结构保持的图像去噪方法研究
|
摘要
图像在获取和传输过程中,不可避免地会受到噪声污染,致使图像质量下降,严重影响了后续图像处理工作(如图像超分辨率、图像分割、图像识别、特征提取等)。为了提高图像质量,为后续图像处理提供更可靠真实的图像,对图像进行去噪处理就成为图像处理中一项基础而重要的研究工作。图像去噪的目的是根据观察到的降质图像估计恢复原始真实图像,即在去除噪声同时更好保持图像中的重要结构信息。研究如何更好保持图像的边缘、纹理等重要结构信息的图像去噪模型和算法具有重要的理论意义和实用价值。
本论文以刻画边缘和纹理的图像先验建模为出发点,利用小波变换、核回归及非局部均值等图像去噪方法,重点研究方法中的纹理、边缘等结构保持问题,提出一系列的结构保持的图像去噪模型和新算法。取得的主要成果及创新点如下：
(1)提出一种新的基于小波系数相关性的图像去噪方法。利用小波系数多尺度相关性及小波系数极大值,定义两种基于最大子结点的相关系数,结合小波阈值进行图像去噪,并且将定义的相关系数推广到分数阶B样条小波域。理论分析和实验结果均表明,所提出相关系数在小波分解的高频子带可以很好地刻画图像结构,因而在去噪过程中保留了更多的边缘与纹理等结构信息,提高了去噪图像的质量。
(2)针对基于正则性指数图像去噪方法的不足,提出正则性指数和图像全变差(Total Variation, TV)正则先验结合的图像去噪模型。该模型利用小波系数与信号正则性之间的关系,在小波分解的不同尺度,通过改变小波系数来提高图像局部正则性。有效克服了正则性指数去噪算方法在图像边缘处所产生的Gibbs现象,具有较好的边缘结构保持和噪声滤除性能。
推广传统小波阈值与TV最小结合的变分模型到分数阶B样条小波,建立分数阶B样条小波域的TV去噪模型。通过分数阶B样条小波闽值和TV范数的结合,得到了对于纹理和边缘等几何结构都有良好保持性能的去噪图像。
(3)利用结构张量矩阵刻画像素局部梯度结构信息,设计了一种新的数据自适应核函数,提出一种基于结构张量的自适应核回归图像去噪及插值模型。理论和实验表明：本文模型能够准确估计图像中的边缘方向,因而在图像去噪和插值中能够有效重建图像的边缘和纹理等几何结构,视觉效果良好；同时,本文模型的均方误差达到了最小,进一步验证了算法的有效性。
针对Steering核回归模型对于细尺度边缘的不稳定性,应用两种更加鲁棒的核函数,提出两种边缘保持的核回归模型。与高斯核函数相比较,新的核函数具有更快的衰减性。当像素点属于细尺度边缘时,新的核函数对边缘附近像素赋予了更小权重,保证了去噪图像中的边缘细节更加清晰,消除了高斯核函数所出现的伪边缘现象。实验结果证明所提出模型对于纹理较少,细节丰富的图像具有很好重建效果。
(4)耦合Patch相似性保真和非局部TV正则性先验,提出一种新的图像去噪变分模型。该模型利用非局部迭代去噪图像和真实图像间的Patch相似性建立保真项,从而保证了所产生的去噪图像和真实图像之问具有结构相似性。非局部TV正则项进
一步保证了图像中边缘及细小纹理结构的有效保持。与现有相关方法相比较,实验结果表明,所提出方法在去噪同时能够有效保持图像中的边缘及纹理结构信息,特别是对于受噪声污染比较严重的图像,去噪性能和结构保持性能都达到了最好。
(5)利用图像中Patch自相似性,结合TV正则先验,提出自适应非局部Patch自相似性正则化模型。与现有非局部权函数计算方法不同,本文利用改进的结构张量矩阵,构造具有自适应和方向性的权函数,得到了对于图像中Patch自相关性的准确估计,从而保证了图像中的纹理等几何结构信息的有效保持。在数值解法上,采用了分裂Bregman迭代进行求解,提高了算法效率。同时将去噪模型推广到图像恢复,实验结果证明了所提出算法在结构保持方面的有效性。
An image is usually corrupted by noise in its acquisition and transmission. The degraded image severely affects the following image processing, such as image superresolution, image segmentation, image recognition, feature extraction. Thus, image denoising becomes a fundamental and important image processing for improving the quality of image. The goal of image denoising is to get a clearer and richer detailed image. Preserving the important structures such as edges and textures has important theoretical significance and application values.
It is well-known that image structures are important for visual perception.Hence; this paper mainly focuses on image denoising model for edge-preservation and texture-preservation. Several new image denoising methods are proposed based on wavelet transform, kernel regression and nonlocal means, respectively. The main achievements and innovations are as follows:
(1) Using the scale correlation and maxima modulus of wavelet coefficients, we define two new wavelet correlation coefficients based on maxima child nodes, and propose a new scale correlation based image denoising method. Furthermore; we extend these definitions to fractional B-spine wavelet coefficients. Both theoretical and experimental results demonstrate that the proposed correlation coefficients can capture the structure information in high frequency sub bands. So more edges and textures are kept in the denoised image and the quality of denoised image is improved.
(2) To overcome the shortcomings of the regularity exponent based image denoising model, a new image denoising model combing the regularity exponent and image total variation (TV) is proposed. The model fully utilizes the relationship between wavelet coefficients and signal regularity. So the image regularity is modified by changing the wavelet coefficients in different scales. The noise is reduced while sharp edges are preserved; meanwhile, the Gibbs phenomenon is disappeared.
With the fractional B-spline wavelet instead of the traditional wavelet, we establish a denoising algorithm based on the fractional B-spline wavelet and total variation. In this case, edges and textures are both maintained in the denoised image.
(3) An adaptive kernel regression model based on structure tensor is proposed. The structure tensor, which can exploit the local gradient structure information, provides information to achieve a data-adaptive kernel function. Due to the accurate estimation of edge orientations, edges and textures structure information are well preserved and a better visual effects are achieved during denoising and interpolation. Meanwhile, the RMSE is also proved the effectiveness of the algorithm.
To overcome the shortcomings of Steering kernel regression, two more robust kernel functions are applied to kernel regression, which are robust to micro-edges. On the image edges, the kernel functions have a faster decay, and the weight of pixels are assigned a small value. Thus it discourages the pseudo-edges. Experimental results of image denoising and interpolation show that the efficiency of the proposed models, especially to the image with less textures and more edge details.
(4) We propose a novel nonlocal TV variation model, where the fidelity term is based on the Patch similarity, and regularity term is nonlocal TV priori. The iterative nonlocal provides structure similarity between noisy and denoised images; while the nonlocal TV preserves the edge and texture details. Compared with other related denoising methods, the proposed model can preserve more structure information in denoised image, especially to the image with much noise.
(5) Combining the nonlocal Patch similarity regularization with TV regularization, we propose a new nonlocal Patch self-similarity regularized image denoising model. The similarity of Patches are said to be accurate, by introducing adaptive structure tensor to compute weight function of nonlocal Patch similarity. So in the denoised image, more structural features can be retained. A simpler and more effective algorithm, Split Bregman algorithm, is used to solve the model iteratively. By extending the model to image restoration, our model improves the quality of restoration image and the efficiency of computational complexity.
本论文以刻画边缘和纹理的图像先验建模为出发点,利用小波变换、核回归及非局部均值等图像去噪方法,重点研究方法中的纹理、边缘等结构保持问题,提出一系列的结构保持的图像去噪模型和新算法。取得的主要成果及创新点如下：
(1)提出一种新的基于小波系数相关性的图像去噪方法。利用小波系数多尺度相关性及小波系数极大值,定义两种基于最大子结点的相关系数,结合小波阈值进行图像去噪,并且将定义的相关系数推广到分数阶B样条小波域。理论分析和实验结果均表明,所提出相关系数在小波分解的高频子带可以很好地刻画图像结构,因而在去噪过程中保留了更多的边缘与纹理等结构信息,提高了去噪图像的质量。
(2)针对基于正则性指数图像去噪方法的不足,提出正则性指数和图像全变差(Total Variation, TV)正则先验结合的图像去噪模型。该模型利用小波系数与信号正则性之间的关系,在小波分解的不同尺度,通过改变小波系数来提高图像局部正则性。有效克服了正则性指数去噪算方法在图像边缘处所产生的Gibbs现象,具有较好的边缘结构保持和噪声滤除性能。
推广传统小波阈值与TV最小结合的变分模型到分数阶B样条小波,建立分数阶B样条小波域的TV去噪模型。通过分数阶B样条小波闽值和TV范数的结合,得到了对于纹理和边缘等几何结构都有良好保持性能的去噪图像。
(3)利用结构张量矩阵刻画像素局部梯度结构信息,设计了一种新的数据自适应核函数,提出一种基于结构张量的自适应核回归图像去噪及插值模型。理论和实验表明：本文模型能够准确估计图像中的边缘方向,因而在图像去噪和插值中能够有效重建图像的边缘和纹理等几何结构,视觉效果良好；同时,本文模型的均方误差达到了最小,进一步验证了算法的有效性。
针对Steering核回归模型对于细尺度边缘的不稳定性,应用两种更加鲁棒的核函数,提出两种边缘保持的核回归模型。与高斯核函数相比较,新的核函数具有更快的衰减性。当像素点属于细尺度边缘时,新的核函数对边缘附近像素赋予了更小权重,保证了去噪图像中的边缘细节更加清晰,消除了高斯核函数所出现的伪边缘现象。实验结果证明所提出模型对于纹理较少,细节丰富的图像具有很好重建效果。
(4)耦合Patch相似性保真和非局部TV正则性先验,提出一种新的图像去噪变分模型。该模型利用非局部迭代去噪图像和真实图像间的Patch相似性建立保真项,从而保证了所产生的去噪图像和真实图像之问具有结构相似性。非局部TV正则项进
一步保证了图像中边缘及细小纹理结构的有效保持。与现有相关方法相比较,实验结果表明,所提出方法在去噪同时能够有效保持图像中的边缘及纹理结构信息,特别是对于受噪声污染比较严重的图像,去噪性能和结构保持性能都达到了最好。
(5)利用图像中Patch自相似性,结合TV正则先验,提出自适应非局部Patch自相似性正则化模型。与现有非局部权函数计算方法不同,本文利用改进的结构张量矩阵,构造具有自适应和方向性的权函数,得到了对于图像中Patch自相关性的准确估计,从而保证了图像中的纹理等几何结构信息的有效保持。在数值解法上,采用了分裂Bregman迭代进行求解,提高了算法效率。同时将去噪模型推广到图像恢复,实验结果证明了所提出算法在结构保持方面的有效性。
An image is usually corrupted by noise in its acquisition and transmission. The degraded image severely affects the following image processing, such as image superresolution, image segmentation, image recognition, feature extraction. Thus, image denoising becomes a fundamental and important image processing for improving the quality of image. The goal of image denoising is to get a clearer and richer detailed image. Preserving the important structures such as edges and textures has important theoretical significance and application values.
