensional PCA:a new approach to appearance-based face representation and recognition.IEEE Transactions on Pattern Analysis and Machine Intelligence,2004,26(1):131-137.
[155]J.Boulanger,C.Kervrann,P.Bouthemy.Adaptive spatio-temporal resoration for 4D fluorescence microscopic imaging[M].Lecture Notes in Computer Science.Heigelbeg:Springer-Verlag,2005,3749:893-901.
[156]A.Almanasa,S.Burand,B.Roug(?).Measuring and improving image resolution by adaptation of the reciprocal cell[J].Journal of Mathematical Imaging and Vision,2004,21(3):235-279
[157]A.Almanasa.Echantillonnage,interpolation et d'etection.Applications en imagerie satellitaire[D].France:Ecole Normale Superieure de Cachan,2002.(in French)(A.Almanasa.Enhancement,interpolation,detection methods and applications to satellite image[D].France:Ecole Normale Superieure de Cachan,2002.)
[158]M.Lionel.Extrapolation de spectre et variation totale pond(?)r(?)e[C].18e colloque sur le traitement du signal et des images,2001.(in French) (M.Lionel.Spectrum extrapolation and weighted total variation[C].Proceedings of 18th symposium on signal and image processing,2001)
[2]L.G.Shapiro,G.C.Stockma著.赵清杰,钱芳,蔡利栋译.计算机视觉[M].北京:电子工业出版社,2005.
[3]史林,赵树杰.数字信号处理[M].北京:科学出版社,2007.
[4]李芳华.数字信号处理[M].保定:河北大学出版社,2003.
[5]G.A.Wright.Magnetic resonance imaging[J].IEEE Signal Processing Magazine,1997,14(1):56-66.
[6]赵喜平.磁共振成像[M].北京:科学出版社,2004.
[7]张直中.机载和星载合成孔径雷达导论[M].北京:电子工业出版社,2004.
[8]张永生,巩丹超等著.高分辨率遥感图像应用:成像模型、处理算法及应用技术[M].北京:科学出版社,2004.
[9]梁顺林著.范闻捷译.定量遥感[M].北京:科学出版社,2009.
[10]吴斌,吴亚东,张红英.基于变分偏微分方程的图像复原技术[M].北京:北京大学出版社,2008.
[11]肖亮.基于变分PDE和多重分形的图像建模理论、算法与应用[D].南京:南京理工大学,2003。
[12]邵文泽.基于图像建模理论的多幅图像正则化超分辨率重建算法研究[D].南京:南京理工大学,2008。
[13]何友,王国宏,彭应宁.多传感器信息融合及应用[M].北京,电子工业出版社,2000.
[14]吴显金.自适应正则化图像复原方法研究[D].长沙:国防科学技术大学,2006.
[15]W.R.Wu,A.Kundu.Image estimation using fast modified reduced update kalman filter[J].IEEE Tranactions On Signal Processing,1992,40(4):915-926.
[16]S.Citrin,M.R.Azimi-Sadjadi.A full-plane block kalman filter for image restoration[J].IEEE Transactions on Image Processing,1992,1(4):488-195.
[17]R.Molina,J.Numez,F.J.Cortijo,et al.Image restorationin astronomy:a Bayesian perspective[J].IEEE signal processing magazine,2001,18(2):11-29.
[18]严佩敏,刘泓等.基于马尔科夫随机场和遗传算法的图像恢复[J].上海大学学报,2000,6(4):355-358.
[19]M.Sigelle.A cumulant expansion technique for simultaneous markov random field image restoration and hyperparameter estimation[J].International Journal of Computer Vision,2000,37(3):275-293.
[20]M.Beige,M.E.Kilmer,E.L.Miller.Wavelet domain image restoration with adaptive edge-preserving regularization[J].IEEE Transactions on Image Processing,2000,9(4):597-608.
[21]R.Molina,J.Mateos,A.K.Katsaggelos,et al.Bayesian multichannel image restoration using compound gauss-markov random fields[J].IEEE Transactions on Image process,2003,12(12):1642-1654.
[22]汪雪林,赵书斌,彭思龙.基于小波域隐马儿可夫树模型的图像复原[J].计算机学报,2005,28(6):1006-1012.
