基于偏微分方程的图像降噪和图像恢复研究
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摘要
偏微分方法在图像处理、信号处理以及图像压缩等领域中得到了广泛的应用,然而其庞大的计算量制约了偏微分方法应用的进一步推广。将偏微分方法与多尺度分析方法结合起来,利用这两种方法各自的优点,形成新的图像处理方法,可以极大地减少偏微分方法所花的计算时间,这是很有理论和实用价值的。目前,偏微分方法已经被应用于边缘提取、特征提取、模式识别、图像分割、机器视觉等领域,显示出很好的应用前景。但是,现有的偏微分方法对噪声比较敏感,这一定程度上限制了它在图像降噪和图像修复领域中的应用。为此,本文全面系统地阐述了偏微分方法的发展动态和基本理论,详细分析了非下采样Contourlet多尺度变换特性,深入研究了在像素域和变换域进行偏微分扩散的图像降噪和图像修复方法。
提出了自适应的P-Laplace的扩散方法。其中关键参数p能根据图像局部几何信息的曲率和梯度自适应地改变,并控制扩散方向和扩散强度。首先,利用变分原理,推导出P-Laplace的扩散方法所对应的欧拉方程,利用图像的局部正交坐标系,分析其扩散能力。扩散过程中,在图像的边缘区域,沿边缘方向扩散应具有较大的扩散系数,沿垂直边缘方向扩散应具有很小的扩散系数;在图像的平坦区域,向周围等强度扩散,而且扩散强度值较大。其次,根据对自适应的P-Laplace扩散方法的分析,利用半点差分格式,设计出图像修复的数值方法。理论分析和实验结果都表明,基于自适应的P-Laplace扩散的图像修复模型比基于TV修复的模型更有效;同时通过实验表明基于自适应的P-Laplace扩散的图像修复模型比基于常数p的P-Laplace扩散的图像修复模型在提高图像修复质量方面更有效。
提出了一种基于非下采样Contourlet变换的自适应降噪方法,先对图像进行非下采样Contourlet变换得到不同尺度和不同方向上的变换系数,然后用分解尺度的系数和区域能量来表示图像的纹理信息。在相同分解尺度下,分解能量越大,表示该方向具有更多的纹理信息,阈值设置应该设置就越低,反之阈值设置就越大。再根据变换系数特征,引入非下采样Contourlet变换的方向因子,自适应地确定降噪阈值。最后对变换系数进行反变换,实现图像降噪。实验结果表明,与小波变换和Contourlet变换相比,非下采样Contourlet变换降噪方法保留了更多的图像轮廓细节,提高了图像的PSNR值。
提出了基于非下采样Contourlet变换和自适应P-Laplace扩散的图像降噪方法。这种方法的主要目的是在图像降噪时,能减少吉普斯震荡现象。同时论文提出了用扩散因子在不同区域控制不同的扩散强度。首先,通过非下采样Contourlet变换阈值得到初步的降噪图像;然后,把阈值变换后本来需要置零的高频系数保留,再利用P-Laplace算法进行扩散,得到高频扩散图像;最后,把这部分高频扩散图像融合到阈值方法得到的降噪图像中,得到最终降噪图像。数值结果表明,论文方法在提高图像质量的同时,能有效保持图像的纹理细节。
提出了在非下采样Contourlet变换域进行自适应P-Laplace扩散的图像修复方法。许多传统的方法是在像素域进行扩散,但是论文中提出的修复方式是在非下采样Contourlet变换域直接进行。由于在图像压缩保存和传输过程中可能丢失部分系数,论文提出的方法可以在变换域直接进行系数修复。理论分析和实验结果都表明,基于变换域的修复方法是有效的,即使在丢失大量系数的情况下,也可以较好地实现修复,明显地提高图像的质量。
针对图像复原问题,提出了一种基于各向异性和非线性规整化的自适应P-Laplace扩散的图像盲复原新算法。该算法主要结合图像梯度和曲率的性质采用基于各向异性的空间自适应规整化处理,建立了具有非线性和空间各向异性的规整化函数,使其在恢复目标图像时能自适应地进行梯度平滑和边缘保留。通过交替最小化方案来极小化代价函数和通过定点迭代策略将非线性方程进行线性化处理,快速地恢复图像。
PDE method has been extensively applied to many fields, such as image processing and signal processing. However, its application is restricted by its computational complexity. Therefore, the PDE and multi-scale image analysis are combined to form a new image processing method. The new method can be applied in image denoising and image inpainting, and can greatly reduce the computation time spent on PDE. The new method has theoretical and practical value. At present, PDE has been applied to many fields, such as edge and feature extracton, pattern recognition, image segmentation as well as computer vision, and showed good prospects. But many PDE methods suffer from the staircase effect easily, which restricts its application in some fields such as image denoising and image inpainting. So, the fundamental theory and developments of PDE were systematically described in this dissertation. The characteristics of PDE and multi-scale image analysis were analyzed for image denoising and image inpainting in pixel domain and transform domain in detail. The principle and implementation of these methods were deeply studied in this paper.
The adaptive P-Laplace diffusion method for images denoising is proposed in this dissertation. An adaptive factor p is proposed based on the local geometry characteristic of curvature and gradient feature of images. The adaptive factor p can control the diffusion direction and diffusion intensity. The Euler-Lagrange equations of the P-Laplace diffusion method are deduced. The diffusion performance of the adaptive P-Laplace diffusion equation is analyzed. The adaptive P-Laplace diffusion has strong diffusion coefficient in the edge direction and has small diffusion coefficient in the gradient direction when diffusion was performed at edge region. But the adaptive P-Laplace diffusion has the same diffusion coefficient at smooth region. The image inpainting algorithm of finite difference is proposed with the half point differential scheme based on the analysis of the adaptive P-Laplace diffusion. Theoretic analysis and experimental results show that the new method has better performances both in vision effect and image quality than the TV method and the constant P-Laplace method.
An adaptive de-noising algorithm was proposed based on the nonsubsampled Contourlet transform. Firstly the coefficients in different scales and different directions are obtained by image decomposition using the nonsubsampled Contourlet transform. The texture of the image information is introduced by using the mean of decomposition scale and the variance of region. The threshold should be set lowly when the image has many textures at each decomposition scale. On the contrary, the threshold should be set large. Threshold functions are set with these coefficients adaptively. After the de-noising and reconstruction of these coefficients, image de-noising is implemented. Comparing to the wavelet transform threshold and Contourlet transform threshold, the nonsubsampled Contourlet transform picks up the image detail better and improves signal-to-noise ratio of the peak.
We proposed a nonsubsampled Contourlet transform (NSCT) formulation combined with the adaptive P-Laplace variation method for images denoising. Our method aims at reducing Gibbs-type artifacts. The diffusion factor has different diffusional intensity at different region. Firstly, the denoised image which by threshold method of nonsubsampled Contourlet transform is obtained. Secondly, the NSCT coefficients which have been set to zero by the threshold procedure are retained, and the P-Laplace diffusion directly to the reconstruction image from the retained coefficients. Finally, the diffusion image is fused with the denoised image with the thresholds method, and the final denoising image is obtained. The experimental results indicate that our method can improve image quality and maintain much more detail information.
We proposed a novel image inpainting method. The new method is anisotropic diffusion. It can control and restore the missing or damaged regions in the nonsubsampled Contourlet transform (NSCT) domain, instead of the pixel domain in which traditional inpainting problems are defined. In the wireless communication of these images, it could happen that certain wavelet packets are randomly lost or damaged during the transmission process. Our method can remedy the lost coefficients in the transform domain. Experimental results show that the proposed algorithm can remedy images effectively and improve image quality significantly, even with relatively large number of lost coefficients.
A blind restoration algorithm of P-Laplace diffusion based on anisotropic and nonlinear regularizations is proposed for restoring degraded images, in which the anisotropic and adaptive regularizations are adopted according to the character of image curvature and gradient. The nonlinear and spatial anisotropic regularization functions are suggested to smooth adaptively in the process of recovering the object image. Finally, the cost functions are minimized by alternate minimization scheme. The nonlinear equations are linear by fixed-point iteration scheme. The images can be recovered quickly.