It is well-known that image structures are important for visual perception.Hence; this paper mainly focuses on image denoising model for edge-preservation and texture-preservation. Several new image denoising methods are proposed based on wavelet transform, kernel regression and nonlocal means, respectively. The main achievements and innovations are as follows:
(1) Using the scale correlation and maxima modulus of wavelet coefficients, we define two new wavelet correlation coefficients based on maxima child nodes, and propose a new scale correlation based image denoising method. Furthermore; we extend these definitions to fractional B-spine wavelet coefficients. Both theoretical and experimental results demonstrate that the proposed correlation coefficients can capture the structure information in high frequency sub bands. So more edges and textures are kept in the denoised image and the quality of denoised image is improved.
(2) To overcome the shortcomings of the regularity exponent based image denoising model, a new image denoising model combing the regularity exponent and image total variation (TV) is proposed. The model fully utilizes the relationship between wavelet coefficients and signal regularity. So the image regularity is modified by changing the wavelet coefficients in different scales. The noise is reduced while sharp edges are preserved; meanwhile, the Gibbs phenomenon is disappeared.
With the fractional B-spline wavelet instead of the traditional wavelet, we establish a denoising algorithm based on the fractional B-spline wavelet and total variation. In this case, edges and textures are both maintained in the denoised image.
(3) An adaptive kernel regression model based on structure tensor is proposed. The structure tensor, which can exploit the local gradient structure information, provides information to achieve a data-adaptive kernel function. Due to the accurate estimation of edge orientations, edges and textures structure information are well preserved and a better visual effects are achieved during denoising and interpolation. Meanwhile, the RMSE is also proved the effectiveness of the algorithm.
To overcome the shortcomings of Steering kernel regression, two more robust kernel functions are applied to kernel regression, which are robust to micro-edges. On the image edges, the kernel functions have a faster decay, and the weight of pixels are assigned a small value. Thus it discourages the pseudo-edges. Experimental results of image denoising and interpolation show that the efficiency of the proposed models, especially to the image with less textures and more edge details.
(4) We propose a novel nonlocal TV variation model, where the fidelity term is based on the Patch similarity, and regularity term is nonlocal TV priori. The iterative nonlocal provides structure similarity between noisy and denoised images; while the nonlocal TV preserves the edge and texture details. Compared with other related denoising methods, the proposed model can preserve more structure information in denoised image, especially to the image with much noise.
(5) Combining the nonlocal Patch similarity regularization with TV regularization, we propose a new nonlocal Patch self-similarity regularized image denoising model. The similarity of Patches are said to be accurate, by introducing adaptive structure tensor to compute weight function of nonlocal Patch similarity. So in the denoised image, more structural features can be retained. A simpler and more effective algorithm, Split Bregman algorithm, is used to solve the model iteratively. By extending the model to image restoration, our model improves the quality of restoration image and the efficiency of computational complexity.
引文
[1]Gonzalez.R.C.,Woods R.E数字图像处理[M].北京：电子工业出版社,2002.
[2]Castleman K.R数字图像处理[M].北京：电子工业出版社,2002.
[3]Jain A. K数字图像处理基础[M].北京：清华大学出版社,2006.
[4]Yaroslavsky L. P. Digital Picture Processing-An Introduction [M]. Berlin Heidelberg:Springer, 1985.
[5]Smith S. M., Brady J. M. SUSAN—a new approach to low level image processing [J]. International Journal of Computer Vision,1997,23(1):45-78.
[6]Tomasi C, Manduchi R. Bilateral filtering for gray and color images [C]. Proceedings of the International Conference on Computer Vision, Bombay, India,1998:839-846.
[7]Elad M. On the bilateral filter and ways to improve it [J]. IEEE Transactions on lmage Processing,2002,11(10):1141-1151.
[8]Barash D. A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(6):844-847.
[9]Takeda H., Farsiu S., Milanfar P. Kernel regression for image processing and reconstruction [J]. IEEE Transaction on Image Processing,2007,16(2):349-366.
[10]Chatterjee, P., Milanfar P. A generalization of non-local means via kernel regression [C]. Proceedings of SPIE Conference on Computational Imaging, San Jose,2008:6814.
[11]印勇,李立琴.图像插值的改进自适应核回归方法[J].光电工程,2011,38(1)：112-116.
[12]田兵兵,胡访宇.基于核回归正则项的图像超分辨率重建[J].信号与信息处理,2009,39(4)：17-19.
[13]李印生,陈阳,罗立民.基于非局部方向性核先验的PET图像Bayesian重建[J].东南大学学报,2010,49(5)：937-942.
[14]高红.基于结构张量的核回归非均匀插值算法及其在图像处理中的应用[D].南京理工大学南京,2009.
[15]Efros A. A., Leung T. K.Texture synthesis by nonparametric sampling [C]. Proceedings of International Conference of Computer Vision, Kerkyra, Greece,1999:1033-1038.
[16]Buades A., Coll B., Morel J. M. A review of image denoising algorithms, with a new one[J]. Multiscale Model Simulation,2005,2(4):490-530.
[17]Buades A., Coll B., Morel J. M. Image denoising methods a new nonlocal principle [J].SIAM Review,2011,52(1):113-147.
[18]Awate S., Whitaker R., Unsupervised, information-theoretic, adaptive image filtering for image restoration [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2006,28(3): 364-376.
[19]Singer A. Diffusion interpretation of nonlocal neighborhood filter for signal denoising[J]. SIAM Journal on Imaging Sciences,2009,2(1):118-139.
[20]Milanfar P. A tour of modern image processing[R]. DRAFT,2011.
[21]Gilboa G., Sarbon J., Osher S.Nonlocal convex functional for image regularization [R]. UCLA CAM Report,06-57,2006.
[22]Brox T., Kleinschmidt O., Cremers D. Efficient nonlocal means for denoising of textural patterns [J]. IEEE Transactions on Image Processing,2008,17(7):1057-1092.
[23]Kervrann C., Boulanger J., Coupe P. Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[C]. Proceedings the International Conference on Scale Space and Variational Methods, Springer-Verlag, Berlin,2007:520-532.
[24]Pizarro L., Mrazek P.,Didas S. Generalized nonlocal image smoothing [J]. International Journal of Computer Vision,2010,90(l):62-87.
[25]Kindermann S., Osher S., Jones P. W. Deblurring and denoising of images by nonlocal functionals [J]. SIAM Journal on Multiscale Modeling and Simulation,2005,4(4):1091-1115.
[26]Gilboa G., Osher S. Nonlocal linear image regularization and supervised segmentation [R]. UCLA,CAM Report,06-47,2006.
[27]Gilboa G.,Osher S. Nonlocal operators with applications for image processing[R]. UCLA,CAM Report,07-23,2007.
[28]Lou Y.F., Zhang X.Q., Osher S. Image restoration via nonlocal operators [J]. Journal of Scientific Computing,2009,42(2):185-197.
[29]Kervrann C, Boulanger J. Optimal Spatial Adaptation for Patch-based image denosing [J].IEEE Transactions on Image Processing,2006,15(10):2866-2878.
[30]Peter D. J., Govinda V. K., Mathew A. T. Robust estimating approach for nonlocal means based on structurally similar Patches [J]. International Journal of Open Problems Compute Science and Mathematics,2009.2(2):293-310.
[31]Zimmer S.,Didas S.,Weickert J. A rotationally invariant block matching strategy improving image denoising with nonlocal means[C]. Proceedings of the International Workshop on Local and Non-Local Approximation in Image Processing, Lausanne, Switzerland,2008:135-142.
[32]Ebrahimi M., Vrscay E. Examining the role of scale in the context of the non-local means filter[C]. Proceedings of the International Conference on Image Analysis and Recognition, Povoa de Varzim, Portugal,2008:170-181.