[23]Willis M,Jeffs B.D,Long D.G.Maximum entropy image restoration revisited[C].Proceedings of IEEE International Conference on Image Processing,2000,1:89-92.
[24]陈春涛,黄步根等.最大熵图像及其新进展[J].光学技术,2004,30(1):36-39.
[25]T.Poggio,V.Torre,C.Koch.Computational vision and regularization theory[J].Nature,1985,317(26):314-319.
[26]A.K.Katsaggelos.Digital image restoration[M].Berlin,Germany:Spriner Verlag,1991.
[27]W.Wang,J.Zhang,G.W.Pan.Solution of inverse problems in image processing by wavelet expansion[J].IEEE Transactions on Image processing,1995,4(5):579-593.
[28]E.Belgeand,M.E.Kilmer,E.L.Miller.Wavelet domain image restoration with adaptive edge-preserving regularization[J].IEEE Transactions on Image processing,2000,9(4):597-608.
[29]周祚峰,水鹏郎.交替使用小波去噪和全变差正则化的盲图像恢复算法[J].电子与信息学报,2008,30(12),2912-1615.
[30]刘晨华,颜兵.基于小波变换和偏微分方程的图像去噪方法[J].山东理工大学学报(自然科学版),2007,21(3):94-100.
[31]袁修贵,王琛.一种基于小波分析的各向异性图像去噪方法[J].数学理论与应用,2007,27(1),121-124.
[32]傅红笋,韩波.偏微分方程参数反演的小波多尺度:正则化方法[J].黑龙江大学自然科学学报,2003,20(2),26-27.
[33]J.Bioucas-Dias,M.Figueiredo.A new TWIST:two-step iterative shrinkage/threshilding algorithms for image restoration[J].IEEE Transactions on Image processing,2007,16(12):2992-3004.
[34]M.Elad.Why simple shrinkage is till relevant for redundant representations[J].IEEE Transactions on Information Theory, 2006, 52(12): 5559-5569.
[35] H.Yang, Y D. Wang. An improved method of wavelets basis image denoising using besov norm regularization[J]. Proceeding of the 4~(th) International Conference on Image and Graphics, 2007, 81-85.
[36] J. J. Koenderink. The structures of images[J]. Biological Cybernetics, 1984, 50(5): 363-370.
[37] A. P. Witkin. Scale-space filtering[C]. Proceedings of International Joint Con-ference on Artificial Intelligence, 1983,1019-1022.
[38] L. Alvarez, F. Guichard, P. L. Lions, J. M. Morel. Axioms and fundamental equations of image processing[J]. Archive Rational Mechanics and Analysis. 1993, 123(3): 199-257.
[39] P. Perona, J. Malik. Scale-space and edge detection using anisotropic diffusion[J]. IEEE Transactions on Pattern Recognition and Machine Intelligence, 1990, 12(7): 629-639.
[40] F. Carte, T. Coll, P. Lions, J. M. Morel. Image selective smoothing and edge detection by nonlinear diffusion[J]. SI AM Journal on Numerical Analysis, 1992, 29: 182-193.
[41] M. J. Black, G. Sapiro, D. H. Marimont, et al. Robust anisotropic diffusion[J]. IEEE Transactions on Image Processing, 1998, 7(3):421-432.
[42] G. Gilboa, Y. Y. Zeevi, N. Sochen. Complex diffusion processes for image filtering[C]. Proceedings of the 3~(rd) International Conference on Scale-Space and Morphology in Computer Vision, 2001, 299-307.
[43] J. Weickert. A review of nonlinear diffusion filtering[C]. Proceedings of the 1~(st) International Conference on Scale-Space Theory in Computer Vision, 1997, 1252: 3-28.
[44] G. W. Wei. Generalized perona-malik equation for image restoration[J]. IEEE Signal Processing Letters, 1999, 6(7):165-167.
[45] S. Esedoglu. Stability properties of perona-malik scheme[J]. SIAM Journal on Numerical Analysis, 2006,44(3): 1297-1313.
[46] J. Weickert. Multiscale Texture enhancement[C]. Proceedings of the 6~(th) International Conference on Computer Analysis of Images and Patterns, 1995, 970: 230-237.