提出了自适应的P-Laplace的扩散方法。其中关键参数p能根据图像局部几何信息的曲率和梯度自适应地改变,并控制扩散方向和扩散强度。首先,利用变分原理,推导出P-Laplace的扩散方法所对应的欧拉方程,利用图像的局部正交坐标系,分析其扩散能力。扩散过程中,在图像的边缘区域,沿边缘方向扩散应具有较大的扩散系数,沿垂直边缘方向扩散应具有很小的扩散系数;在图像的平坦区域,向周围等强度扩散,而且扩散强度值较大。其次,根据对自适应的P-Laplace扩散方法的分析,利用半点差分格式,设计出图像修复的数值方法。理论分析和实验结果都表明,基于自适应的P-Laplace扩散的图像修复模型比基于TV修复的模型更有效;同时通过实验表明基于自适应的P-Laplace扩散的图像修复模型比基于常数p的P-Laplace扩散的图像修复模型在提高图像修复质量方面更有效。
提出了一种基于非下采样Contourlet变换的自适应降噪方法,先对图像进行非下采样Contourlet变换得到不同尺度和不同方向上的变换系数,然后用分解尺度的系数和区域能量来表示图像的纹理信息。在相同分解尺度下,分解能量越大,表示该方向具有更多的纹理信息,阈值设置应该设置就越低,反之阈值设置就越大。再根据变换系数特征,引入非下采样Contourlet变换的方向因子,自适应地确定降噪阈值。最后对变换系数进行反变换,实现图像降噪。实验结果表明,与小波变换和Contourlet变换相比,非下采样Contourlet变换降噪方法保留了更多的图像轮廓细节,提高了图像的PSNR值。
提出了基于非下采样Contourlet变换和自适应P-Laplace扩散的图像降噪方法。这种方法的主要目的是在图像降噪时,能减少吉普斯震荡现象。同时论文提出了用扩散因子在不同区域控制不同的扩散强度。首先,通过非下采样Contourlet变换阈值得到初步的降噪图像;然后,把阈值变换后本来需要置零的高频系数保留,再利用P-Laplace算法进行扩散,得到高频扩散图像;最后,把这部分高频扩散图像融合到阈值方法得到的降噪图像中,得到最终降噪图像。数值结果表明,论文方法在提高图像质量的同时,能有效保持图像的纹理细节。
提出了在非下采样Contourlet变换域进行自适应P-Laplace扩散的图像修复方法。许多传统的方法是在像素域进行扩散,但是论文中提出的修复方式是在非下采样Contourlet变换域直接进行。由于在图像压缩保存和传输过程中可能丢失部分系数,论文提出的方法可以在变换域直接进行系数修复。理论分析和实验结果都表明,基于变换域的修复方法是有效的,即使在丢失大量系数的情况下,也可以较好地实现修复,明显地提高图像的质量。
针对图像复原问题,提出了一种基于各向异性和非线性规整化的自适应P-Laplace扩散的图像盲复原新算法。该算法主要结合图像梯度和曲率的性质采用基于各向异性的空间自适应规整化处理,建立了具有非线性和空间各向异性的规整化函数,使其在恢复目标图像时能自适应地进行梯度平滑和边缘保留。通过交替最小化方案来极小化代价函数和通过定点迭代策略将非线性方程进行线性化处理,快速地恢复图像。
PDE method has been extensively applied to many fields, such as image processing and signal processing. However, its application is restricted by its computational complexity. Therefore, the PDE and multi-scale image analysis are combined to form a new image processing method. The new method can be applied in image denoising and image inpainting, and can greatly reduce the computation time spent on PDE. The new method has theoretical and practical value. At present, PDE has been applied to many fields, such as edge and feature extracton, pattern recognition, image segmentation as well as computer vision, and showed good prospects. But many PDE methods suffer from the staircase effect easily, which restricts its application in some fields such as image denoising and image inpainting. So, the fundamental theory and developments of PDE were systematically described in this dissertation. The characteristics of PDE and multi-scale image analysis were analyzed for image denoising and image inpainting in pixel domain and transform domain in detail. The principle and implementation of these methods were deeply studied in this paper.
The adaptive P-Laplace diffusion method for images denoising is proposed in this dissertation. An adaptive factor p is proposed based on the local geometry characteristic of curvature and gradient feature of images. The adaptive factor p can control the diffusion direction and diffusion intensity. The Euler-Lagrange equations of the P-Laplace diffusion method are deduced. The diffusion performance of the adaptive P-Laplace diffusion equation is analyzed. The adaptive P-Laplace diffusion has strong diffusion coefficient in the edge direction and has small diffusion coefficient in the gradient direction when diffusion was performed at edge region. But the adaptive P-Laplace diffusion has the same diffusion coefficient at smooth region. The image inpainting algorithm of finite difference is proposed with the half point differential scheme based on the analysis of the adaptive P-Laplace diffusion. Theoretic analysis and experimental results show that the new method has better performances both in vision effect and image quality than the TV method and the constant P-Laplace method.
An adaptive de-noising algorithm was proposed based on the nonsubsampled Contourlet transform. Firstly the coefficients in different scales and different directions are obtained by image decomposition using the nonsubsampled Contourlet transform. The texture of the image information is introduced by using the mean of decomposition scale and the variance of region. The threshold should be set lowly when the image has many textures at each decomposition scale. On the contrary, the threshold should be set large. Threshold functions are set with these coefficients adaptively. After the de-noising and reconstruction of these coefficients, image de-noising is implemented. Comparing to the wavelet transform threshold and Contourlet transform threshold, the nonsubsampled Contourlet transform picks up the image detail better and improves signal-to-noise ratio of the peak.
We proposed a nonsubsampled Contourlet transform (NSCT) formulation combined with the adaptive P-Laplace variation method for images denoising. Our method aims at reducing Gibbs-type artifacts. The diffusion factor has different diffusional intensity at different region. Firstly, the denoised image which by threshold method of nonsubsampled Contourlet transform is obtained. Secondly, the NSCT coefficients which have been set to zero by the threshold procedure are retained, and the P-Laplace diffusion directly to the reconstruction image from the retained coefficients. Finally, the diffusion image is fused with the denoised image with the thresholds method, and the final denoising image is obtained. The experimental results indicate that our method can improve image quality and maintain much more detail information.
We proposed a novel image inpainting method. The new method is anisotropic diffusion. It can control and restore the missing or damaged regions in the nonsubsampled Contourlet transform (NSCT) domain, instead of the pixel domain in which traditional inpainting problems are defined. In the wireless communication of these images, it could happen that certain wavelet packets are randomly lost or damaged during the transmission process. Our method can remedy the lost coefficients in the transform domain. Experimental results show that the proposed algorithm can remedy images effectively and improve image quality significantly, even with relatively large number of lost coefficients.
A blind restoration algorithm of P-Laplace diffusion based on anisotropic and nonlinear regularizations is proposed for restoring degraded images, in which the anisotropic and adaptive regularizations are adopted according to the character of image curvature and gradient. The nonlinear and spatial anisotropic regularization functions are suggested to smooth adaptively in the process of recovering the object image. Finally, the cost functions are minimized by alternate minimization scheme. The nonlinear equations are linear by fixed-point iteration scheme. The images can be recovered quickly.
引文
[1] M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, Image inpainting [C]. in Proc. ACM SIGGRAPH, 2000: 417-424.
[2] T. F. Chan and J. Shen, Mathematical models for local nontexture inpaintings [J]. SIAM J. Appl. Math., 62(3): 1019-1043, Feb.2002.
[3] G. Landi, A Truncated lgrange method for total variation-based image restoration [J]. J Math Imaging Vis., 28: 113-123, Jun.2007.
[4] Lianghai Jin, Dehua Li, and Enmin Song, Combining vector ordering and spatial information for color image interpolation [J]. Image and Vision Computing, vol.27: 410-416, 2009.
[5] Jean-Fran?ois Aujol, Some first-order algorithms for total Variation based image restoration [J]. J Math Imaging Vis., vol. 34: 307-327, 2009.
[6] Brendt Wohlberg and Paul Rodríguez, An iteratively reweighted norm algorithm for minimization of total variation functionals [J]. IEEE Signal Processing Letters, Vol. 14, No. 12: 948-951, Dec. 2007.
[7] Haoying Fu , Michael K. Ng , and Mila Nik Olova, On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization and sides [J]. SIAM J. Numer. Anal., 42(2): 686–713, 2004.
[8] Junmei Zhong and Huifang Sun, Wavelet-based multiscale anisotropic diffusion with adaptive statistical analysis for image restoration [J]. IEEE Trans. Circuits and Systems-I: Regular Papets., 55 (9): 2716-2725, Oct. 2008.
[9] Jinjun Xu and Stanley Osher, Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising [J]. IEEE Trans. Image Process., 16 (2): 534-544, Feb. 2007.
[10] Glenn R. Easley, Demetrio Labate, and Flavia Colonna, Shearlet- based total variation diffusion for denoising [J]. IEEE Trans. Image Process., 18 (2): 260-268, Feb. 2009.
[11] J. Ma and M. Fenn, Combined complex ridgelet shrinkage and total variation minimization [J]. SIAM J. Sci. Comput., 28 (3): 984-1000, 2006.
[12] Jianwei Ma and Gerlind Plonka, Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion [J]. IEEE Trans. Image Process., 16 (9): 2198-2206, Sep. 2009.
[13] C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro, and J. Verdera, Filling-in by joint interpolation of vector fields and gray levels [J]. IEEE Trans. Image Process., 10 (8): 1200–1211, Aug. 2001.
[14] G. Plonka and J. Ma, Nonlinear regularized reaction-diffusion filters for denoising of images with textures [J]. IEEE Trans. Image Process., 17 (8): 1283-1294, Aug. 2008.
[15] T. F. Chan and J. Shen, Non-texture inpainting by curvature-driven diffusions (CDD) [J]. J. Visual Communication Image Represent, 12 (4): 436-449, Dec. 2001.
[16] S. Rane, G. Sapiro and M. Bertalmio, Structure and texture filling-in of missing image blocks in wireless transmission and compression applications [J]. IEEE Trans. Image Proc., vol. 12(3): 296-303, Mar.2003.
[17] S. S. Hemami and R. M. Gray, Subband-coded Image Reconstruction for Lossy Packet Networks [J]. IEEE Trans. Image Proc., 6 (4): 523-539, Apr. 1997.
[18] S. Durand and J. Froment, Reconstruction of wavelet coefficients using total variation minimization [J]. SIAM J. Sci. Comput., 24(5): 1754-1767, 2003.
[19] E. J. Candès and F. Guo, New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction [J]. Signal Process., 82(11): 1519-1543, 2002.
[20] T. F. Chan, J. Shen, and H.-M. Zhou, Total variation wavelet inpainting [J]. J. Math. Imag Vis., 25(1): 107-125, Jul. 2006.
[21] Zhang H Y, Peng Q C and Wu Y D. Wavelet inpainting based on p- laplace operator [J]. Acta automatica sinica, 33 (5): 546-549, May. 2007.
[22] Marcelo Bertalmio, Strong continuation, contrast invariant inpainting with a third-order optimal PDE [J]. IEEE Trans. Image Process., 15 (7): 1934-1938, Sep. 2006.
[23] A. Bertozzi, S. Esedoglu, and A. Gillette, Inpainting of binary images using the Cahn–Hilliard equation[J]. IEEE Trans. Image Process., 16 (1):285-291, Jan. 2007.