[33]Mayer G., Vrscay E., Lauzon M.Self-similarity of Images in the Fourier Domain, with Applications to MRI [J]. Nonlinear Analysis:Theory, Method and Applications,2009, 17(12):e855-e864.
[34]Orchard J., Ebrahimi M., Wong A. Efficient non-local-means denoising using the SVD[C]. Proceedings of the International Conference on Image Processing, San Diego, California, USA, 2008:1732-1735.
[35]Wang J., Guo Y., Ying Y. Fast non-local algorithm for image denoising[C]. Proceedings of the International Conference on Image Processing, Atlanta, GA, USA,2006:1429-1432.
[36]Bilcu R., Vehvilainen M. Combined non-local averaging and intersection of confidence intervals for image denoising[C]. Proceedings of the International Conference on Image Processing, San Diego, California, USA,2008:1736-1739.
[37]Tasdizen T. Principal neighborhood dictionaries for nonlocal means image denosing[J]. IEEE Transactions on Image Processing,2009,18(12):2649-2660.
[38]Mahmoudi M.,Sapiro G. Fast image and video denoising via non local means of similar[J]. Signal Processing Letters,2005,12(12):839-842.
[39]Chatterjee J., Milanfar P.Clustering-based denoising with locally learned dictionaries [J]. IEEE Transactions on Image Processing,2009,18(7):1438-1451.
[40]Dabov, K., Foi, A., Katkovnik V. Image denoising by sparse 3-D transform-domain collaborative filtering [J]. IEEE Transactions on Image Processing,2007.16(8):2080-2095.
[41]Dabov, K., Foi, A., Katkovnik, V. A nonlocal and shape-adaptive transform-domain collaborative filtering[C]. Proceedings of International Workshop on Local and Non-Local Approximation in Image Processing, Lausanne, Switzerland.2008.
[42]Dabov, K., Foi, A., Katkovnik V. BM3D image denoising with shape-adaptive principal component analysis[C]. Proceedings of International Workshop on Signal Processing with Adaptive Sparse Structured Representations, Saint-Malo, France,2009.
[43]Katkovnik A.,Foi A.,Egiazarian K.From local kernel to nonlocal multiple-model image denoising[J]. International Journal of Compute Vision,2010,86(1):1-32.
[44]Protter M., Elad M. Generalizing the nonlocal-means to super-resolution reconstruction [J]. IEEE Transactions on Image Processing 2009,18(1):36-51.
[45]Dong W.S., Zhang L.,Shi G.M. Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization [J]. IEEE Transactions on Image Processing, 2010,20(7):1838-1857.
[46]Dong W.S., Shi.G.M. Zhang L. Super-resolution with nonlocal regularized sparse representation[C].Proceedings of the Vision Communications and Image Processing,Huang shan,An Hui,China,2010.
[47]孙伟峰,彭玉华.一种改进的非局部平均去噪方法[J].电子学报,2010,38(4)：923-928.
[48]肖亮,吴慧忠,韦志辉.NLTV：非局部数字全变差滤波[J].中国图像图形学报,2010,15(9)：1318-1325.
[49]冯象初,郝彬彬,朱见广.图像去噪的改进迭代非局部平均滤波方法[J].西安电子科技大学学报,2010,37(4)：722-725.
[50]郝言,冯象初,许建楼.一种非局部扩散的图像修复模型[J].西安电子科技大学学报,2010,37(5)：825-828.
[51]王卫卫,李莉,韩雨.基于非局部曲率驱动扩散的图像修复方法[J].光学学报,2010,30(6)：1634-1638.
[52]王志明,张丽.自适应的快速非局部图像去噪算法[J].中国图像图形学报,2009,14(4)：669-675.
[53]徐大宏,王润生.基于非局部正则化得图像去噪[J].计算机应用研究,2009,26(12)：4830-4832.
[54]胡杰,潘振宽,魏伟波.基于非局部均值去噪算法的PM模型及其Split-Bregman迭代实现[J].青岛大学学报,2010,23(1)：54-57.
[55]Mallat S., Zhong Z. Characterization of signals from multiscale edges [J].IEEE Transactions on Patter Analysis and Machine Intelligence,1992,14(7):710-732.
[56]Donoho D.L. De-noising by soft-thresholding [J]. IEEE Transactions on Information Theory, 1995.41 (3):613-627.
[57]Donoho D.L., Johnstone I. M. Ideal spatial adaptation via wavelet shrinkage [J]. Compute and Information Science,1994,81(3):425-455.
[58]Durand S., Nikolova M. Restoration of wavelet coefficients by minimizing a specially designed objective function[C].Proceedings of the International Workshop on Variational and Level Set Methods in Computer Vision,2003:145-152.
[59]Coifman R. R., Donoho D. Translation-invariant de-noising[M].Wavelets and Statistics,Lecture Notes in Statistics, Springer-Verlag, New York,1995:125-150.
[60]Brouce A. G, Gao H. Y. Waveshrink with firm shrinkage [J]. Statistica sinica,1997,7(4):83-95.
[61]Abramovich F., Sapatinas T., Silverman B. Wavelet thresholding via a Bayesian approach [J]. Journal of Royal Statistical Society, Series B,1998,1(2):725-749.
[62]Chang S. G.,Yu B.,Vetterli M. Adaptive wavelet thresholding of image denoising and compression[J].IEEE Transactions on Image Porcessnig,2000,9(9):1532-1546.
[63]Johnstone I. M., Silveman B.Wavelet threshold estimators for data with correlated noise[J]. Journal of Royal Statistics Society, Series B,1997,59(2):319-351.
[64]Jansen M., Malfait M., Bultheel A. Generalized cross validation for wavelet thresholding [J]. Signal Processing,1997.56(1):56-33.
[65]Luisier F. Blu T., Unser M. A new SURE approach to image denoising:Interscale orthonormal wavelet thresholding[J]. IEEE Transactions on Image Processing,2007,16(3):593-606.
[66]Mallat S.A theory of multiresolution signal decomposition:the wavelet presentation [J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(7):674-693.
[67]Witkin A. P. Scale space filtering [C].Proceedings of the International Joint Conference on Artificial Intelligence,1983:1019-1021.
[68]Xu Y., Weaver J. B., Lu J. Wavelet transform domain filters:a spatially selective noise filtration technique [J]. IEEE Transactions on Image Processing,1994,3(11):747-758.
[69]Moulin P.,Liu J. Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors [J].IEEE Transactions on Information Theory,1999,45(3): 909-919.
[70]Portilla J.,Strela V.,Wainwright M. Image denoising using scale mixtures of Gaussians in the wavelet domain[J].IEEE Transactions on Image Processing,2004,12(11):1338-1351.
[71]Chipman H, Kolaczyk E, Mcculloeh R. Adaptive Bayesian wavelet shrinkage [J].Journal of American Statistical Association,1997,92(440):1413-1421.
[72]Crouse M. S.,Nowak R. D., Baraniuk R. G. Wavelet-based statistical signal processing using hidden markov models[J].IEEE Transactions on Signal Processing,1998,46(4):886-902.
[73]Rombeg J.K. Choi H., Baraniuk R. Bayesian tree-structured image modeling using wavelet-domain hidden Markov models [J]. IEEE Transactions on Image Processing,2001, 10(7):1056-1068.
[74]Chambolle A, Devore R, Lee N.Y.Nonlinear wavelet image processing:variation problems, compression and noise removal through Wavelet Shrinkage[J]. IEEE Transactions on Image Processing,1998,7(3):319-335.
[75]Durand S., Froment J. Reconstruction of wavelet coefficients using total variation minimization [J].SIAM Journal on Scientific Computing,2003,24(5):1745-1767.
[76]Chan T.F., Zhou H.M. Optimal constructions of wavelet coefficients using total variation regularization in image compression[R]. UCLA,CAM Report:00-27,2000.
[77]Daubechies I., Tesehke G. Variational image restoration by means of wavelets:simultaneous decomposition, deblurring and denoising [J]. Applied and Computational Harmonic Analysis,2005,19(1):1-16.
[78]Candes E. J., Guo F. New multiscale transforms minimum total variation synthesis:Applications to edge-preserving image reconstruction [J]. Signal Processing,2002,82:1519-1543.
[79]Coifman R.R., Sowa A. Combining the calculus of variations and wavelets for image enhancement [J]. Applied and Computational Harmonic Analysis,2000,9(1):1-18.
[80]Coifman R. R., Sowa A. New methods of controlled total variation reduction for digital functions [J]. SIAM Journal on Numerical Analysis,2001,39(2):480-498.
[81]Mrazek P., Weickert J. Rotationaliy invariant wavelet shrinkage[C]. DAGM 2003, LNCS 2781, Springer, Berlin,2003:156-163.
[82]Steidl G., Weickert J. Relations between soft wavelet shrinkage and total variation denoising [J]. DAGM 2002, LNCS 2449:198-205
[83]Weickert J., Steidl G., Mrazek P. Diffusion filters and wavelets:What can they learn from each other [M]. The Handbook of Mathematical Models in Computer Vision. Springer, New York, 2005.
[84]Steidl G. Weickert J, Brox T. On the equivalence of soft wavelet shrinkage,total variation diffusion,total variation regularization and SIDEs[J]. SIAM Journal on Numerical Analysis,2004,42(2):686-71.
[85]Do M. N., Vetterli M. The finite ridgelet transform for image representation [J]. IEEE Transactions on Image Processing,2003,12(1):16-28.