[47] J. Weickert, C. Schnorr. A theoretical framework for convex regularizers in PDE-based computation of image motion[J]. International Journal of Computer Vision, 2001,45(3): 245-264.
[48] J. Weickert. Theoretical foundations of anisotropic diffusion in image processing[C]. Proceedings of the 7~(th) conference on Theoretical Foundations of Computer Vision,1994,221-236.
[49]D.Tschumperle,R.Deriche.Vector-valued image regularization with PDE's:a common framework for different applications[J].IEEE Transactions on Pattern Recognition and Machine Intelligence.2005,27(4):506-517.
[50]D.Tschumperle.PDE's based regularization of multivalued images and applications[D].France:University of Nice-Sophia Antipolis,2002.
[51]D.Tschumperle.Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE's[J].International Journal of Computer Vision,2006,68(1),65-82.
[52]石澄贤.几何图像模型及其在医学图像处理中的应用研究[D].南京理工大学博士论文,2005.
[53]L.Rudin,S.Osher,E.Fatemi.Nonlinear total variation based noise removal algorithms[J].Physica D.1992,60(1-4):259-268.
[54]A.Chambolle,P.-L.Lions.Image recovery via total variation minimization and related problems[J].Numerische Mathematik.,1997,76(2):167-188.
[55]T.F.Chan,G.H.Golub,and P.Mulet,A nonlinear primal-dual method for total variation-based image restoration[J].SIAM Journal on Scientific Computing,1999,20(6):1964-1977.
[56]C.Vogel,M.Oman.Iterative methods for total variation denoising[J].SIAM Journal on Scientific Computing,1996,14(1-4):227-238.
[57]C.Vogel.Computational methods for inverse problems[M].Philadelphia:Society for Industrial and Applied Mathematics,2002.
[58]A.Chambolle.An algorithm for total variation minimization and applications[J].Journal of Mathematical Imaging and Vision,2004,20(1-2):89-97.
[59]H.Fu,M.K.Ng,M.Nikolova,and J.L.Barlow.Efficient minimization methods of mixed L2-L1 and L1-L1 norms for image restoration[J].SIAM Journal on Scientific Computing,2006,27(6):1881-1902.
[60]P.Rodriguez,B.Wohlberg.Efficient minimization method for a generalized total variation functional[J].IEEE Transactions on image processing,2009,18(2):322-332.
[61]T.F.Chan,S.Esedoglu.Aspects of total variation regularized L1 function approximation[J].SIAM Journal Applied Mathematics,2005,65(5):1817-1837.
[62]P.Mrazek,M.Navara.Selection of optimal stopping time for nonlinear diffusion filtering[J].International Journal of Computer Vision,2003,52(2/3):189-203.
[63]Y.Meyer.Osillating patterns in image processing and nonlinear evolution equation[M]Providence:American Mathematical Society,2001.
[64]G.Gilboa,N.Sochen,Y.Y.Zeevi.Variational denoising of partly textured images by spatially varying constraints[J].IEEE Transactions on image processing,2006,15(8):2281-2289.
[65]朱立新,王平安,夏德深.非线性扩散图像去噪中的耦合自适应保真项研究[J].计算机辅助设计与图形学报,2006,18(10):1519-1524.
[66]Y.Chan,A.Marquina,P.Mulet.High-order total variation-based image restoration[J].SIAM Journal on Scientific Computing,2000,22(2):503-516.
[67]S.Didas,S.Setzer,G.Steidl.Combined l_2 data and gradient fitting in conjunction with l_1 regularization[J].Advances in Computational Mathematics,2009,30(1):79-99.
[68]L.X.Zhu,D.S.Xia.Staircase effect alleviation by couping gradient fidelity term[J].Image and Vision Computing,2008,26(8):1163-1170.
[69]D.Mumford,J.Shah.Optimal approximation by piecewise smooth functions and associated variational problems[J].Communication on Pure and Applied Mathematics,1989,42(5):577-685.
[70]E.Giorgi,De,M.Carriero,A.Leac.Existence theorem for a minimum problem with free discontinuity set[J].Archive for Rational Mechanics and Analysis.1989,108(3):195-218.