[24] M. F. Auclair-Fortier and Djemel Ziou, A global approach for solving evolutive heat transfer for image denoising and inpainting [J]. IEEE Trans. Image Process., 15 (9): 2258-2574, Sep. 2006.
[25] Chan T F and Shen J H, Mathematical models for local nontexture inpainting [J]. SIAM Journal on Applied Mathematics, 62 (3): 1019-1043, 2001.
[26] M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, Simultaneous structure and texture image inpainting [J]. IEEE Trans. Image Process., 12 (8): 882-889, Aug. 2003.
[27] Julia A. Dobrosotskaya and Andrea L. Bertozzi, A wavelet-laplace variational technique for image deconvolution and inpainting [J]. IEEE Trans. Image Process., 17 (5): 657-663, May. 2008.
[28] M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, Simultaneous cartoon texture image inpaitning using morphological component analysis [J]. Appl. Comput. Harmon. Anal.,19:340-358, 2005.
[29] J. Sun, L. Yuan, J. Jia, and H.-Y. Shum,“Image completion with structure propagation [J].”in Proc. ACM SIGGRAPH, 2005: 861-868.
[30] J. Morlet, G. Arens, E. Fourgeau, D. Giard. Wave propagation and sampling theory-Part 1: Complex signal scattering in multilayered media [J]. Geophysics, 1982, 47 (2): 203-221.
[31] T Chan, C Wong. Convergence of the alternating minimization algorithm for blind deconvolution [J]. ELSEVIER, Linear Algebra and its Application, 2000,316 (3): 259-285.
[32] C A ZBareclos,Y Chen. Heat flows and related minimization problem in image restoration [J]. Computers and Mathematics with Applications, 2000, 39 (7):81-97.
[33] Ramesh Neelamani, Hyeokho Choi, Richard Baraniuk, Fourier-wavelet regularized deconvolution for III-coditioned systems [J]. IEEE Trans on Signal Prodessing, 2004, 52 (2): 418-433.
[34] Teboul S ,B Lance-Feraud L, Aubert G, Variatinal approach for edge-preserving regularization using coupled PEDS[J]. IEEE Trans on Signal Prodessing,1998, 7 (3): 387-397.
[35]张航,罗大庸.图像盲复原算法研究现状及其展望[J].中国图象图形学报,2004,10 (9): 1145-1152.
[36]罗林,王黎,程卫东等.天文图像多帧盲反卷积收敛性的增强方法[J].物理学报,2006, 55:6708-6714.
[37] J. Morlet, G. Arens, E. Fourgeau, D. Giard. Wave propagation and sampling theory-Part 2: Sampling theory and complex waves [J]. Geophysics, 1982, 47 (2): 222-236.
[38] A. Grossmann, J. Morlet. Decomposition of Hardy functions into square integrable wavelets of constant shape [J]. SIAM J. of Math. Anal., 1984, 15(4): 723-736.
[39] A. Grossmann, J. Morlet, T. Paul. Transforms associated to square integrable group representations - general results [J]. Math. Phys, 1985, 26(10): 2473-2479.
[40] Y. Meyer. Principe d’incertitude, bases hillbertiennes et al, gebrasd operateurs [D]. In Seminaire Bourbaki, Paris, 1986.
[41] Y. Meyer著,小波与算子[M].尤众译.北京:世界图书出版公司,1992.
[42] I. Daubechies. Orthonomal bases of compactly supported wavelets [D]. Comm. Pure Appl. Math, 1998, 41:909-996
[43] I. Daubechies. Ten Lectures on Wavelets [D]. CBMS Conference Series in Applied Mathematics, SIAM, Philadelphia, 1992
[44] A. Cohen, I. Daubechies and J. C. Feauveeau. Biorthogonal bases of compactly supported wavelets [D]. Commun. Pure Appl. Math., 1992.5, 45(5):485-560
[45] Ingrid Daubechies. Where Do Wavelets Come From, A Personal Point of View [J].Proceeding of the IEEE, 1996, 84(4):510-513.
[46] S. Mallat. A theory for multiresolution signal decomposition: the wavelet representation [J]. IEEE Trans. On PAMI, 1989.7, 11(7):674-693
[47] S. Mallat. A Wavelet Tour of Signal Processing [M].北京:机械工业出版社,2003.
[48] S. Mallat. An efficient image representation for multiscale analysis. Proc. of Mschine Vision Conference[C]. Lake Taho: 1987.
[49] S. Mallat. A Compact Multiresolution Representation: The Wavelet Model. Proc. IEEE Computer Society Workshop on Computer Vision[C]. Washington. D.C.: IEEE Computer Society Press, 1987.
[50] S. Mallat. Multiresolution Approximations and Wavelet Orthonormal Bases of L2(R)[J]. Trans. of the Amercian Math. Society, 1989, 315(1):69-87.
[51] S. Mallat. Multifrequency Channel Decompositions of Images and Wavelet Models [J]. IEEE Tran on acoustics speech and signal processing, 1989, 37(12):2091-2110.
[52] S. Mallat. Multiresolution Approximations and Wavelet Orthonormal Bases of L2(R) [J]. Trans. of the American Math. Society, 1989, 315(1):69-87.
[53]秦前清,杨宗凯编著.实用小波分析[M].西安:西安电子科技大学出版社,2002.
[54]杨福生著.小波变换的工程分析与应用[M].北京:科学出版社,2003.
[55]孙延奎编著.小波分析及其应用[M].北京:机械工业出版社,2005.
[56]程正兴,杨守志,冯晓霞著.小波分析的理论、算法、进展和应用[M].北京:国防工业出版社,2007.
[57]程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,2003.
[58]成礼智,郭汉伟.小波与离散变换理论及工程实践[M].北京:清华大学出版社,2005.
[59]冯象初,甘小冰,宋国乡编著.数值泛函与小波理论[M].西安:西安电子科技大学出版社,2003.
[60]崔锦泰著,程正兴译.小波分析导论[M].西安:西安交通大学出版社,1997.
[61]龙瑞麟著.高维小波分析[M].北京:世界图书出版公司,1995.
[62] E J. Candès. Harmonic analysis of neural networks [J]. Applied and Computational Harmonic Analysis, 1999, 6(2): 197-218.
[63] E J. Candès. Ridgelet: theory and applications [D]. Ph. D. dissertation. Stanford University, 1998.
[64] E J. Candès, D. L. Donoho. Ridgelet: a key to higher-dimensional intermittency? Technical report [Z]. Stanford University, 1999.
[65] D. L. Donoho. Orthonormal ridgelets and linear singularities [D]. Technical report, Stanford Univ ersity, 1998.
[66] D. L. Donoho. Ridge Functions and Orthonormal ridgelets[D]. Technical report, Stanford University, 1998.
[67] E J. Candès, D. L. Donoho. Curvelets-A surprisingly Effective Nonadaptive Representation for Objects with Edges [D]. Technical report, Stanford University, 1999.
[68] E J. Candès, D. L. Donoho. Curvelets. Technical Report [D]. Stanford University, 1999.
[69] D. L. Donoho, M. R. Ducan. Digital curvelet transform: strategy, implementation and experiments [D]. Technical report, Stanford University, 1999.
[70] E J. Candès, D. L. Donoho. Continuous curvelet transform: I. Resolution of the wavefront set [D]. Technical Report, Stanford University, 2002.
[71] E J. Candès, D. L. Donoho. Continuous curvelet transform: II. Discretization into frames [D]. Technical Report, Stanford University, 2002.
[72] E J. Candès, D. L. Donoho. DCTvUSFFT: Digital curvelet transforms via unequispaced fast fourirer transforms [D]. Technical Report, California Institute of technology, 2004.
[73] E J. Candès, D. L. Donoho. New Tight Frames of Curvelets and Optimal Representations of Objects with Piecewise C2 Singularities [C]. Communications on Pure and Applied Mathematics, 2003, 57(2): 219–266 .
[74] E J. Candès, L. Demant and D. L. Donoho. Fast discrete curvelet transforms, applied and computational mathematics [C], California Institute of technology, 2005: 1-43
[75] Bovike AC, M. Clark. Multichannel texture analysis using localized spatial filters[J]. IEEE, PAMI, 1990, 12(1): 55-72.
[76] M. N. DO, M. Vetterli. Contourlets. Beyond wavelets [C]. New York: Academic Press, 2002: 1-27.
[77] M. N. DO, M. Vetterli. Contourlet: A directional multiresolution image representation [C]. Proc of IEEE International Conference on Image Processing, 2002: 357-360.
[78] M. N. DO, M. Vetterli. The contourlet ransform: An efficient directional multiresolution image representation [J]. IEEE Transactions on Image Processing, 2003, 14(12): 2091-2106.
[79] L. D. Cunha, J. P Zhou and M. N. Do. The Nonsubsampled Contourlet Transform: Theory, Design, and Applications [M]. IEEE Transactions on Image Processing, October 2006, 15(10): 3089-3101.
[80] R. Eslami, H. Radha. Wavelet-based contourlet transform and its application to image coding [C]. International conference on image processing, 2004, 5: 3189-3192.
[81] R. Eslami, H. Radha. Wavelet-based contourlet coding using an SPIHT-like algorithm. In proc of conference on information science and systems [C], Princeton, 2004: 784-788.
[82] R. Eslami, H. Radha. Wavelet-based contourlet transform and its application to image coding[J]. IEEE International Conference on Image Processing, Singapore, Oct. 2004.
[83] P. E. Le, S. Mallat. Sparse geometric image representations with bandelets [J]. IEEE Trans on Image Processing, 2005, 14(4): 423-438.
[84] P. E. Le, S. Mallat. Image compression with geometrical wavelets [J]. IEEEE International Conference on Image Processing, 2000, 1: 661-664.
[85] E. Le, S. Mallat. Bandelet image approximation and compression. Multiscale Model [D]. Simulation, 2005, 4(3): 992-1039.