[86]Candes E. J., Donoho D. L.New tight frames of curvelets and optimal representations of objects with piecewise singularities [J]. Communications on Pure Applied Mathematics,2004,57: 219-266.
[87]Candes E.J., Demanet L., Donoho D. L. Fast discrete curve let transforms [J]. SIAM Journal on Multiscale Modeling and Simulation,2006,5(3):861-899.
[88]Pennec E. L., Mallat S. Image compression with geometrical wavelets [J]. Proceddings of International Conference on Image Processing, Vancouver, Canada,2000:661-664.
[89]Do M.N., Vetteri M. The contourlet transform:an efficient directional multiresolution image representation [J].IEEE Transactions on Image Processing,2005,14(12):2091-2106.
[90]Meyer F. G., Coifman R. R. Brushlet: A tool for directional image analysis and image compression [J]. Applied and Computational Harmonic Analysis,1997,4(2):147-187.
[91]Mallat S. Geometrical grouplets [J].Applied and Computational Harmonic Analysis,2009, 26(2):161-180.
[92]Starck J. L., Candes E. J., Donoho D. L. The curvelet transform for image denoising[J]. IEEE Transactions on Image Processing,2002,6(11):670-684.
[93]Zhou Z.F., Cao J.Z., Liu W.H. Contourlet-based Image Denoising Algorithm using Adaptive Windows[C]. Proceedings of International Conference on Industrial Electronics and Applications, Xi'an, China,2009:3654-3657.
[94]Zhang X., Jing X. Image denoising in contourlet domain based on a normal inverse Gaussian prior [J]. Digital Signal Process,2010,20(5):1439-1446.
[95]Starck J.L., Elad M., Donoho D.L. Redundant multiscale transforms and their application for morphological component analysis[J].Advances in Imaging and Electron Physics,2004,132: 287-348.
[96]Jiang L., Feng X.,Yin H.Variational image restoration and decomposition with curvelet shrinkage[J].Journal of mathematical Imaging and Vision,2008,30:125-132.
[97]Mallat S著,杨力华等译.信号处理的小波导引[M].北京,机械工业出版社,2002.
[98]Unser M., Blu T. Fractional spline and wavelets [J].SIAM Review,2000,42(1):43-67.
[99]Bul T.,Unser M. The fractional spline wavelet transform:definition and implementation [C].Proceedings of the International Conference on Acoustics, Speech and Signal Processing, Istanbul Turkey,2000,1:512-515.
[100]Schoenberg I. J. Cardinal interpolation and spline functions [J]. Approximation Theory,1969,2: 167-206.
[101]Unser M., Aldroubi A., Eden M. B-spline image processing part Ⅰ-theory[J].IEEE Transactions on Signal Processing,1993,40(2):821-832.
[102]Unser M., Aldroubi A., Eden M. B-spline image processing part Ⅱ-efficient design and applications [J].IEEE Transcatins on Signal Processing,1993,40(2):834-848.
[103]Unser M., Blu T.Self-Similarity:part Ⅰ-Splines and operators [J].IEEE Transactions on Signal Processing,2007,55(4):1352-1363.
[104]Unser M., Blu T. Self-Similarity:part Ⅱ-Optimal Estimation of Fractal Processes [J]. IEEE Transactions on Signal Processing,2007,55(4):1364-1378.
[105]Blu T., Thevenaz P., Unser M. Linear Interpolation revitalized [J].IEEE Transactions on Image Processing,2004,13(5):710-719.
[106]Unser M. Splines:A perfect fit for signal and image processing [J].IEEE Signal Processing Magazine,1999,16(6):22-38.
[107]Arigovindan M., Suhling M., Hunziker P. Variational image reconstruction from arbitrarily spaced samples:a fast multiresolution spline solution [J]. IEEE Transactions on Image Processing,2005,14(4):450-460.
[108]Ramani S., Ville D.V., Blu T. Nonideal sampling and regularization theory[J].IEEE Transactions on Image Processing,2008,56(3):1055-1069.
[109]Ramani S., Thevenaz P., Unser M. Regularized interpolation for noisy images[J].IEEE Transactions on Medical Imaging,2010,19(2):543-558.
[110]Keys R.Cubic convolution interpolation for digital image processing[J].IEEE Tran on Acoustics Speech and Signal Processing,1981,29(6):1153-1160.
[111]杨朝霞,逯峰,关氯泰.用B样条的尺度来关系实现了图像任意精度的放大缩小[J].计算机辅助设计与图形学学报,2001,13(9)：824-827.
[112]冯杰飞,韩慧建.基于非均匀B样条插值算法的图像放大[J].计算机应用,2010,3(1)：82-84.
[l13]李开宇.基于B样条的数字边缘检测[J].南京航空航天大学学报,2007,39(2)：298-202.
[114]Gabor D. Information theory in electron microscopy [J].Laboratory Investigation.1965,14 801-807.
[115]Jain A. K. Partial differential equations and finite-difference Methods in Image Processing, part I: image representation [J].Journal of Optimization Theory and Applications,1977,23:65-91.
[116]Koenderink J. J.The structure of images [J].]Biological Cybernetics.1984,50(5):363-370.
[117]Perona P., Malic J.Scale space and edge detection using anisotropic diffusion [J]. IEEE Transaction on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[118]Alvarez L., Mazorra L. Signal and image restoration using shock filter and anisotropic diffusion [J]. SIAM Journal on Numerical Analysis,1994,31(2):590-605.
[119]Catte F., Lions P.L., Morel J. M. Image selective smoothing and edge detection by nonlinear diffusion [J]. SIAM Journal on Numerical Analysis,1992,29(1):182-193.
[120]Weickert J. Theoretical foundation of anisotropic diffusion in image processing [C]. Proceedings of the International Conference on Theoretical Foundation Compute Vision,1994:221-236.
[121]Weickert J. Coherence-enhancing diffusion filtering [J]. International Journal of Computer Vision,1999,31(2/3):111-127.
[122]Weickert J., Welk M. Tensor field interpolation with PDES [J].Mathematics and Visualization, 2006,4:315-325.
[123]Osher S.,Rudin L. Feature-oriented image enhancement using shock filters [J]. SIAM Journal on Numerical Analysis,1990,27(4):919-940.
[124]Alvarez L.,Guichard F., Lions P. L. Axioms and fundamental equation of image processing[J]. Archive Rational Mechsnics Analysis,1993,123(3):199-257.
[125]Whitaker R.T., Piaer S.M. A Multi-scale approach to uniform diffusion [J]. International Journal of Computer Vision,1993,57(1):99-110.
[126]Torkamani A., Tait F. Image recovery using the anisotropic diffusion equation[J]. IEEE Transactions on Image Processing,1996,5(11):1573-1578.
[127]You Y.L., Xu W.Y., Tanncnbaum A. Behavioral Analysis of Anisotropic Diffusion in Image Processing [J]. IEEE Transactions on Image Processing,1996,5(11):1539-1553.
[128]You Y.L., Kaveh M. Blind Image Restoration by Anisotropic Regularization [J].IEEE Transactions on Image Processing,1999,8(3):396-407.
[129]Wu Z.Y., Herman G.T., Browen J.A. Edge preserving reconstruction using adaptive smoothing in wavelet domain [C]. Proceed ings of International Conference on Nuclear Sciences Symposium and Medical Imaging,1993,3:1917-1921.
[130]Osher S., Sethian J. A. Fronts propagating with curvature dependent speed:algorithm based on Hamilton-Jacobi formulation [J]. Journal of Computational Physics,1998,79:12-49.
[131]Malladi R.,Sethian J.A. Image processing,flows under min/max curvature and mean curvature[J].Graphical Models and Image Processing,1996,66(1):1-31.
[132]Malladi R., Sethian J.A., Vemuri B.C. A fast level set based algorithm for topology independent shape modeling [J].Journal of Mathematical Imaging and Vision,1996,6(2):269-289.
[133]Sapiro G. Gemotric partial differential equations and image analysis [M].Cambridge University Press.2001.
[134]Kass M., Witkin A., Terzopoulos D. Snakes:active contour models[C]. Proceedings of the International Conference on Computer Vision, London,1987:259-268.
[135]Cohen L. D. Finite-element methods for active contour models and balloons for 2-D and 3-D images [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1993,15(11): 1131-1147.
[136]Cohen L. D. Note on active contour models and balloons [J]. Graphical Models and Image Processing,1991,53(2):211-218.
[137]Xu C.Y., Prince J. L. Generalized gradient vector flow external force for active contours [J]. Signal Processing,1998,71 (2):131-139.
[138]Rudin L., Osher S., Fatemi E. Nonlinear total variation based noise removal algorithms [M]. PhysicaD,1992,60:259-268.
[139]Shu X.B., Ahuja N. Hybrid compressive sampling via a new total variation TVLl[C].Proceedings of European Conference on Computer Vision,2010.
[140]Chan T.,Marquina A T.,Muler P.High-order total variation-based image restoration[J].SIAM Journal on Scientific Computing,2000,22(2):503-516.
[141]Chan T. F., Esedoglu S. A fourth order dual method for staircase reduction in texture extraction and image restoration problems[R].UCLA CAM Report,05-28,2005.
[142]You Y.L., Kaveh M. Fourth-order partial differential equations for noise removal [J].IEEE Transactions on Image Processing,2000,9(10):1723-1730.