[71]G.Sapiro.Geometric partial differential equations and image analysis[M].Cambridge:Cambridge University Press,2001.
[72]R.Malladi,J.A.Sethian.Image processing:flows under min/max curvatureand mean curvature[J].Graphical models and image processing,1996,58(2):127-141.
[73]N.Sochen,R.Kimmel,R.Malladi.A general framework for low level vision[J].IEEE Transactions on Image Processing,1998,7(3):310-318.
[74]Suk-Ho Lee,Jin Keun Seo.Noise removal with gauss curvature-driven diffusion[J].IEEE Transactions on Image Processing.2005,14(7):904-909.
[75]C.Tomasi,R.Manduchi.Bilateral filtering for gray and color images[C].Processings of IEEE International Conference on Computer Vision,1998:839-846.
[76]A.Buades,B.Coil,J.M.Morel.A review of image denoising algorithms,with a new one[J].SIAM Multiscale Modeling and Simulation,2005,4(2):490-530.
[77]A.Buades,B.Coll,J.M.Morel.The staircasing effect in neighborhood filters and its solution[J].IEEE Transactions Image Processing,2006,15(6):1499-1505.
[78] A. Buades, B. Coll, J. M. Morel. A non-local algorithm for image denoising[C]. Prococessings of IEEE International Conference on Computer Vision and Pattern Recognition, 2005, 60-65.
[79] C. Kervrann, J. Boulanger, P.Coupe. Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[M]. Lecture Notes in Computer Science. Heigelbeg: Springer-Verlag, 2007, 4485: 520-532.
[80] G. Gilboa, J. Darbon, S. Osher, T. Chan. Nonlocal convex functionals for image regularization[R]. UCLA, CAM, Report, 06-57, 2006.
[81] D. Zhou, B. Scholkopf. Regularization on discrete spaces[C]. Processings of German Pattern Recognition Symposium, 2005, 361-368.
[82] A. Elmoataz, O.Lezoray, S. Bougleus. Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing[J]. IEEE Transactions Image Processing, 2008, 17(7): 1047-1060.
[83] G. Peyre, S.Bougleux, L. Cohen. Non-local regularization of inverse problem[C]. Proceedngs of the 10~(th) European Conference on Computer Vision, 2008, 7-68.
[84] D. Tschumperle, L. Brun. Defining some variational methods on the space of patches: applications to multi-valued image denoising and registration[R]. Les cahiers du GREYC, Report, 06-01, 2008.
[85] O. Kleinschmidt, T. Brox, D. Cremers. Nonlocal texture filtering with efficient tree structures and invariant patch similarity measures [C]. International Workshop on local and nonlocal Approximation, Invited paper, 2008.
[86] M. Mahmoudi, G. Sapiro. Fast image and video denoising via nonlocal means of similar neighborhoods [J]. IEEE Signal Processing letters, 2005, 12(12): 839-842.
[87] T. Brox, O. Kleinschmidt, D.Cremers. Efficient nonlocal means for denoising of textural Patterns[J]. IEEE Transactions on Image Processing, 2008, 17(7): 1083-1092.
[88] P. Coupe, P. Yger, S. Prima, et al. An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images[J]. IEEE Transactions on Medical Imaging, 2008, 27(4): 425-440.
[89] S. K. Nath, K. Palaniappan. Adaptive robust structure tensors for orientation estimation and image segmentation[M]. Lecture Notes in Computer Science. Heigelbeg: Springer-Verlag, 2005, 3804: 445-453.
[90] J. Bigun, G. H. Granlund, J. Wiklund. Multidimensional orientation estimation with applications to texture analysis and optical flow[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(8): 775-790.
[91]T.Brox,J.Weickert,B.Burgeth.et al.Nonlinear structure tensors[J].Image and Vision Computing,2006,24(1):41-55.
[92]W.F(o|¨)rstner,E.G(u|¨)lch.A fast operator for detection and precise location of distinct points,corners and centres of circular features[C].Proceedings of ISPRS Intercommission Workshop on Fast Processing of Photogrammetric Data,Interlaken,1987:281-305.