[86] PG. Oeyre, S. Mallat. Discrete bandelets with geometric orthogonal filters [C]. IEEE International Conference in Image Processing, Genova, 2005, 1: 65-68.
[87] G. Oeyre, S. Mallat. Surface compression with geometric bandelets [J]. ACM Transactions on Graphics, 2005, 24(3): 601-608.
[88] Y. Lu, M. N. Do. Multidimensional directional filter banks and surfacelets [J]. IEEE Transactions on Image Processing, 2007, 16(4): 918-931.
[89] D. L. Donoho, X. Huo. Beamlets and multiscale image analysis, multiscale and multiresolutiop methods [D]. Springer Lecture Notes in Computational Science and Engineering, 2002, 20: 149-196.
[90] D. L. Donoho, O. Levi, J. L. Starch, et al. Multiscale geometric analysis for 3-D catalogues [D]. Astronomical Data Analysis II. Processing of SPIE, Hawaii, 2002, 4847: 101-111.
[91] J. Chen, X. Huo. Beamlet coder: a tree-based, hierarchical contour representation and coding method [C]. International Conference on Acoustic Speech and Signal Processing, ICASSP, Orland, 2002.
[92] D. L. Donoho. Wedgelets: nearly minimax estimation of edges [C]. Ann. Statist, 1999, 27: 859-897.
[93] V. Velisavljevic, B. beferull-Lozano, M. Vetterli, et al. Directionlets: Anisotropic Multidirectional Representation with Separable Filtering [J]. IEEE Trans on Image processing, 2006, 15(7): 1916-1933.
[94] V. Velisavljevic. Directionlets: anisotropic multidirectional representation with separable filtering [D]. Ph. D. Thesis. School of Computer and Communication Sciences, Lausanne, Switzland, Oct, 2005.
[95] F. G. Meyer, R. R. Coifman. Brushlets. A tool for directional image analysis and image compression [J]. Applied and Computational Harmonic Analysis, 1997, 6(4): 147-187.
[96] F. G. Meyer, R. R. Coifman. Directional image compression with brushlets [C]. Proceeding of the IEEE-SP International Symposium, 1996, 189-192.
[97] K. Guo, D. Labate. Optimally Sparse Multidimensional Representation Using Shearlets [J].SIAM J Math. Anal, 2007, 39: 298-318.
[98] G. Easley, D. Labate. Sparse directional image representations using the discrete shearlet transform [J]. Applied and Computational Harmonic Analysis, 2008, 25: 25-46.
[99] K. Guo, D. Labate, Sparse Shearlet Representation of Fourier Integral Operators [D]. Electr. Res. Announc, 2007, 14: 7-19.
[100] G. Kutyniok, D. Labate. The Construction of Regular and Irregular Shearlet Frames [J]. Wavelet Theory and Application, 2007, 1: 1-10.
[101] Cunha A L, Zhou J and Do M N.“The non-subsampled contourlet transform: theory, design and applications [J],”IEEE Trans. Image Process., vol.15, no.10, pp. 3089-3101, Aug. 2006.
[102]焦李成,谭山.图像的多尺度几何分析回顾和展望[J],电子学报,2003,31 (12A): 1975- 1981
[103] Mink N Do and Martin Vetterli. The finite ridgelet transform for image representation[J]. IEEE Transactions on Image Processing, 2002,1 (12): 16-28.
[104] Do M N and Vetterli M. Contourlets:a directional multi-resolution image representation[A]. IEEE International Conference on Image Processing[C]. Rochester, NY:IEEE, 2002:357-36.
[105] Ramin Eslami and Hayder Radha, Translation-invariant contourlet tansform and its application to image denoising [J]. IEEE Tansactions on Image Processing, 2006, 15( 11): 3362-3374.
[106] Bei-bei Li, Xin Li and Shu-xun Wang, A multiscale and multidirectional image denoising algorithm based on contourlet transform [A]. IEEE Proceedings of the 2006 International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP'06) [C].
[107] Duncan D. Po and Minh N. Do, Directional multiscale modeling of images using the contourlet transform [J]. IEEE Tansactions on Image Processing, 2006,15 ( 6):1610-1620
[108] Minh N. Do and Martin Vetterli, The contourlet transform: an efficient directional multiresolution image Representation [J]. IEEE Tansactions on Image Processing, 2005, 14(12): 2091-2106.
[109] Eslami R and RadhaH. Wavelet based contourlet transform and it’s application to image coding [C]. IEEE International Conference on Image Processing.Singapore, 2004: 3189- 3192.
[110] Donoho D L. De-noising by soft-thresholding [J]. IEEE Trans.on Information Theory. 1995, 41: 613-62
[111] Bin Yang, Shutao Li and Fengmei Sun, Image fusion using nonsubsampled contourlet transform [C]. Fourth International Conference on Image and Graphics . 2007: 719-724.
[112] Lei Tang, Feng Zhao and Zong-gui Zhao, The nonsubsampled contourlet transform for image fusion [A]. Proceedings of the 2007 International Conference on Wavelet Analysis and Pattern Recognition. Beijing, China, 2007:305-310.
[113] Weyrich N and Warhola G T. Wavelet shrinkage and generalized crossvalidation for image denoising [J]. IEEE Trans. Image Proc. 1998, 7(1): 82-90.
[114] Chang S G, Yu B and Vetterli M. Adaptive wavelet threshoding for image denoising and compression [J]. IEEE Trans. Image Proc. 2000, 9(9):1532-1546.
[115]梁栋,沈敏,高清维等.一种基于Contourlet递归cycle spinning的图像降噪方法[J].电子学报,2005,33(11): 2044-2046
[116]郁梅,易文娟,蒋刚毅.基于Contourlet变换尺度间相关的图像降噪[J].光电工程,2006,35(6):73-77.
[117]查宇飞,毕笃彦.基于小波变换的自适应多阈值图像降噪[J].中国图象图形学报,2005, 10(5): 567-570.
[118]邓承志,曹汉强,汪胜前.非高斯双变量模型图像降噪[J].红外与激光工程,2006,35(2):234-237.
[119]张绘,张弓,郭琦南.基于域结构的图像相干斑抑制算法[J].南京航空航天大学学报,2006,38(6):743-748.
[120]易文娟,郁梅,蒋刚毅.一种有效的方向多尺度变换分析方法[J].计算机应用研究,2006,23(9):18-22.
[121]喻汉龙,余胜生,周敬利等.一种基于改进的Contourlet变换的图像压缩算法[J].计算机工程与应用,2005,41(14):40-43.
[122]倪伟,郭宝龙,杨锣.图像多尺度儿何分析新进展[J].计算机科学,2006,33(2):234-236.
[123]李光鑫,王坷.基于Contourlet变换的彩色图像融合算法[J].电子学报,2007,35(1):112-117.
[124]陈蜜,李德仁,秦前清等.基于Contourlet变换的遥感影像融合算法[J].小型微型计算机系统,2006,27(11):2052-2055.
[125]沙宇恒,丛琳,孙强等.基于Contourlet域模型的多尺度图像分割[J].红外与毫米波学报,2005,34(12):472-476.
[126]蔡超,丁明跃,周成平等.小波域中的双边滤波[J].电子学报,2004,32(1):128-131.
[127]郭旭静,王祖林.基于尺度间相关的非下采样Contourlet图像降噪算法[J].光电子.激光, 2007, 18(9): 1116~1119.
[128]闫敬文,屈小波.超小波分析及应用[M].北京:国防工业出版社, 2008.
[129]贾建,焦李成,项海林.基于双变量阈值的非下采样Contourlet变换图像降噪[J].电子与信息学报, 2009, 31(3): 532-536.
[130]贾建,焦李成.利用方向特性实现非下采样Contourlet变换阈值降噪[J].西安电子科技大学学报, 2009, 36 (2): 269-273.
[131]贾建,焦李成,魏玲.基于概率模型的非下采样Contourlet变换图像降噪[J].西北大学学报(自然科学版), 2009, 39 (1): 13-18.
[132]边策,钟桦,焦李成.基于非下采样Contourlet变换和双变量模型的图像降噪[J].电子与信息学报, 2009, 31 (3): 561-565.
[133]陈志刚,尹福昌.基于Contourlet变换的遥感图像增强算法[J].光学精密工程, 2008, 16 (10): 2030-2037.
[134]焦李成,谭山.图像的多尺度几何分析:回顾与展望[J].电子学报, 2003, 31(12A):1975-1981.
[135]焦李成,侯彪,王爽等.多尺度几何分析理论与应用[M].西安:西安电子科技大学出版社, 2008.
[136] Firoiu I, Nafornita C, Boucher J M, and Isar A, Image denoising using a new implementation of the hyperanalytic wavelet transform [J]. IEEE Trans. Image Process., vol.58, no.8, pp. 2410-2416, Aug. 2009.
[137] Mark Miller and Nick Kingsbury, Image denoising using derotated complex wavelet coefficients [J], IEEE Trans. Image Process., vol.17, no.9, pp. 1500-1511, Sep. 2008.
[138] Donoho D L, Denoising by soft-thresholding [J]. IEEE Trans. Information Theory., vol.41, no.3, pp. 613-627, 1995.
[139] Alexandru Kristaly, Hannelore Lisei, and Csaba Varga, Multiple solutions for p-laplacian type equations [J]. Nonlinear Analysis-Theory Methods & Applications, vol.68, no. 5, pp. 1375-1381, 2008.
[140] Junmei Zhong and Huifang Sun. Wavelet-based multiscale anisotropic diffusion with adaptive statistical analysis for image restoration [J]. IEEE Trans. Circuits and Systems-I: Regular Papets., 2008, 55 (9): 2716-2725.
[141]王大凯,候榆青,彭进业.图像处理的偏微分方程方法[M].科学出版社,2008
[142]张红英,数字破损图像的非线性各向异性扩散修补算法[J].计算机辅助设计与图形学学报,2006, 18(10:1541-1546
[143] Jean Luc Starck, Candes E J and Donoho D L, The curvelet transform for image denoising [J]. IEEE Trans. Image Process., 11 (6): 670-684, Jun. 2002.