[143]Lysaker M.,Loudervold A.,Tai X.C. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time[J].IEEE Transactions on Image Processing,2003,12(12):1579-1590.
[144]肖亮,吴慧中,韦志辉.基于鲁棒统计的图像去噪耦合变分模型及其应用[J].南京理工大学学报,2007,31(4)：418-421.
[145]陈利霞,宋国乡,丁宣浩.改进的总变分去噪算法[J].光子学报,2009.38(4)：1001-1004.
[146]邵文泽,韦志辉.数字双边TV滤波器及非线性图像平滑[J].中国图象图形学报,2007,12(7)：1178-1185.
[147]Zhang J., Wei Z.H. Fractional variational model and algorithm for image denoising[C].Proceedings of the International Conference on Natural Computation,2008,5: 524-528.
[148]Meyer Y. Oscillating patterns in image processing and nonlinear evolution equation [M]. Volume 22 of University Lecture Series, AMS, Providence,2001.
[149]Osher S., Sole A., Vese L.A. Image decomposition and restoration using total variation minimization and the H-1 norm [J]. Multiscale Modeling and Simulation,2003,1(3):349-370.
[150]Vese L.A., Osher S. Modeling textures with total variation minimization and oscillating patterns in image processing [J].Journal of Scientific Computing,2003,19(l):553-572.
[151]Lieu L., Vese L. A. Image restoration and decomposion via bounded total variation and negative Hibert-Sobolev space[R].UCLA CAM Report,05-33,2005.
[152]Aujol J.F., Gilboa G., Chan T.F. Structure-Texture Image Decomposition Modeling, Algorithms, and Parameter Selection [J].International Journal of Compute Vision,2006,67(1):111-136.
[153]Aliney S. A property of the minimum vectors of a regularizing functional defined by means of the absolute norm[J]. IEEE Transactions on Signal Processing,1997,45(4):913-917.
[154]Nikolova M. A variational approach to remove outlier and impulse noise[J].Journal of Mathematical Imaging and Vision,2004,20:99-120.
[155]Aujol J.F., Chambolle A. Dual norms and image decomposition models[J]. International Journal on Computer Vision,2005,63(1):85-104.
[156]Starck J.L., Elad M., Donoho D.L. Image decomposition:separation of texture from piecewise smooth content [C].Proceedings of SPIE Annual Meeting,2003.
[157]Starck J.L., Elad M., Donoho D.L. Image decomposition via the combination of sparse representations and variational approach [J]. IEEE Transactions on Image Processing,2005, 14(10):1570-1582.
[158]Chambolle A., Lions P.L. Image recovery via total variation minimization and related problems [J]. Numerische Mathematik,1997,76(3):167-188.
[159]Chambolle A. An algorithm for total variation minimization and applications [J]. Journal of Mathematical Imaging and Vision,2004,20(1):89-97.
[160]Bioueas J., Diasand M., Figueiredo. A new TwIST: two step iterative shrinkage thresholding algorithms for image restoration [J]. IEEE Transactions on Image Processing,2007,16(12): 2992-3004.
[161]Wang Y.,Yin W.,Zhang Y. A Fast algorithm for image deblurring with total variation regularization[R].UCLA CAM Report,07-22,2007.
[162]Wang Y.A new alternating minimization algorithm for total variation image reconstruction [J]. SIAM Journal on Imaging Sciences,2008,1(3):248-272.
[163]Lions P.L.,Mercier B. Splitting algorithms for the sum of two nonlinear operators[J].SIAM Journal on Numerical Analysis,1979,16(6):964-979.
[164]Osher S.,Mao Y.,Dong B. Fast linearized Bregman iteration for compressive sensing and sparse denoising[J]. Communications in Mathematical Sciences,2010,8(1):93-111.
[165]Goldstein T.,Osher S. The Split Bregman method for L1 regularized problem[J].SIAM Journal on imaging and Sciences,2009,2(2):323-343.
[166]Jaffard S., Beyond Besov spaces Part 1:Distribution of wavelet coefficients [J]. The Journal of Fourier analysis and applications,2004,10(3):221-246.
[167]Shin G.S, Kang .M. G. Wavelet-based denoising considering interscale and intrascale dependences [J]. Optical Engineering.2005,44(6):067002 1-9.
[168]Jaffard S. Pointwise smoothness, two-mircrolocalization and wavelet coefficients [J]. Publications Matematiques,1991,35(1):152-168.
[169]Bony J.M. Second microloclaizatin and propagation of singularities for semilinear hyperbolic equation[C]. Proceedings of hyperbolic equations and related topics, Boston, MA,1986:11-49.
[170]Frazier M.Jawerth B. Decomposition of Besov Spaces[J]. Indiana University Mathematics Journal,1985,34:777-789.
[171]Jaffard S. Beyond Besov spaces Part 2:Oscillation spaces [J]. Constructive approximation,2005, 21:29-61.
[172]Melot C. Oscillating singularities in Besov spaces [J].Journal of Mathematics and Pure Applications,2004,83(3):367-416.
[173]Vehel J. L. Signal enhancement based on Holder regularity analysis[J]. IMA Volumes in Mathematics and its Applications.2002,132:197-209.
[174]李会芳,俞卞章.基于小波的多重分形图像去噪新算法[J].2004,12(3)：305-310.
[175]Jansen K., D.Anstassiou. Subpixel edge localization and the interpolation of still images [J].IEEE Transactions on Image Processing,1995,4(3):285-295.
[176]Li X., Orchard M.T. New edge-directed interpolation [J]. IEEE Transactions on Image Processing,2001,10(10):1521-1527.
[177]Shao W.Z., Wei Z.H. Edge-and-coner preserving regularization for image interpolation and reconstruction[J].Image and Vision Computing,2008,26(12):1591-1606.
[178]Hwang J.W., Lee H.S.Adaptive image interpolation based on local gradient features[J].IEEE Signal Process Letters,2004,11(3):359-362.
[179]Casciola G., Montefusco L.B., Morigi S. Edge-driven image interpolation using adaptive anisotropic Radial Basis Function [J]. Journal of Mathematical Imaging Vision, 2010,36(2):125-139.
[180]Yang P.,Tong X., Zheng X.Z. A gradient based adaptive interpolation filter for multiple view synthesis[C]. Proceedings of the Pacific Rim Conference on Multimedia:Advances in Multimedia Information Processing, Bangkok, Thailand,2009:551-560.
[181]Black J., Sapiro G., Marimont D. H. Robust anisotropic diffusion [J].IEEE Transactions on Image Processing,1998,7(3):421-432.
[182]Tian J., Yu W.Y., Xie S.L. On the kernel selection of nonlocal filtering for image denoising[C].In Proceedings of International Conference on Machine Learning and Cybernetics.2008:12-12.
[183]Wang Z., Bovik A. C., Sheikh H. R. lmage quality assessment:From error visibility to structural similarity [J]. IEEE Transaction on Image Processing,2004,13(4):600-612.
[184]Zhang X.Q., Burger M., Bresson X.Osher S.Bregmanized nonlocal for deconvolution and sparse reconstruction [R].UCLA CAM Report,09-03,2009.
[2]Castleman K.R数字图像处理[M].北京：电子工业出版社,2002.
[3]Jain A. K数字图像处理基础[M].北京：清华大学出版社,2006.
[4]Yaroslavsky L. P. Digital Picture Processing-An Introduction [M]. Berlin Heidelberg:Springer, 1985.
[5]Smith S. M., Brady J. M. SUSAN—a new approach to low level image processing [J]. International Journal of Computer Vision,1997,23(1):45-78.
[6]Tomasi C, Manduchi R. Bilateral filtering for gray and color images [C]. Proceedings of the International Conference on Computer Vision, Bombay, India,1998:839-846.
[7]Elad M. On the bilateral filter and ways to improve it [J]. IEEE Transactions on lmage Processing,2002,11(10):1141-1151.
[8]Barash D. A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(6):844-847.
[9]Takeda H., Farsiu S., Milanfar P. Kernel regression for image processing and reconstruction [J]. IEEE Transaction on Image Processing,2007,16(2):349-366.
[10]Chatterjee, P., Milanfar P. A generalization of non-local means via kernel regression [C]. Proceedings of SPIE Conference on Computational Imaging, San Jose,2008:6814.
[11]印勇,李立琴.图像插值的改进自适应核回归方法[J].光电工程,2011,38(1)：112-116.
[12]田兵兵,胡访宇.基于核回归正则项的图像超分辨率重建[J].信号与信息处理,2009,39(4)：17-19.
[13]李印生,陈阳,罗立民.基于非局部方向性核先验的PET图像Bayesian重建[J].东南大学学报,2010,49(5)：937-942.
[14]高红.基于结构张量的核回归非均匀插值算法及其在图像处理中的应用[D].南京理工大学南京,2009.
[15]Efros A. A., Leung T. K.Texture synthesis by nonparametric sampling [C]. Proceedings of International Conference of Computer Vision, Kerkyra, Greece,1999:1033-1038.
[16]Buades A., Coll B., Morel J. M. A review of image denoising algorithms, with a new one[J]. Multiscale Model Simulation,2005,2(4):490-530.
[17]Buades A., Coll B., Morel J. M. Image denoising methods a new nonlocal principle [J].SIAM Review,2011,52(1):113-147.
[18]Awate S., Whitaker R., Unsupervised, information-theoretic, adaptive image filtering for image restoration [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2006,28(3): 364-376.