[93]U.K(o|¨)the.Edge and junction detection with an improved structure tensor[M].Lecture Notes in Computer Science.Heigelbeg:Springer-Verlag,2003,2781:25-32.
[94]J.Weickert.Coherence-enhancing diffusion of colour images[J].Image and Vision Computing,1999,17(3):201-212.
[95]J.Weickert.Anisotropic Diffusion in Image processing[M].Stuttgart:Teubner-Verlag,1998.
[96]M.Middendorf,H.-H.Nagel.Estimation and interpretation of discontinuities in optical flow fields[C].Proceedings of IEEE International Conference on Computer Vision,2001:178-183.
[97]H.-H.Nagel,A.Gehrke.Spatiotemporally adaptive estimation and segmentation of OF-fields[M].Lecture Notes in Computer Science.Heigelbeg:Springer-Verlag,1998,1407:86-102.
[98]J.Weijier,R.Boomgaard.Least squares and robust estimation of local image structure[J].International Journal of Computer Vision,2005,64(2/3):143-155.
[99]郑钰辉,潘渝,王平安等.基于迹的非线性结构张量[J].计算机辅助设计与图形学学报,2008,20(2):259-266.
[100]H.R.Sheikh,M.F.Sabir,A.C.Bovik.A statistical evaluation of Recent Full Reference Image Quality Assessment Algorithms[J].IEEE Transactions on image processing,2006,15(11):3441-3452.
[101]R.Y.Tasiand,T.S.Huang.Multiframe image restoration and registration[J].Advances in computer vision and Image Processing,1984,1(2):317-339.
[102]A.M.Tekalp,M.K.Ozkan,M.L.Sezan.High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration[C].Proceedings of IEEE International Conference on Acoustics,Speech and Signal Processing.1992,3:169-172.
[103]S.P.Kim,N.K.Bose,H.M.Valenzuela.Recursive reconstruction of high-resolution image from noisy undersampled frames[J].IEEE Transaction on Acoustics,Speech and Signal.Processing,1990,38(6):1013-1027.
[104]Z.Zhang and R.S.Blum.Region-based image fusion scheme for concealed weapon detection[C].Proceedings of the 31~(th) Annual Conference on Information Sciences and Systems,1997,168-173.
[105]P.E.Eren,M.I.Sezan,A.M.Tekalp.Robust,object-based high-resolution image reconstruction from low-resolution video[J].IEEE Transactions Image Processing,1997,6(10):1446-1451.
[106]J.G.Nagy,D.P.O'leary.Image restoration through subimages and confidence images[J].Electronic Transaction Numerical Analysis,2002,13(1):22-37.
[107]Weerasinghe C,Ji L and Yan H.ROI extraction from motion affected MRI images based on fuzzy and active contour models[C].Proceedings of IEEE International Conference on Acoustics,Speech and Signal Processing.1999,6:3405-3408.
[108]S.Baker,T.Kanade.Limits on super-resolution and how to break them[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(9):1167-1183.
[109]S.Baker,Y.Kanade.Hallucinating Faces[C].Proceedings.of 4~(th) International Conferece on Automatic Face and Gesture Recognition.2000,83-88.
[110]W.T.Freeman,T.R.Jones,E.C.Pasztor.Example-based super-resolution[J].IEEE Computer Graphics and Applications,2002,22(2):56-65.
[111]W.Freeman,E.Pasztor,O.T.Carmichael.Learning low-level vision[J].International Journal of Computer Vision,2000,40(1):25-47.
[112]F.M.Candocia,J.C.Principe.Super-resolution of images based on local correlations[J].IEEE Transcation on Neural Networks,1999,10(2):372-380
[113]S.Borman,R.L.Stevenson.Super-resolution from image sequences-A review[C].Proceedings of 1998 Midwest Symposium on Circuits and Systems.1998,374-378.
[114]H.Ur,D.Gross.Improved resolution from subpixel shifted pictures[J].Graphical Models and Image Processing,1992,54(2):181-186.