[144] E. J. Candès and D. L. Donoho, New tight frames of curvelets and optimal representations of objects with piecewise singularities [J], Commun. Pure Appl. Math., 57(2): 219–266, 2004.
[145] E J Candès, L Demanet, D L Donoho, and L Ying, Fast discrete curvelet transforms [J]. Multiscale Model. Simul., 5 (3): 861–899, 2006.
[146] Easley G, Labate D and Lim WQ, Sparse directional image representations using the discrete shearlet transform [J], Applied and computational harmonic analysis, 25 (1): 25-46, 2008.
[147] Tan S, Jiao L C, Image denoising using the ridgelet biframe [J]. Journal of the optical society of America A-optics image science and vision, 23 (10): 2449-246, 2006.
[148] Do M N and Vetterli M, The finite ridgelet transform for image representation [J]. IEEE Trans. Image Process., 12 (1):16-28, Jun. 2003
[149] Fangfang Dong, Zhen Liu, Dexing Kong and Kefeng Liu, An improved LOT model for image restoration, [J]. J Math Imaging Vis., 34: 98-106, 2009.
[150] Marie-Flavie Auclair-Fortier and Djemel Zi, A global approach for solving evolutive heat transfer for image denoising and inpainting [J]. IEEE Trans. Image Process., 15(9) :260-268, Sep. 2006.
[151] Harry M. Salinas and Delia Cabrera Fernández, Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography [J]. IEEE Trans. Image Process., 26 (6): 761-771, Jun. 2007.
[152] Song Gao and Tien D Bui, Image segmentation and selective smoothing by using mumford–shah model [J]. IEEE Trans. Image Process., 14 (10): 1537-1549, Oct. 2005.
[153] Suk-Ho Lee and Jin Keun Seo, Noise removal with gauss curvature- driven diffusion [J]. IEEE Trans. Image Process., 14 (7): 904-909, Jul. 2005.
[154] Antoni Buades, Bartomeu Coll and Jean-Michel Morel, The staircasing effect in neighborhood filters and its solution [J]. IEEE Trans. Image Process., 15 (6): 1499-1505, Jun. 2006.
[155] Marquina and Osher S, Explicit algorithm for a new time dependent model based on level set moton for nonlinear deblurring and noise removal [J]. SIAM J. Sci. Comput., 22: 387-405, 2000.
[156] Jinjun Xu and Stanley Osher, Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising [J]. IEEE Trans. Image Process., 16 (2): 534-544, Feb. 2007
[157] E. J. Candès and F. Guo, New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction [J]. Signal Process., 82(11): 1519–1543, 2002.
[158] O. Scherzer, Scale space methods and regularization for denoising and inverse problems [J]. Adv. Imag. Electron. Phys., 128: 445–530,2003.
[159] Zeng Gengsheng L; Allred, Richard J, Partitioned image filtering for reduction of the Gibbs phenomenon [J]. J Nucl Med Technol., 37 (2) : 96-100, Jun. 2009
[160] R. R. Coifman and A. Sowa, Combining the calculus of variations and wavelets for image enhancement [J]. Appl. Comput. Harmon. Anal., 9: 1–18, 2000.
[161] S. Durand and J. Froment, Reconstruction of wavelet coefficients using total variation minimization [J]. SIAM J. Sci. Comput., 24:1754–1767, 2003.
[162] C. Vogel ,and M. Oman. Fast, Robust Total Variation-based Reconstruction of Noisy,Blurred Images [J]. IEEE Trans. Image Processing. 1998, 7 :pp. 813-824 .
[163] Glenn R. Easley, Demetrio Labate and Flavia Colonna,“Shearlet-based total variation diffusion for denoising [J]. IEEE Trans. Image Process.,18(2):260-268, Feb. 2009.
[164] Mila Nikolova. A Variational Approach to Remove Outliers and Impulse Noise [J]. Journal of Mathematical Imaging and Vision, 2004, 20, (1-2) :99~120.
[165] G Landi and E Loli Piccolomini, An algorithm for image denoising with automatic noise estimate [J]. J Math Imaging Vis.,34: 98-106, 2009.
[166] Fang Li , Chaomin Shen , Chunli Shen and Guixu Zhang, Variational denoising of partly textured images [J]. J. Vis. Commun. Image R.. 20 :293-300, 2009.
[167] G. Gilboa, Y. Y. Zeevi, and N. Sochen, Texture preserving variational denoising using an adaptive fidelity term [J]. in Proc. VLSM, Nice : 137–144. 2003.
[168] Marquina and Osher S, Explicit algorithm for a new time dependent model based on level set moton for nonlinear deblurring and noise removal [J]. SIAM J. Sci. Comput., vol. 22: 387-405, 2000.
[169] M. F. Auclair-Fortier and Djemel Ziou, A global approach for solving evolutive heat transfer for image denoising and inpainting [J]. IEEE Trans. Image Process., 15(9): 2258-2574, Sep. 2006.
[170] G. Plonka and J. Ma, Nonlinear regularized reaction-diffusion filters for denoising of images with textures [J]. IEEE Trans. Image Process., 17 (8): 1283-1294, Aug. 2008
[171] Gabor D. Information theory in electron microscopy [D]. Lab. Invest.1965, 14:801-807
[172] Jain A K. Partial diferential equations and finite-difference Methods in Image Processing [J]. part I: I mage representation. J. Optimiz. Theory and Applications.1977, 23:65-91
[173] Koenderink J J. The structure of images [D]. Biol, Cybern. 1984, 50 (5): 363-370
[174] Chan T F, Osher S and Shen J H. The digital TV filter and nonlinear denoising [J]. IEEE Transaction on Image Processing, 2001, 10 (2): 231-241.
[175] M Ceccarelli, V de Simone and A Murli. Well posed anisotropic diffusion for image d enoising [J]. IEEE Proceedings Vision Image and Signal Processing, 2002, 149 (4): 244-252.
[176] Perona P. and Malik J. Scale space and edge detection using anisotropic diffusion [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1990, 12 (7): 629-639
[177] CattéF, Lions P L. and Morel J M. et. al. Image selective smoothing and edge detection by nonlinear diffusion [J]. SIAM J. Numerical Analysis, 1992,29 (1): 182-193
[178] Chan T F, Zhou H M. Total variation improved wavelet thresholding in image compression. In: Proc Seventh International Conf on Image Processing [C]. 2000: 391-394.
[179] Osher S. and Rudin L I. Feature-oriented image enhancement using shock filters [J]. SIAM J. Numer. Anal. 1990, 27(4):919-940
[180] L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithm [D] Phys. D, vol. 60: 259–268, 1992.
[181]薛梅,邹采荣,杨娟,杨绿溪,一种空间自适应正则化图像盲复原算法[J].中国图象图形学报,2002,7 (4):356-362
[182]张航,罗大勇,图像盲复原算法研究现状及其展望[J].中国图象图形学报,2004,9 (10): 1145-11152
[183]曾三友,康立山,丁立新,黄元江,一种基于正则化方法的准最佳图像复原技术[J].软件学报,2003,14 (3): 689-696.
[184] YOU Y L, KAVEH M. Blind image restoration by anisotropic regularization [J]. IEEE Trans on Image Processing, 1999, 8 (3):396- 407.
[185] CHAN T F, WONG C K. Total variation blind deconvolution [J]. IEEE Transactions On Image Processing, 1998, 7 (3):370- 375.
[186] Dey N, Blanc-Féraud C, Zimmer C. A deconvolution method for con focal microscopy with total variation regularization [J]. IEEE Biomedical Imaging, 2004 (2): 1223-1226
[2] T. F. Chan and J. Shen, Mathematical models for local nontexture inpaintings [J]. SIAM J. Appl. Math., 62(3): 1019-1043, Feb.2002.
[3] G. Landi, A Truncated lgrange method for total variation-based image restoration [J]. J Math Imaging Vis., 28: 113-123, Jun.2007.
[4] Lianghai Jin, Dehua Li, and Enmin Song, Combining vector ordering and spatial information for color image interpolation [J]. Image and Vision Computing, vol.27: 410-416, 2009.
[5] Jean-Fran?ois Aujol, Some first-order algorithms for total Variation based image restoration [J]. J Math Imaging Vis., vol. 34: 307-327, 2009.
[6] Brendt Wohlberg and Paul Rodríguez, An iteratively reweighted norm algorithm for minimization of total variation functionals [J]. IEEE Signal Processing Letters, Vol. 14, No. 12: 948-951, Dec. 2007.
[7] Haoying Fu , Michael K. Ng , and Mila Nik Olova, On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization and sides [J]. SIAM J. Numer. Anal., 42(2): 686–713, 2004.
[8] Junmei Zhong and Huifang Sun, Wavelet-based multiscale anisotropic diffusion with adaptive statistical analysis for image restoration [J]. IEEE Trans. Circuits and Systems-I: Regular Papets., 55 (9): 2716-2725, Oct. 2008.
[9] Jinjun Xu and Stanley Osher, Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising [J]. IEEE Trans. Image Process., 16 (2): 534-544, Feb. 2007.
[10] Glenn R. Easley, Demetrio Labate, and Flavia Colonna, Shearlet- based total variation diffusion for denoising [J]. IEEE Trans. Image Process., 18 (2): 260-268, Feb. 2009.
[11] J. Ma and M. Fenn, Combined complex ridgelet shrinkage and total variation minimization [J]. SIAM J. Sci. Comput., 28 (3): 984-1000, 2006.
[12] Jianwei Ma and Gerlind Plonka, Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion [J]. IEEE Trans. Image Process., 16 (9): 2198-2206, Sep. 2009.