[19]Singer A. Diffusion interpretation of nonlocal neighborhood filter for signal denoising[J]. SIAM Journal on Imaging Sciences,2009,2(1):118-139.
[20]Milanfar P. A tour of modern image processing[R]. DRAFT,2011.
[21]Gilboa G., Sarbon J., Osher S.Nonlocal convex functional for image regularization [R]. UCLA CAM Report,06-57,2006.
[22]Brox T., Kleinschmidt O., Cremers D. Efficient nonlocal means for denoising of textural patterns [J]. IEEE Transactions on Image Processing,2008,17(7):1057-1092.
[23]Kervrann C., Boulanger J., Coupe P. Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[C]. Proceedings the International Conference on Scale Space and Variational Methods, Springer-Verlag, Berlin,2007:520-532.
[24]Pizarro L., Mrazek P.,Didas S. Generalized nonlocal image smoothing [J]. International Journal of Computer Vision,2010,90(l):62-87.
[25]Kindermann S., Osher S., Jones P. W. Deblurring and denoising of images by nonlocal functionals [J]. SIAM Journal on Multiscale Modeling and Simulation,2005,4(4):1091-1115.
[26]Gilboa G., Osher S. Nonlocal linear image regularization and supervised segmentation [R]. UCLA,CAM Report,06-47,2006.
[27]Gilboa G.,Osher S. Nonlocal operators with applications for image processing[R]. UCLA,CAM Report,07-23,2007.
[28]Lou Y.F., Zhang X.Q., Osher S. Image restoration via nonlocal operators [J]. Journal of Scientific Computing,2009,42(2):185-197.
[29]Kervrann C, Boulanger J. Optimal Spatial Adaptation for Patch-based image denosing [J].IEEE Transactions on Image Processing,2006,15(10):2866-2878.
[30]Peter D. J., Govinda V. K., Mathew A. T. Robust estimating approach for nonlocal means based on structurally similar Patches [J]. International Journal of Open Problems Compute Science and Mathematics,2009.2(2):293-310.
[31]Zimmer S.,Didas S.,Weickert J. A rotationally invariant block matching strategy improving image denoising with nonlocal means[C]. Proceedings of the International Workshop on Local and Non-Local Approximation in Image Processing, Lausanne, Switzerland,2008:135-142.
[32]Ebrahimi M., Vrscay E. Examining the role of scale in the context of the non-local means filter[C]. Proceedings of the International Conference on Image Analysis and Recognition, Povoa de Varzim, Portugal,2008:170-181.
[33]Mayer G., Vrscay E., Lauzon M.Self-similarity of Images in the Fourier Domain, with Applications to MRI [J]. Nonlinear Analysis:Theory, Method and Applications,2009, 17(12):e855-e864.
[34]Orchard J., Ebrahimi M., Wong A. Efficient non-local-means denoising using the SVD[C]. Proceedings of the International Conference on Image Processing, San Diego, California, USA, 2008:1732-1735.
[35]Wang J., Guo Y., Ying Y. Fast non-local algorithm for image denoising[C]. Proceedings of the International Conference on Image Processing, Atlanta, GA, USA,2006:1429-1432.
[36]Bilcu R., Vehvilainen M. Combined non-local averaging and intersection of confidence intervals for image denoising[C]. Proceedings of the International Conference on Image Processing, San Diego, California, USA,2008:1736-1739.
[37]Tasdizen T. Principal neighborhood dictionaries for nonlocal means image denosing[J]. IEEE Transactions on Image Processing,2009,18(12):2649-2660.
[38]Mahmoudi M.,Sapiro G. Fast image and video denoising via non local means of similar[J]. Signal Processing Letters,2005,12(12):839-842.
[39]Chatterjee J., Milanfar P.Clustering-based denoising with locally learned dictionaries [J]. IEEE Transactions on Image Processing,2009,18(7):1438-1451.
[40]Dabov, K., Foi, A., Katkovnik V. Image denoising by sparse 3-D transform-domain collaborative filtering [J]. IEEE Transactions on Image Processing,2007.16(8):2080-2095.
[41]Dabov, K., Foi, A., Katkovnik, V. A nonlocal and shape-adaptive transform-domain collaborative filtering[C]. Proceedings of International Workshop on Local and Non-Local Approximation in Image Processing, Lausanne, Switzerland.2008.
[42]Dabov, K., Foi, A., Katkovnik V. BM3D image denoising with shape-adaptive principal component analysis[C]. Proceedings of International Workshop on Signal Processing with Adaptive Sparse Structured Representations, Saint-Malo, France,2009.
[43]Katkovnik A.,Foi A.,Egiazarian K.From local kernel to nonlocal multiple-model image denoising[J]. International Journal of Compute Vision,2010,86(1):1-32.
[44]Protter M., Elad M. Generalizing the nonlocal-means to super-resolution reconstruction [J]. IEEE Transactions on Image Processing 2009,18(1):36-51.
[45]Dong W.S., Zhang L.,Shi G.M. Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization [J]. IEEE Transactions on Image Processing, 2010,20(7):1838-1857.
[46]Dong W.S., Shi.G.M. Zhang L. Super-resolution with nonlocal regularized sparse representation[C].Proceedings of the Vision Communications and Image Processing,Huang shan,An Hui,China,2010.
[47]孙伟峰,彭玉华.一种改进的非局部平均去噪方法[J].电子学报,2010,38(4)：923-928.
[48]肖亮,吴慧忠,韦志辉.NLTV：非局部数字全变差滤波[J].中国图像图形学报,2010,15(9)：1318-1325.
[49]冯象初,郝彬彬,朱见广.图像去噪的改进迭代非局部平均滤波方法[J].西安电子科技大学学报,2010,37(4)：722-725.
[50]郝言,冯象初,许建楼.一种非局部扩散的图像修复模型[J].西安电子科技大学学报,2010,37(5)：825-828.
[51]王卫卫,李莉,韩雨.基于非局部曲率驱动扩散的图像修复方法[J].光学学报,2010,30(6)：1634-1638.
[52]王志明,张丽.自适应的快速非局部图像去噪算法[J].中国图像图形学报,2009,14(4)：669-675.
[53]徐大宏,王润生.基于非局部正则化得图像去噪[J].计算机应用研究,2009,26(12)：4830-4832.
[54]胡杰,潘振宽,魏伟波.基于非局部均值去噪算法的PM模型及其Split-Bregman迭代实现[J].青岛大学学报,2010,23(1)：54-57.
[55]Mallat S., Zhong Z. Characterization of signals from multiscale edges [J].IEEE Transactions on Patter Analysis and Machine Intelligence,1992,14(7):710-732.
[56]Donoho D.L. De-noising by soft-thresholding [J]. IEEE Transactions on Information Theory, 1995.41 (3):613-627.
[57]Donoho D.L., Johnstone I. M. Ideal spatial adaptation via wavelet shrinkage [J]. Compute and Information Science,1994,81(3):425-455.
[58]Durand S., Nikolova M. Restoration of wavelet coefficients by minimizing a specially designed objective function[C].Proceedings of the International Workshop on Variational and Level Set Methods in Computer Vision,2003:145-152.
[59]Coifman R. R., Donoho D. Translation-invariant de-noising[M].Wavelets and Statistics,Lecture Notes in Statistics, Springer-Verlag, New York,1995:125-150.
[60]Brouce A. G, Gao H. Y. Waveshrink with firm shrinkage [J]. Statistica sinica,1997,7(4):83-95.
[61]Abramovich F., Sapatinas T., Silverman B. Wavelet thresholding via a Bayesian approach [J]. Journal of Royal Statistical Society, Series B,1998,1(2):725-749.
[62]Chang S. G.,Yu B.,Vetterli M. Adaptive wavelet thresholding of image denoising and compression[J].IEEE Transactions on Image Porcessnig,2000,9(9):1532-1546.
[63]Johnstone I. M., Silveman B.Wavelet threshold estimators for data with correlated noise[J]. Journal of Royal Statistics Society, Series B,1997,59(2):319-351.
[64]Jansen M., Malfait M., Bultheel A. Generalized cross validation for wavelet thresholding [J]. Signal Processing,1997.56(1):56-33.
[65]Luisier F. Blu T., Unser M. A new SURE approach to image denoising:Interscale orthonormal wavelet thresholding[J]. IEEE Transactions on Image Processing,2007,16(3):593-606.
[66]Mallat S.A theory of multiresolution signal decomposition:the wavelet presentation [J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(7):674-693.
[67]Witkin A. P. Scale space filtering [C].Proceedings of the International Joint Conference on Artificial Intelligence,1983:1019-1021.
[68]Xu Y., Weaver J. B., Lu J. Wavelet transform domain filters:a spatially selective noise filtration technique [J]. IEEE Transactions on Image Processing,1994,3(11):747-758.
[69]Moulin P.,Liu J. Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors [J].IEEE Transactions on Information Theory,1999,45(3): 909-919.
[70]Portilla J.,Strela V.,Wainwright M. Image denoising using scale mixtures of Gaussians in the wavelet domain[J].IEEE Transactions on Image Processing,2004,12(11):1338-1351.
[71]Chipman H, Kolaczyk E, Mcculloeh R. Adaptive Bayesian wavelet shrinkage [J].Journal of American Statistical Association,1997,92(440):1413-1421.
[72]Crouse M. S.,Nowak R. D., Baraniuk R. G. Wavelet-based statistical signal processing using hidden markov models[J].IEEE Transactions on Signal Processing,1998,46(4):886-902.