[115]T.Komatsu,T.Igarashi,K.AIZAWA.Very high resolution imaging scheme with mutiple difference aperture cameras[J].Signal Processing Image Communication,1993,5(5-6):511-526
[116]N.Nguyen,P.A Milanfar.A Wavelet-Based interpolation-restoration method for superresolution[J].Circuits,Systems,and Signal Processing,Special issue on advanced signal and image reconstruction,2000,19(4):321-338.
[117]S.Lertrattanapanich,H.K.Bose.High resolution image formation from low resolution frames using delaunay triangulation[J].IEEE Transations on Image Processing,2002,11(12):1427-1441.
[118] M. Irani, S, Peleg. Motion analysis for image enhancement: Resolution, occlusion and transparency[J]. Jouranl of Visual Communications and Image Representation, 1993,4(4): 324-335.
[119] R. R. Schultz, R. L Stevenson. Extraction of high resolution frames from video sequences[J]. IEEE Transactions Image Processing, 1996, 5(6): 996-1011
[120] P. Cheeseman, B. Kanefsky, R.Kraft, et al. Super-resolved surface reconstruction from multiple images[M]. G. R. Heidbreder. Maximum Entropy and Bayesian Methods, Santa Barbarra: Kluwer, 1996,293-308.
[121] R. C. Hardie, K. J. Barnard and Armstrong E E. Joint MAP registration and high-resolution image estimation using a sequences of undersampled images [J]. IEEE Transations Image Processing, 1997, 6(12): 1621-1633.
[122] D. Capel, A. Zisserman. Computer Vision Applied to Super Resolution[J]. IEEE Signal Processing, 2003, 20(3): 75-86.
[123] B.C. Tom, A.K. Katsaggelos. Reconstruction of a high resolution image from multiple degraded mis-registered low resolution images [C]. Proceedings of SPIE Conference on Visual Communications and Image Processing, 1994, 2308: 971-981.
[124] A.K. Patti, M.I. Sezan, A. M. Tekalp. Super resolution video reconstruction with arbitrary sampling lattices and nonzero aperture time[J]. IEEE Transacions on Image Processing, 1997,6(8): 1064-1076.
[125] T. F. Chan, C. K. Wong. Multichannel image deconvolution by total variation regularization[C]. Proceedings of SPIE Conference on Advanced Signal Processing: Algorithms, Architectures, and Implementations, 1997, 3162: 358-366.
[126] H. W. Kim, J. H. Jang, K. S. Hong. Edge-enhancing super-resolution using anisotropic diffusion[C]. Proceedings of IEEE International Conferrence on Image Process, 2001,130-133.
[127] M. C. Hong, M. G. Kang, A. K. Katsaggelos. A regularized multichannel restoration approach for globally optimal high resolution video sequence [C]. The International Society for Optical Engineering, 1997, 3024: 1306-1316.
[128] M. Ng, J. Koo, N.K.Bose. Constrained total least-squares computations for high-resolution image reconstruction with multisensors[J]. International Journal of Imaging Systems and Technology, 2002,12(1): 35-42.
[129] H. Y. Fu, J. Barlow. A regularized structured total least squares algorithm for high resolution image reconstruction [J]. Linear Algebra and its Applications, 2004, 391: 75-98.
[130]S.Farsiu,M.D.Robinson,M.Elad,et al.Fast and Robust multiframe Super-Resolution[J].IEEE Transaction on Image Processing,2004,13(10):1327-1344.
[131]周峰.提高采样式光学遥感器图像空间分辨率的方法研究[D].北京:中国空间技术研究院,2005.
[132]J.P.Gleyzes,A.Meygret,C.Fratter,et al.SPOT5:system overview and image ground segment[C].Proceedings of IEEE international Geoscience and Remote sensing symposium,2003,21-25.
[133]谭兵,邢帅,徐青等.SPOT5超模式数据处理技术研究[J].遥感技术与应用,2004,19(4):249-252
[134]郝云彩,纪强.提高线阵CCD相机MTF的细分采样理论与方法[J].航天返回与遥感,1999,20(2):27-31.
[135]钱霖,叶燕.一种提高CCD像元分辨率方法的初步探讨[J].光学技术,2002,28(4):374-375.
[136]周峰,王怀义,马文坡等.传输型光学遥感器斜模式采样新方法研究[J].航天返回与遥感,2005,26(3):47-51.