[13] C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro, and J. Verdera, Filling-in by joint interpolation of vector fields and gray levels [J]. IEEE Trans. Image Process., 10 (8): 1200–1211, Aug. 2001.
[14] G. Plonka and J. Ma, Nonlinear regularized reaction-diffusion filters for denoising of images with textures [J]. IEEE Trans. Image Process., 17 (8): 1283-1294, Aug. 2008.
[15] T. F. Chan and J. Shen, Non-texture inpainting by curvature-driven diffusions (CDD) [J]. J. Visual Communication Image Represent, 12 (4): 436-449, Dec. 2001.
[16] S. Rane, G. Sapiro and M. Bertalmio, Structure and texture filling-in of missing image blocks in wireless transmission and compression applications [J]. IEEE Trans. Image Proc., vol. 12(3): 296-303, Mar.2003.
[17] S. S. Hemami and R. M. Gray, Subband-coded Image Reconstruction for Lossy Packet Networks [J]. IEEE Trans. Image Proc., 6 (4): 523-539, Apr. 1997.
[18] S. Durand and J. Froment, Reconstruction of wavelet coefficients using total variation minimization [J]. SIAM J. Sci. Comput., 24(5): 1754-1767, 2003.
[19] E. J. Candès and F. Guo, New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction [J]. Signal Process., 82(11): 1519-1543, 2002.
[20] T. F. Chan, J. Shen, and H.-M. Zhou, Total variation wavelet inpainting [J]. J. Math. Imag Vis., 25(1): 107-125, Jul. 2006.
[21] Zhang H Y, Peng Q C and Wu Y D. Wavelet inpainting based on p- laplace operator [J]. Acta automatica sinica, 33 (5): 546-549, May. 2007.
[22] Marcelo Bertalmio, Strong continuation, contrast invariant inpainting with a third-order optimal PDE [J]. IEEE Trans. Image Process., 15 (7): 1934-1938, Sep. 2006.
[23] A. Bertozzi, S. Esedoglu, and A. Gillette, Inpainting of binary images using the Cahn–Hilliard equation[J]. IEEE Trans. Image Process., 16 (1):285-291, Jan. 2007.
[24] M. F. Auclair-Fortier and Djemel Ziou, A global approach for solving evolutive heat transfer for image denoising and inpainting [J]. IEEE Trans. Image Process., 15 (9): 2258-2574, Sep. 2006.
[25] Chan T F and Shen J H, Mathematical models for local nontexture inpainting [J]. SIAM Journal on Applied Mathematics, 62 (3): 1019-1043, 2001.
[26] M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, Simultaneous structure and texture image inpainting [J]. IEEE Trans. Image Process., 12 (8): 882-889, Aug. 2003.
[27] Julia A. Dobrosotskaya and Andrea L. Bertozzi, A wavelet-laplace variational technique for image deconvolution and inpainting [J]. IEEE Trans. Image Process., 17 (5): 657-663, May. 2008.
[28] M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, Simultaneous cartoon texture image inpaitning using morphological component analysis [J]. Appl. Comput. Harmon. Anal.,19:340-358, 2005.
[29] J. Sun, L. Yuan, J. Jia, and H.-Y. Shum,“Image completion with structure propagation [J].”in Proc. ACM SIGGRAPH, 2005: 861-868.
[30] J. Morlet, G. Arens, E. Fourgeau, D. Giard. Wave propagation and sampling theory-Part 1: Complex signal scattering in multilayered media [J]. Geophysics, 1982, 47 (2): 203-221.
[31] T Chan, C Wong. Convergence of the alternating minimization algorithm for blind deconvolution [J]. ELSEVIER, Linear Algebra and its Application, 2000,316 (3): 259-285.
[32] C A ZBareclos,Y Chen. Heat flows and related minimization problem in image restoration [J]. Computers and Mathematics with Applications, 2000, 39 (7):81-97.
[33] Ramesh Neelamani, Hyeokho Choi, Richard Baraniuk, Fourier-wavelet regularized deconvolution for III-coditioned systems [J]. IEEE Trans on Signal Prodessing, 2004, 52 (2): 418-433.
[34] Teboul S ,B Lance-Feraud L, Aubert G, Variatinal approach for edge-preserving regularization using coupled PEDS[J]. IEEE Trans on Signal Prodessing,1998, 7 (3): 387-397.
[35]张航,罗大庸.图像盲复原算法研究现状及其展望[J].中国图象图形学报,2004,10 (9): 1145-1152.
[36]罗林,王黎,程卫东等.天文图像多帧盲反卷积收敛性的增强方法[J].物理学报,2006, 55:6708-6714.
[37] J. Morlet, G. Arens, E. Fourgeau, D. Giard. Wave propagation and sampling theory-Part 2: Sampling theory and complex waves [J]. Geophysics, 1982, 47 (2): 222-236.
[38] A. Grossmann, J. Morlet. Decomposition of Hardy functions into square integrable wavelets of constant shape [J]. SIAM J. of Math. Anal., 1984, 15(4): 723-736.
[39] A. Grossmann, J. Morlet, T. Paul. Transforms associated to square integrable group representations - general results [J]. Math. Phys, 1985, 26(10): 2473-2479.
[40] Y. Meyer. Principe d’incertitude, bases hillbertiennes et al, gebrasd operateurs [D]. In Seminaire Bourbaki, Paris, 1986.
[41] Y. Meyer著,小波与算子[M].尤众译.北京:世界图书出版公司,1992.
[42] I. Daubechies. Orthonomal bases of compactly supported wavelets [D]. Comm. Pure Appl. Math, 1998, 41:909-996
[43] I. Daubechies. Ten Lectures on Wavelets [D]. CBMS Conference Series in Applied Mathematics, SIAM, Philadelphia, 1992
[44] A. Cohen, I. Daubechies and J. C. Feauveeau. Biorthogonal bases of compactly supported wavelets [D]. Commun. Pure Appl. Math., 1992.5, 45(5):485-560
[45] Ingrid Daubechies. Where Do Wavelets Come From, A Personal Point of View [J].Proceeding of the IEEE, 1996, 84(4):510-513.
[46] S. Mallat. A theory for multiresolution signal decomposition: the wavelet representation [J]. IEEE Trans. On PAMI, 1989.7, 11(7):674-693
[47] S. Mallat. A Wavelet Tour of Signal Processing [M].北京:机械工业出版社,2003.
[48] S. Mallat. An efficient image representation for multiscale analysis. Proc. of Mschine Vision Conference[C]. Lake Taho: 1987.
[49] S. Mallat. A Compact Multiresolution Representation: The Wavelet Model. Proc. IEEE Computer Society Workshop on Computer Vision[C]. Washington. D.C.: IEEE Computer Society Press, 1987.
[50] S. Mallat. Multiresolution Approximations and Wavelet Orthonormal Bases of L2(R)[J]. Trans. of the Amercian Math. Society, 1989, 315(1):69-87.
[51] S. Mallat. Multifrequency Channel Decompositions of Images and Wavelet Models [J]. IEEE Tran on acoustics speech and signal processing, 1989, 37(12):2091-2110.
[52] S. Mallat. Multiresolution Approximations and Wavelet Orthonormal Bases of L2(R) [J]. Trans. of the American Math. Society, 1989, 315(1):69-87.
[53]秦前清,杨宗凯编著.实用小波分析[M].西安:西安电子科技大学出版社,2002.
[54]杨福生著.小波变换的工程分析与应用[M].北京:科学出版社,2003.
[55]孙延奎编著.小波分析及其应用[M].北京:机械工业出版社,2005.
[56]程正兴,杨守志,冯晓霞著.小波分析的理论、算法、进展和应用[M].北京:国防工业出版社,2007.
[57]程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,2003.
[58]成礼智,郭汉伟.小波与离散变换理论及工程实践[M].北京:清华大学出版社,2005.
[59]冯象初,甘小冰,宋国乡编著.数值泛函与小波理论[M].西安:西安电子科技大学出版社,2003.
[60]崔锦泰著,程正兴译.小波分析导论[M].西安:西安交通大学出版社,1997.
[61]龙瑞麟著.高维小波分析[M].北京:世界图书出版公司,1995.
[62] E J. Candès. Harmonic analysis of neural networks [J]. Applied and Computational Harmonic Analysis, 1999, 6(2): 197-218.
[63] E J. Candès. Ridgelet: theory and applications [D]. Ph. D. dissertation. Stanford University, 1998.
[64] E J. Candès, D. L. Donoho. Ridgelet: a key to higher-dimensional intermittency? Technical report [Z]. Stanford University, 1999.
[65] D. L. Donoho. Orthonormal ridgelets and linear singularities [D]. Technical report, Stanford Univ ersity, 1998.
[66] D. L. Donoho. Ridge Functions and Orthonormal ridgelets[D]. Technical report, Stanford University, 1998.
[67] E J. Candès, D. L. Donoho. Curvelets-A surprisingly Effective Nonadaptive Representation for Objects with Edges [D]. Technical report, Stanford University, 1999.
[68] E J. Candès, D. L. Donoho. Curvelets. Technical Report [D]. Stanford University, 1999.
[69] D. L. Donoho, M. R. Ducan. Digital curvelet transform: strategy, implementation and experiments [D]. Technical report, Stanford University, 1999.
[70] E J. Candès, D. L. Donoho. Continuous curvelet transform: I. Resolution of the wavefront set [D]. Technical Report, Stanford University, 2002.
[71] E J. Candès, D. L. Donoho. Continuous curvelet transform: II. Discretization into frames [D]. Technical Report, Stanford University, 2002.
[72] E J. Candès, D. L. Donoho. DCTvUSFFT: Digital curvelet transforms via unequispaced fast fourirer transforms [D]. Technical Report, California Institute of technology, 2004.
[73] E J. Candès, D. L. Donoho. New Tight Frames of Curvelets and Optimal Representations of Objects with Piecewise C2 Singularities [C]. Communications on Pure and Applied Mathematics, 2003, 57(2): 219–266 .