[73]Rombeg J.K. Choi H., Baraniuk R. Bayesian tree-structured image modeling using wavelet-domain hidden Markov models [J]. IEEE Transactions on Image Processing,2001, 10(7):1056-1068.
[74]Chambolle A, Devore R, Lee N.Y.Nonlinear wavelet image processing:variation problems, compression and noise removal through Wavelet Shrinkage[J]. IEEE Transactions on Image Processing,1998,7(3):319-335.
[75]Durand S., Froment J. Reconstruction of wavelet coefficients using total variation minimization [J].SIAM Journal on Scientific Computing,2003,24(5):1745-1767.
[76]Chan T.F., Zhou H.M. Optimal constructions of wavelet coefficients using total variation regularization in image compression[R]. UCLA,CAM Report:00-27,2000.
[77]Daubechies I., Tesehke G. Variational image restoration by means of wavelets:simultaneous decomposition, deblurring and denoising [J]. Applied and Computational Harmonic Analysis,2005,19(1):1-16.
[78]Candes E. J., Guo F. New multiscale transforms minimum total variation synthesis:Applications to edge-preserving image reconstruction [J]. Signal Processing,2002,82:1519-1543.
[79]Coifman R.R., Sowa A. Combining the calculus of variations and wavelets for image enhancement [J]. Applied and Computational Harmonic Analysis,2000,9(1):1-18.
[80]Coifman R. R., Sowa A. New methods of controlled total variation reduction for digital functions [J]. SIAM Journal on Numerical Analysis,2001,39(2):480-498.
[81]Mrazek P., Weickert J. Rotationaliy invariant wavelet shrinkage[C]. DAGM 2003, LNCS 2781, Springer, Berlin,2003:156-163.
[82]Steidl G., Weickert J. Relations between soft wavelet shrinkage and total variation denoising [J]. DAGM 2002, LNCS 2449:198-205
[83]Weickert J., Steidl G., Mrazek P. Diffusion filters and wavelets:What can they learn from each other [M]. The Handbook of Mathematical Models in Computer Vision. Springer, New York, 2005.
[84]Steidl G. Weickert J, Brox T. On the equivalence of soft wavelet shrinkage,total variation diffusion,total variation regularization and SIDEs[J]. SIAM Journal on Numerical Analysis,2004,42(2):686-71.
[85]Do M. N., Vetterli M. The finite ridgelet transform for image representation [J]. IEEE Transactions on Image Processing,2003,12(1):16-28.
[86]Candes E. J., Donoho D. L.New tight frames of curvelets and optimal representations of objects with piecewise singularities [J]. Communications on Pure Applied Mathematics,2004,57: 219-266.
[87]Candes E.J., Demanet L., Donoho D. L. Fast discrete curve let transforms [J]. SIAM Journal on Multiscale Modeling and Simulation,2006,5(3):861-899.
[88]Pennec E. L., Mallat S. Image compression with geometrical wavelets [J]. Proceddings of International Conference on Image Processing, Vancouver, Canada,2000:661-664.
[89]Do M.N., Vetteri M. The contourlet transform:an efficient directional multiresolution image representation [J].IEEE Transactions on Image Processing,2005,14(12):2091-2106.
[90]Meyer F. G., Coifman R. R. Brushlet: A tool for directional image analysis and image compression [J]. Applied and Computational Harmonic Analysis,1997,4(2):147-187.
[91]Mallat S. Geometrical grouplets [J].Applied and Computational Harmonic Analysis,2009, 26(2):161-180.
[92]Starck J. L., Candes E. J., Donoho D. L. The curvelet transform for image denoising[J]. IEEE Transactions on Image Processing,2002,6(11):670-684.
[93]Zhou Z.F., Cao J.Z., Liu W.H. Contourlet-based Image Denoising Algorithm using Adaptive Windows[C]. Proceedings of International Conference on Industrial Electronics and Applications, Xi'an, China,2009:3654-3657.
[94]Zhang X., Jing X. Image denoising in contourlet domain based on a normal inverse Gaussian prior [J]. Digital Signal Process,2010,20(5):1439-1446.
[95]Starck J.L., Elad M., Donoho D.L. Redundant multiscale transforms and their application for morphological component analysis[J].Advances in Imaging and Electron Physics,2004,132: 287-348.
[96]Jiang L., Feng X.,Yin H.Variational image restoration and decomposition with curvelet shrinkage[J].Journal of mathematical Imaging and Vision,2008,30:125-132.
[97]Mallat S著,杨力华等译.信号处理的小波导引[M].北京,机械工业出版社,2002.
[98]Unser M., Blu T. Fractional spline and wavelets [J].SIAM Review,2000,42(1):43-67.
[99]Bul T.,Unser M. The fractional spline wavelet transform:definition and implementation [C].Proceedings of the International Conference on Acoustics, Speech and Signal Processing, Istanbul Turkey,2000,1:512-515.
[100]Schoenberg I. J. Cardinal interpolation and spline functions [J]. Approximation Theory,1969,2: 167-206.
[101]Unser M., Aldroubi A., Eden M. B-spline image processing part Ⅰ-theory[J].IEEE Transactions on Signal Processing,1993,40(2):821-832.
[102]Unser M., Aldroubi A., Eden M. B-spline image processing part Ⅱ-efficient design and applications [J].IEEE Transcatins on Signal Processing,1993,40(2):834-848.
[103]Unser M., Blu T.Self-Similarity:part Ⅰ-Splines and operators [J].IEEE Transactions on Signal Processing,2007,55(4):1352-1363.
[104]Unser M., Blu T. Self-Similarity:part Ⅱ-Optimal Estimation of Fractal Processes [J]. IEEE Transactions on Signal Processing,2007,55(4):1364-1378.
[105]Blu T., Thevenaz P., Unser M. Linear Interpolation revitalized [J].IEEE Transactions on Image Processing,2004,13(5):710-719.
[106]Unser M. Splines:A perfect fit for signal and image processing [J].IEEE Signal Processing Magazine,1999,16(6):22-38.
[107]Arigovindan M., Suhling M., Hunziker P. Variational image reconstruction from arbitrarily spaced samples:a fast multiresolution spline solution [J]. IEEE Transactions on Image Processing,2005,14(4):450-460.
[108]Ramani S., Ville D.V., Blu T. Nonideal sampling and regularization theory[J].IEEE Transactions on Image Processing,2008,56(3):1055-1069.
[109]Ramani S., Thevenaz P., Unser M. Regularized interpolation for noisy images[J].IEEE Transactions on Medical Imaging,2010,19(2):543-558.
[110]Keys R.Cubic convolution interpolation for digital image processing[J].IEEE Tran on Acoustics Speech and Signal Processing,1981,29(6):1153-1160.
[111]杨朝霞,逯峰,关氯泰.用B样条的尺度来关系实现了图像任意精度的放大缩小[J].计算机辅助设计与图形学学报,2001,13(9)：824-827.
[112]冯杰飞,韩慧建.基于非均匀B样条插值算法的图像放大[J].计算机应用,2010,3(1)：82-84.
[l13]李开宇.基于B样条的数字边缘检测[J].南京航空航天大学学报,2007,39(2)：298-202.
[114]Gabor D. Information theory in electron microscopy [J].Laboratory Investigation.1965,14 801-807.
[115]Jain A. K. Partial differential equations and finite-difference Methods in Image Processing, part I: image representation [J].Journal of Optimization Theory and Applications,1977,23:65-91.
[116]Koenderink J. J.The structure of images [J].]Biological Cybernetics.1984,50(5):363-370.
[117]Perona P., Malic J.Scale space and edge detection using anisotropic diffusion [J]. IEEE Transaction on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[118]Alvarez L., Mazorra L. Signal and image restoration using shock filter and anisotropic diffusion [J]. SIAM Journal on Numerical Analysis,1994,31(2):590-605.
[119]Catte F., Lions P.L., Morel J. M. Image selective smoothing and edge detection by nonlinear diffusion [J]. SIAM Journal on Numerical Analysis,1992,29(1):182-193.
[120]Weickert J. Theoretical foundation of anisotropic diffusion in image processing [C]. Proceedings of the International Conference on Theoretical Foundation Compute Vision,1994:221-236.
[121]Weickert J. Coherence-enhancing diffusion filtering [J]. International Journal of Computer Vision,1999,31(2/3):111-127.
[122]Weickert J., Welk M. Tensor field interpolation with PDES [J].Mathematics and Visualization, 2006,4:315-325.
[123]Osher S.,Rudin L. Feature-oriented image enhancement using shock filters [J]. SIAM Journal on Numerical Analysis,1990,27(4):919-940.
[124]Alvarez L.,Guichard F., Lions P. L. Axioms and fundamental equation of image processing[J]. Archive Rational Mechsnics Analysis,1993,123(3):199-257.
[125]Whitaker R.T., Piaer S.M. A Multi-scale approach to uniform diffusion [J]. International Journal of Computer Vision,1993,57(1):99-110.
[126]Torkamani A., Tait F. Image recovery using the anisotropic diffusion equation[J]. IEEE Transactions on Image Processing,1996,5(11):1573-1578.
[127]You Y.L., Xu W.Y., Tanncnbaum A. Behavioral Analysis of Anisotropic Diffusion in Image Processing [J]. IEEE Transactions on Image Processing,1996,5(11):1539-1553.
[128]You Y.L., Kaveh M. Blind Image Restoration by Anisotropic Regularization [J].IEEE Transactions on Image Processing,1999,8(3):396-407.