[137]周峰,王怀义,马文坡等.提高线阵采样式光学遥感器图像空间分辨率的新方法研究[J].宇航学报,2006,27(2):227-232.
[138]L.Alvarez,L.L.Pierre,J.M.Morel.Image selective smoothing and edge detection by nonlinear diffusion[J].SIAM Journal of Numerical Analysis,1992,29(3):845-866.
[139]C.Vogel,M.Oman.Fast,robust total variation-based reconstruction of noisy,blurred images[J].IEEE Transactions on image processing,1998,7(6):227-238.
[140]Y.Chan,C.-K.Wong.Total variation blind deconvolution[J].IEEE Transactions on image processing,1998,7(3):370-375.
[141]Y.Wang,W.Yin,Y Zhang.A Fast Algorithm for image deblurring with total variation regularization.Rice University Houstion Tx,tech.Report,2007.
[142]W.Guo,L.H.Qiao.Inpainting based on total variation[C].Proceedings of International Conference on Wavelet Analysis and Pattern Recognition,2007,2,939-943.
[143]T.F.Chan,J.Shen,H.M.Zhou.Total variation wavelet inpainting[J].Journal of Mathematical Imaging and Vision,2006,25(1):107-125.
[144]肖亮,吴慧中,韦志辉等.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.
[145]A.Chambolle.An algorithm for total variation minimization and applications[J].Journal of Mathematical Imaging and Vision,2004,20(1-2):89-97.
[146]袁小华.超分辨率图像恢复中的方法研究[D].南京:南京理工大学,2005.
[147]F.Malgouyres,F.Guichard.Edge direction preserving imag zooming:a mathematical and numerical analysis[J].SIAM Journal on numerical analysis,2001,39(1):1-37.
[148]朱立新.基于偏微分方程的图像去噪和增强研究[D].南京:南京理工大学,2007.
[149]C.F.Westin,S.E.Maier,B.Khidhir,et al.Image processing for diffusion tensor magnetic resonance imaging[C].Proceedings of the 2~(nd) International Conference on Medical Image Computing and Computer-Assisted Intervention,1999,441-452.
[150]M.Welk,J.Weichert,F.Becker et al.Median and related local filters for tensor-valued images[J].Signal Processing,2007,87(2).
[151]M.Welk,C.Feddern,B.Burgeth,et al,Tensor median filtering and M-smoothing[M].J.Weickert,H.Hagen.Visualization and Processing of Tensor Fields,Springer,Berlin,2006,345-356.
[152]J.Weickert,H.Hagen.visualization and processing of tensor fields[M].Berlin:Springer,2006.
[153]D.Tschumperl(?),R.Deriche.Tensor field visualization with PDE's and application to DT-MRI fiber visualization[M].Porceedings of IEEE Workshop on Variational and Level Set Methods,Nice,2003.
[154]J.Yang,D.Zhang,A.F.Frangi,et al.Two-dimensional PCA:a new approach to appearance-based face representation and recognition.IEEE Transactions on Pattern Analysis and Machine Intelligence,2004,26(1):131-137.
[155]J.Boulanger,C.Kervrann,P.Bouthemy.Adaptive spatio-temporal resoration for 4D fluorescence microscopic imaging[M].Lecture Notes in Computer Science.Heigelbeg:Springer-Verlag,2005,3749:893-901.
[156]A.Almanasa,S.Burand,B.Roug(?).Measuring and improving image resolution by adaptation of the reciprocal cell[J].Journal of Mathematical Imaging and Vision,2004,21(3):235-279
[157]A.Almanasa.Echantillonnage,interpolation et d'etection.Applications en imagerie satellitaire[D].France:Ecole Normale Superieure de Cachan,2002.(in French)(A.Almanasa.Enhancement,interpolation,detection methods and applications to satellite image[D].France:Ecole Normale Superieure de Cachan,2002.)
[158]M.Lionel.Extrapolation de spectre et variation totale pond(?)r(?)e[C].18e colloque sur le traitement du signal et des images,2001.(in French) (M.Lionel.Spectrum extrapolation and weighted total variation[C].Proceedings of 18th symposium on signal and image processing,2001)