[74] E J. Candès, L. Demant and D. L. Donoho. Fast discrete curvelet transforms, applied and computational mathematics [C], California Institute of technology, 2005: 1-43
[75] Bovike AC, M. Clark. Multichannel texture analysis using localized spatial filters[J]. IEEE, PAMI, 1990, 12(1): 55-72.
[76] M. N. DO, M. Vetterli. Contourlets. Beyond wavelets [C]. New York: Academic Press, 2002: 1-27.
[77] M. N. DO, M. Vetterli. Contourlet: A directional multiresolution image representation [C]. Proc of IEEE International Conference on Image Processing, 2002: 357-360.
[78] M. N. DO, M. Vetterli. The contourlet ransform: An efficient directional multiresolution image representation [J]. IEEE Transactions on Image Processing, 2003, 14(12): 2091-2106.
[79] L. D. Cunha, J. P Zhou and M. N. Do. The Nonsubsampled Contourlet Transform: Theory, Design, and Applications [M]. IEEE Transactions on Image Processing, October 2006, 15(10): 3089-3101.
[80] R. Eslami, H. Radha. Wavelet-based contourlet transform and its application to image coding [C]. International conference on image processing, 2004, 5: 3189-3192.
[81] R. Eslami, H. Radha. Wavelet-based contourlet coding using an SPIHT-like algorithm. In proc of conference on information science and systems [C], Princeton, 2004: 784-788.
[82] R. Eslami, H. Radha. Wavelet-based contourlet transform and its application to image coding[J]. IEEE International Conference on Image Processing, Singapore, Oct. 2004.
[83] P. E. Le, S. Mallat. Sparse geometric image representations with bandelets [J]. IEEE Trans on Image Processing, 2005, 14(4): 423-438.
[84] P. E. Le, S. Mallat. Image compression with geometrical wavelets [J]. IEEEE International Conference on Image Processing, 2000, 1: 661-664.
[85] E. Le, S. Mallat. Bandelet image approximation and compression. Multiscale Model [D]. Simulation, 2005, 4(3): 992-1039.
[86] PG. Oeyre, S. Mallat. Discrete bandelets with geometric orthogonal filters [C]. IEEE International Conference in Image Processing, Genova, 2005, 1: 65-68.
[87] G. Oeyre, S. Mallat. Surface compression with geometric bandelets [J]. ACM Transactions on Graphics, 2005, 24(3): 601-608.
[88] Y. Lu, M. N. Do. Multidimensional directional filter banks and surfacelets [J]. IEEE Transactions on Image Processing, 2007, 16(4): 918-931.
[89] D. L. Donoho, X. Huo. Beamlets and multiscale image analysis, multiscale and multiresolutiop methods [D]. Springer Lecture Notes in Computational Science and Engineering, 2002, 20: 149-196.
[90] D. L. Donoho, O. Levi, J. L. Starch, et al. Multiscale geometric analysis for 3-D catalogues [D]. Astronomical Data Analysis II. Processing of SPIE, Hawaii, 2002, 4847: 101-111.
[91] J. Chen, X. Huo. Beamlet coder: a tree-based, hierarchical contour representation and coding method [C]. International Conference on Acoustic Speech and Signal Processing, ICASSP, Orland, 2002.
[92] D. L. Donoho. Wedgelets: nearly minimax estimation of edges [C]. Ann. Statist, 1999, 27: 859-897.
[93] V. Velisavljevic, B. beferull-Lozano, M. Vetterli, et al. Directionlets: Anisotropic Multidirectional Representation with Separable Filtering [J]. IEEE Trans on Image processing, 2006, 15(7): 1916-1933.
[94] V. Velisavljevic. Directionlets: anisotropic multidirectional representation with separable filtering [D]. Ph. D. Thesis. School of Computer and Communication Sciences, Lausanne, Switzland, Oct, 2005.
[95] F. G. Meyer, R. R. Coifman. Brushlets. A tool for directional image analysis and image compression [J]. Applied and Computational Harmonic Analysis, 1997, 6(4): 147-187.
[96] F. G. Meyer, R. R. Coifman. Directional image compression with brushlets [C]. Proceeding of the IEEE-SP International Symposium, 1996, 189-192.
[97] K. Guo, D. Labate. Optimally Sparse Multidimensional Representation Using Shearlets [J].SIAM J Math. Anal, 2007, 39: 298-318.
[98] G. Easley, D. Labate. Sparse directional image representations using the discrete shearlet transform [J]. Applied and Computational Harmonic Analysis, 2008, 25: 25-46.
[99] K. Guo, D. Labate, Sparse Shearlet Representation of Fourier Integral Operators [D]. Electr. Res. Announc, 2007, 14: 7-19.
[100] G. Kutyniok, D. Labate. The Construction of Regular and Irregular Shearlet Frames [J]. Wavelet Theory and Application, 2007, 1: 1-10.
[101] Cunha A L, Zhou J and Do M N.“The non-subsampled contourlet transform: theory, design and applications [J],”IEEE Trans. Image Process., vol.15, no.10, pp. 3089-3101, Aug. 2006.
[102]焦李成,谭山.图像的多尺度几何分析回顾和展望[J],电子学报,2003,31 (12A): 1975- 1981
[103] Mink N Do and Martin Vetterli. The finite ridgelet transform for image representation[J]. IEEE Transactions on Image Processing, 2002,1 (12): 16-28.
[104] Do M N and Vetterli M. Contourlets:a directional multi-resolution image representation[A]. IEEE International Conference on Image Processing[C]. Rochester, NY:IEEE, 2002:357-36.
[105] Ramin Eslami and Hayder Radha, Translation-invariant contourlet tansform and its application to image denoising [J]. IEEE Tansactions on Image Processing, 2006, 15( 11): 3362-3374.
[106] Bei-bei Li, Xin Li and Shu-xun Wang, A multiscale and multidirectional image denoising algorithm based on contourlet transform [A]. IEEE Proceedings of the 2006 International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP'06) [C].
[107] Duncan D. Po and Minh N. Do, Directional multiscale modeling of images using the contourlet transform [J]. IEEE Tansactions on Image Processing, 2006,15 ( 6):1610-1620
[108] Minh N. Do and Martin Vetterli, The contourlet transform: an efficient directional multiresolution image Representation [J]. IEEE Tansactions on Image Processing, 2005, 14(12): 2091-2106.
[109] Eslami R and RadhaH. Wavelet based contourlet transform and it’s application to image coding [C]. IEEE International Conference on Image Processing.Singapore, 2004: 3189- 3192.
[110] Donoho D L. De-noising by soft-thresholding [J]. IEEE Trans.on Information Theory. 1995, 41: 613-62
[111] Bin Yang, Shutao Li and Fengmei Sun, Image fusion using nonsubsampled contourlet transform [C]. Fourth International Conference on Image and Graphics . 2007: 719-724.
[112] Lei Tang, Feng Zhao and Zong-gui Zhao, The nonsubsampled contourlet transform for image fusion [A]. Proceedings of the 2007 International Conference on Wavelet Analysis and Pattern Recognition. Beijing, China, 2007:305-310.
[113] Weyrich N and Warhola G T. Wavelet shrinkage and generalized crossvalidation for image denoising [J]. IEEE Trans. Image Proc. 1998, 7(1): 82-90.
[114] Chang S G, Yu B and Vetterli M. Adaptive wavelet threshoding for image denoising and compression [J]. IEEE Trans. Image Proc. 2000, 9(9):1532-1546.
[115]梁栋,沈敏,高清维等.一种基于Contourlet递归cycle spinning的图像降噪方法[J].电子学报,2005,33(11): 2044-2046
[116]郁梅,易文娟,蒋刚毅.基于Contourlet变换尺度间相关的图像降噪[J].光电工程,2006,35(6):73-77.
[117]查宇飞,毕笃彦.基于小波变换的自适应多阈值图像降噪[J].中国图象图形学报,2005, 10(5): 567-570.
[118]邓承志,曹汉强,汪胜前.非高斯双变量模型图像降噪[J].红外与激光工程,2006,35(2):234-237.
[119]张绘,张弓,郭琦南.基于域结构的图像相干斑抑制算法[J].南京航空航天大学学报,2006,38(6):743-748.
[120]易文娟,郁梅,蒋刚毅.一种有效的方向多尺度变换分析方法[J].计算机应用研究,2006,23(9):18-22.
[121]喻汉龙,余胜生,周敬利等.一种基于改进的Contourlet变换的图像压缩算法[J].计算机工程与应用,2005,41(14):40-43.
[122]倪伟,郭宝龙,杨锣.图像多尺度儿何分析新进展[J].计算机科学,2006,33(2):234-236.
[123]李光鑫,王坷.基于Contourlet变换的彩色图像融合算法[J].电子学报,2007,35(1):112-117.
[124]陈蜜,李德仁,秦前清等.基于Contourlet变换的遥感影像融合算法[J].小型微型计算机系统,2006,27(11):2052-2055.
[125]沙宇恒,丛琳,孙强等.基于Contourlet域模型的多尺度图像分割[J].红外与毫米波学报,2005,34(12):472-476.
[126]蔡超,丁明跃,周成平等.小波域中的双边滤波[J].电子学报,2004,32(1):128-131.
[127]郭旭静,王祖林.基于尺度间相关的非下采样Contourlet图像降噪算法[J].光电子.激光, 2007, 18(9): 1116~1119.
[128]闫敬文,屈小波.超小波分析及应用[M].北京:国防工业出版社, 2008.
[129]贾建,焦李成,项海林.基于双变量阈值的非下采样Contourlet变换图像降噪[J].电子与信息学报, 2009, 31(3): 532-536.
[130]贾建,焦李成.利用方向特性实现非下采样Contourlet变换阈值降噪[J].西安电子科技大学学报, 2009, 36 (2): 269-273.