[129]Wu Z.Y., Herman G.T., Browen J.A. Edge preserving reconstruction using adaptive smoothing in wavelet domain [C]. Proceed ings of International Conference on Nuclear Sciences Symposium and Medical Imaging,1993,3:1917-1921.
[130]Osher S., Sethian J. A. Fronts propagating with curvature dependent speed:algorithm based on Hamilton-Jacobi formulation [J]. Journal of Computational Physics,1998,79:12-49.
[131]Malladi R.,Sethian J.A. Image processing,flows under min/max curvature and mean curvature[J].Graphical Models and Image Processing,1996,66(1):1-31.
[132]Malladi R., Sethian J.A., Vemuri B.C. A fast level set based algorithm for topology independent shape modeling [J].Journal of Mathematical Imaging and Vision,1996,6(2):269-289.
[133]Sapiro G. Gemotric partial differential equations and image analysis [M].Cambridge University Press.2001.
[134]Kass M., Witkin A., Terzopoulos D. Snakes:active contour models[C]. Proceedings of the International Conference on Computer Vision, London,1987:259-268.
[135]Cohen L. D. Finite-element methods for active contour models and balloons for 2-D and 3-D images [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1993,15(11): 1131-1147.
[136]Cohen L. D. Note on active contour models and balloons [J]. Graphical Models and Image Processing,1991,53(2):211-218.
[137]Xu C.Y., Prince J. L. Generalized gradient vector flow external force for active contours [J]. Signal Processing,1998,71 (2):131-139.
[138]Rudin L., Osher S., Fatemi E. Nonlinear total variation based noise removal algorithms [M]. PhysicaD,1992,60:259-268.
[139]Shu X.B., Ahuja N. Hybrid compressive sampling via a new total variation TVLl[C].Proceedings of European Conference on Computer Vision,2010.
[140]Chan T.,Marquina A T.,Muler P.High-order total variation-based image restoration[J].SIAM Journal on Scientific Computing,2000,22(2):503-516.
[141]Chan T. F., Esedoglu S. A fourth order dual method for staircase reduction in texture extraction and image restoration problems[R].UCLA CAM Report,05-28,2005.
[142]You Y.L., Kaveh M. Fourth-order partial differential equations for noise removal [J].IEEE Transactions on Image Processing,2000,9(10):1723-1730.
[143]Lysaker M.,Loudervold A.,Tai X.C. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time[J].IEEE Transactions on Image Processing,2003,12(12):1579-1590.
[144]肖亮,吴慧中,韦志辉.基于鲁棒统计的图像去噪耦合变分模型及其应用[J].南京理工大学学报,2007,31(4)：418-421.
[145]陈利霞,宋国乡,丁宣浩.改进的总变分去噪算法[J].光子学报,2009.38(4)：1001-1004.
[146]邵文泽,韦志辉.数字双边TV滤波器及非线性图像平滑[J].中国图象图形学报,2007,12(7)：1178-1185.
[147]Zhang J., Wei Z.H. Fractional variational model and algorithm for image denoising[C].Proceedings of the International Conference on Natural Computation,2008,5: 524-528.
[148]Meyer Y. Oscillating patterns in image processing and nonlinear evolution equation [M]. Volume 22 of University Lecture Series, AMS, Providence,2001.
[149]Osher S., Sole A., Vese L.A. Image decomposition and restoration using total variation minimization and the H-1 norm [J]. Multiscale Modeling and Simulation,2003,1(3):349-370.
[150]Vese L.A., Osher S. Modeling textures with total variation minimization and oscillating patterns in image processing [J].Journal of Scientific Computing,2003,19(l):553-572.
[151]Lieu L., Vese L. A. Image restoration and decomposion via bounded total variation and negative Hibert-Sobolev space[R].UCLA CAM Report,05-33,2005.
[152]Aujol J.F., Gilboa G., Chan T.F. Structure-Texture Image Decomposition Modeling, Algorithms, and Parameter Selection [J].International Journal of Compute Vision,2006,67(1):111-136.
[153]Aliney S. A property of the minimum vectors of a regularizing functional defined by means of the absolute norm[J]. IEEE Transactions on Signal Processing,1997,45(4):913-917.
[154]Nikolova M. A variational approach to remove outlier and impulse noise[J].Journal of Mathematical Imaging and Vision,2004,20:99-120.
[155]Aujol J.F., Chambolle A. Dual norms and image decomposition models[J]. International Journal on Computer Vision,2005,63(1):85-104.
[156]Starck J.L., Elad M., Donoho D.L. Image decomposition:separation of texture from piecewise smooth content [C].Proceedings of SPIE Annual Meeting,2003.
[157]Starck J.L., Elad M., Donoho D.L. Image decomposition via the combination of sparse representations and variational approach [J]. IEEE Transactions on Image Processing,2005, 14(10):1570-1582.
[158]Chambolle A., Lions P.L. Image recovery via total variation minimization and related problems [J]. Numerische Mathematik,1997,76(3):167-188.
[159]Chambolle A. An algorithm for total variation minimization and applications [J]. Journal of Mathematical Imaging and Vision,2004,20(1):89-97.
[160]Bioueas J., Diasand M., Figueiredo. A new TwIST: two step iterative shrinkage thresholding algorithms for image restoration [J]. IEEE Transactions on Image Processing,2007,16(12): 2992-3004.
[161]Wang Y.,Yin W.,Zhang Y. A Fast algorithm for image deblurring with total variation regularization[R].UCLA CAM Report,07-22,2007.
[162]Wang Y.A new alternating minimization algorithm for total variation image reconstruction [J]. SIAM Journal on Imaging Sciences,2008,1(3):248-272.
[163]Lions P.L.,Mercier B. Splitting algorithms for the sum of two nonlinear operators[J].SIAM Journal on Numerical Analysis,1979,16(6):964-979.
[164]Osher S.,Mao Y.,Dong B. Fast linearized Bregman iteration for compressive sensing and sparse denoising[J]. Communications in Mathematical Sciences,2010,8(1):93-111.
[165]Goldstein T.,Osher S. The Split Bregman method for L1 regularized problem[J].SIAM Journal on imaging and Sciences,2009,2(2):323-343.
[166]Jaffard S., Beyond Besov spaces Part 1:Distribution of wavelet coefficients [J]. The Journal of Fourier analysis and applications,2004,10(3):221-246.
[167]Shin G.S, Kang .M. G. Wavelet-based denoising considering interscale and intrascale dependences [J]. Optical Engineering.2005,44(6):067002 1-9.
[168]Jaffard S. Pointwise smoothness, two-mircrolocalization and wavelet coefficients [J]. Publications Matematiques,1991,35(1):152-168.
[169]Bony J.M. Second microloclaizatin and propagation of singularities for semilinear hyperbolic equation[C]. Proceedings of hyperbolic equations and related topics, Boston, MA,1986:11-49.
[170]Frazier M.Jawerth B. Decomposition of Besov Spaces[J]. Indiana University Mathematics Journal,1985,34:777-789.
[171]Jaffard S. Beyond Besov spaces Part 2:Oscillation spaces [J]. Constructive approximation,2005, 21:29-61.
[172]Melot C. Oscillating singularities in Besov spaces [J].Journal of Mathematics and Pure Applications,2004,83(3):367-416.
[173]Vehel J. L. Signal enhancement based on Holder regularity analysis[J]. IMA Volumes in Mathematics and its Applications.2002,132:197-209.
[174]李会芳,俞卞章.基于小波的多重分形图像去噪新算法[J].2004,12(3)：305-310.
[175]Jansen K., D.Anstassiou. Subpixel edge localization and the interpolation of still images [J].IEEE Transactions on Image Processing,1995,4(3):285-295.
[176]Li X., Orchard M.T. New edge-directed interpolation [J]. IEEE Transactions on Image Processing,2001,10(10):1521-1527.
[177]Shao W.Z., Wei Z.H. Edge-and-coner preserving regularization for image interpolation and reconstruction[J].Image and Vision Computing,2008,26(12):1591-1606.
[178]Hwang J.W., Lee H.S.Adaptive image interpolation based on local gradient features[J].IEEE Signal Process Letters,2004,11(3):359-362.
[179]Casciola G., Montefusco L.B., Morigi S. Edge-driven image interpolation using adaptive anisotropic Radial Basis Function [J]. Journal of Mathematical Imaging Vision, 2010,36(2):125-139.
[180]Yang P.,Tong X., Zheng X.Z. A gradient based adaptive interpolation filter for multiple view synthesis[C]. Proceedings of the Pacific Rim Conference on Multimedia:Advances in Multimedia Information Processing, Bangkok, Thailand,2009:551-560.
[181]Black J., Sapiro G., Marimont D. H. Robust anisotropic diffusion [J].IEEE Transactions on Image Processing,1998,7(3):421-432.
[182]Tian J., Yu W.Y., Xie S.L. On the kernel selection of nonlocal filtering for image denoising[C].In Proceedings of International Conference on Machine Learning and Cybernetics.2008:12-12.
[183]Wang Z., Bovik A. C., Sheikh H. R. lmage quality assessment:From error visibility to structural similarity [J]. IEEE Transaction on Image Processing,2004,13(4):600-612.
[184]Zhang X.Q., Burger M., Bresson X.Osher S.Bregmanized nonlocal for deconvolution and sparse reconstruction [R].UCLA CAM Report,09-03,2009.