[131]贾建,焦李成,魏玲.基于概率模型的非下采样Contourlet变换图像降噪[J].西北大学学报(自然科学版), 2009, 39 (1): 13-18.
[132]边策,钟桦,焦李成.基于非下采样Contourlet变换和双变量模型的图像降噪[J].电子与信息学报, 2009, 31 (3): 561-565.
[133]陈志刚,尹福昌.基于Contourlet变换的遥感图像增强算法[J].光学精密工程, 2008, 16 (10): 2030-2037.
[134]焦李成,谭山.图像的多尺度几何分析:回顾与展望[J].电子学报, 2003, 31(12A):1975-1981.
[135]焦李成,侯彪,王爽等.多尺度几何分析理论与应用[M].西安:西安电子科技大学出版社, 2008.
[136] Firoiu I, Nafornita C, Boucher J M, and Isar A, Image denoising using a new implementation of the hyperanalytic wavelet transform [J]. IEEE Trans. Image Process., vol.58, no.8, pp. 2410-2416, Aug. 2009.
[137] Mark Miller and Nick Kingsbury, Image denoising using derotated complex wavelet coefficients [J], IEEE Trans. Image Process., vol.17, no.9, pp. 1500-1511, Sep. 2008.
[138] Donoho D L, Denoising by soft-thresholding [J]. IEEE Trans. Information Theory., vol.41, no.3, pp. 613-627, 1995.
[139] Alexandru Kristaly, Hannelore Lisei, and Csaba Varga, Multiple solutions for p-laplacian type equations [J]. Nonlinear Analysis-Theory Methods & Applications, vol.68, no. 5, pp. 1375-1381, 2008.
[140] Junmei Zhong and Huifang Sun. Wavelet-based multiscale anisotropic diffusion with adaptive statistical analysis for image restoration [J]. IEEE Trans. Circuits and Systems-I: Regular Papets., 2008, 55 (9): 2716-2725.
[141]王大凯,候榆青,彭进业.图像处理的偏微分方程方法[M].科学出版社,2008
[142]张红英,数字破损图像的非线性各向异性扩散修补算法[J].计算机辅助设计与图形学学报,2006, 18(10:1541-1546
[143] Jean Luc Starck, Candes E J and Donoho D L, The curvelet transform for image denoising [J]. IEEE Trans. Image Process., 11 (6): 670-684, Jun. 2002.
[144] E. J. Candès and D. L. Donoho, New tight frames of curvelets and optimal representations of objects with piecewise singularities [J], Commun. Pure Appl. Math., 57(2): 219–266, 2004.
[145] E J Candès, L Demanet, D L Donoho, and L Ying, Fast discrete curvelet transforms [J]. Multiscale Model. Simul., 5 (3): 861–899, 2006.
[146] Easley G, Labate D and Lim WQ, Sparse directional image representations using the discrete shearlet transform [J], Applied and computational harmonic analysis, 25 (1): 25-46, 2008.
[147] Tan S, Jiao L C, Image denoising using the ridgelet biframe [J]. Journal of the optical society of America A-optics image science and vision, 23 (10): 2449-246, 2006.
[148] Do M N and Vetterli M, The finite ridgelet transform for image representation [J]. IEEE Trans. Image Process., 12 (1):16-28, Jun. 2003
[149] Fangfang Dong, Zhen Liu, Dexing Kong and Kefeng Liu, An improved LOT model for image restoration, [J]. J Math Imaging Vis., 34: 98-106, 2009.
[150] Marie-Flavie Auclair-Fortier and Djemel Zi, A global approach for solving evolutive heat transfer for image denoising and inpainting [J]. IEEE Trans. Image Process., 15(9) :260-268, Sep. 2006.
[151] Harry M. Salinas and Delia Cabrera Fernández, Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography [J]. IEEE Trans. Image Process., 26 (6): 761-771, Jun. 2007.
[152] Song Gao and Tien D Bui, Image segmentation and selective smoothing by using mumford–shah model [J]. IEEE Trans. Image Process., 14 (10): 1537-1549, Oct. 2005.
[153] Suk-Ho Lee and Jin Keun Seo, Noise removal with gauss curvature- driven diffusion [J]. IEEE Trans. Image Process., 14 (7): 904-909, Jul. 2005.
[154] Antoni Buades, Bartomeu Coll and Jean-Michel Morel, The staircasing effect in neighborhood filters and its solution [J]. IEEE Trans. Image Process., 15 (6): 1499-1505, Jun. 2006.
[155] Marquina and Osher S, Explicit algorithm for a new time dependent model based on level set moton for nonlinear deblurring and noise removal [J]. SIAM J. Sci. Comput., 22: 387-405, 2000.
[156] Jinjun Xu and Stanley Osher, Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising [J]. IEEE Trans. Image Process., 16 (2): 534-544, Feb. 2007
[157] E. J. Candès and F. Guo, New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction [J]. Signal Process., 82(11): 1519–1543, 2002.
[158] O. Scherzer, Scale space methods and regularization for denoising and inverse problems [J]. Adv. Imag. Electron. Phys., 128: 445–530,2003.
[159] Zeng Gengsheng L; Allred, Richard J, Partitioned image filtering for reduction of the Gibbs phenomenon [J]. J Nucl Med Technol., 37 (2) : 96-100, Jun. 2009
[160] R. R. Coifman and A. Sowa, Combining the calculus of variations and wavelets for image enhancement [J]. Appl. Comput. Harmon. Anal., 9: 1–18, 2000.
[161] S. Durand and J. Froment, Reconstruction of wavelet coefficients using total variation minimization [J]. SIAM J. Sci. Comput., 24:1754–1767, 2003.
[162] C. Vogel ,and M. Oman. Fast, Robust Total Variation-based Reconstruction of Noisy,Blurred Images [J]. IEEE Trans. Image Processing. 1998, 7 :pp. 813-824 .
[163] Glenn R. Easley, Demetrio Labate and Flavia Colonna,“Shearlet-based total variation diffusion for denoising [J]. IEEE Trans. Image Process.,18(2):260-268, Feb. 2009.
[164] Mila Nikolova. A Variational Approach to Remove Outliers and Impulse Noise [J]. Journal of Mathematical Imaging and Vision, 2004, 20, (1-2) :99~120.
[165] G Landi and E Loli Piccolomini, An algorithm for image denoising with automatic noise estimate [J]. J Math Imaging Vis.,34: 98-106, 2009.
[166] Fang Li , Chaomin Shen , Chunli Shen and Guixu Zhang, Variational denoising of partly textured images [J]. J. Vis. Commun. Image R.. 20 :293-300, 2009.
[167] G. Gilboa, Y. Y. Zeevi, and N. Sochen, Texture preserving variational denoising using an adaptive fidelity term [J]. in Proc. VLSM, Nice : 137–144. 2003.
[168] Marquina and Osher S, Explicit algorithm for a new time dependent model based on level set moton for nonlinear deblurring and noise removal [J]. SIAM J. Sci. Comput., vol. 22: 387-405, 2000.
[169] M. F. Auclair-Fortier and Djemel Ziou, A global approach for solving evolutive heat transfer for image denoising and inpainting [J]. IEEE Trans. Image Process., 15(9): 2258-2574, Sep. 2006.
[170] G. Plonka and J. Ma, Nonlinear regularized reaction-diffusion filters for denoising of images with textures [J]. IEEE Trans. Image Process., 17 (8): 1283-1294, Aug. 2008
[171] Gabor D. Information theory in electron microscopy [D]. Lab. Invest.1965, 14:801-807
[172] Jain A K. Partial diferential equations and finite-difference Methods in Image Processing [J]. part I: I mage representation. J. Optimiz. Theory and Applications.1977, 23:65-91
[173] Koenderink J J. The structure of images [D]. Biol, Cybern. 1984, 50 (5): 363-370
[174] Chan T F, Osher S and Shen J H. The digital TV filter and nonlinear denoising [J]. IEEE Transaction on Image Processing, 2001, 10 (2): 231-241.
[175] M Ceccarelli, V de Simone and A Murli. Well posed anisotropic diffusion for image d enoising [J]. IEEE Proceedings Vision Image and Signal Processing, 2002, 149 (4): 244-252.
[176] Perona P. and Malik J. Scale space and edge detection using anisotropic diffusion [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1990, 12 (7): 629-639
[177] CattéF, Lions P L. and Morel J M. et. al. Image selective smoothing and edge detection by nonlinear diffusion [J]. SIAM J. Numerical Analysis, 1992,29 (1): 182-193
[178] Chan T F, Zhou H M. Total variation improved wavelet thresholding in image compression. In: Proc Seventh International Conf on Image Processing [C]. 2000: 391-394.
[179] Osher S. and Rudin L I. Feature-oriented image enhancement using shock filters [J]. SIAM J. Numer. Anal. 1990, 27(4):919-940
[180] L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithm [D] Phys. D, vol. 60: 259–268, 1992.
[181]薛梅,邹采荣,杨娟,杨绿溪,一种空间自适应正则化图像盲复原算法[J].中国图象图形学报,2002,7 (4):356-362
[182]张航,罗大勇,图像盲复原算法研究现状及其展望[J].中国图象图形学报,2004,9 (10): 1145-11152
[183]曾三友,康立山,丁立新,黄元江,一种基于正则化方法的准最佳图像复原技术[J].软件学报,2003,14 (3): 689-696.
[184] YOU Y L, KAVEH M. Blind image restoration by anisotropic regularization [J]. IEEE Trans on Image Processing, 1999, 8 (3):396- 407.
[185] CHAN T F, WONG C K. Total variation blind deconvolution [J]. IEEE Transactions On Image Processing, 1998, 7 (3):370- 375.
[186] Dey N, Blanc-Féraud C, Zimmer C. A deconvolution method for con focal microscopy with total variation regularization [J]. IEEE Biomedical Imaging, 2004 (2): 1223-1226