基于稀疏表示模型的图像复原技术研究
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摘要
随着信息技术的蓬勃发展，社交网络和移动互联网的全面兴起，以及大数据时代的汹涌来袭，数字化的多媒体技术已经无处不在，在人类社会的各个领域都得到了广泛的应用。图像/视频等视觉信号已经成为数字多媒体内容的主要载体。数字图像的质量可以说在人们进行交流通信和视觉感知的过程中起着至关重要的作用。在数字图像的采集、存储、传输和处理过程中，由于拍摄设备及人为操作不当等诸多因素不可避免使得最终获得的图像失真，或称为图像退化，从而影响图像质量。因此，利用退化图像对原始真实图像进行重建的图像复原技术，一直以来都是数字图像处理领域里的研究热点,对其具有十分重要的理论和现实意义。目前，图像复原已经演变成图像处理、计算机视觉和计算成像三者之间的一个交叉领域。由于图像在退化过程中丢失了信息，图像复原逆问题通常具有病态特性。图像的先验模型在图像复原问题中起着重要作用。利用自然图像的先验模型可以对真实解空间进行正则化约束，从而将具有不适定性的图像复原病态问题转换为适定问题，获得符合人眼视觉特性的稳定解。本文以图像稀疏表示先验模型为出发点，重点针对图像修补、图像去模糊、图像噪声去除、图像超分辨率以及图像压缩感知重建五个图像复原问题展开深入的研究。具体研究内容分为以下四个部分：
第一，提出了一种基于空间-变换域上联合稀疏统计模型的图像复原算法。传统的基于图像先验模型正则化图像复原算法存在着两个缺陷。一方面，通常是只利用一个图像的先验特性，不能得到令人满意的复原效果；另一方面，在刻画图像的非局部自相似性时大多数都是利用一种加权的方式，没能够充分利用这一特性。针对以上问题，本文从图像统计的角度出发，分别在图像二维空间域上建立了刻画图像局部平滑特性的像素级稀疏统计模型和在图像三维变换域上建立了刻画图像非局部自相似特性的图像块级稀疏统计模型，并将以上两种稀疏统计模型合并，构成了一个混合空间-变换域上能够同时刻画图像局部平滑特性和非局部自相似性的联合稀疏统计模型。将联合稀疏统计模型嵌入正则化框架中，提出了一个新颖的求解一般图像复原逆问题的目标函数。通过图像修补、图像去模糊和图像混合高斯和脉冲噪声去除三种应用验证了提出算法的有效性、鲁棒性和收敛性。
第二，提出了一种基于图像结构组稀疏表示模型的图像复原算法。传统的基于自然图像块的稀疏表示通常面临两个问题。一是在字典学习的过程中需要求解一个具有非常高计算复杂度的大规模优化问题；二是在稀疏编码和字典的学习过程中，每一个图像块都是独立考虑，忽略了块与块之间的相关性，从而导致了稀疏编码系数不够准确。为了解决以上两个问题，本文打破了传统的基于图像块为图像稀疏表示基本单位的束缚，提出了一个新颖的以结构组为像稀疏表示基本单位的图像结构组稀疏表示模型。图像结构组是由具有相似结构的图像块组合，从而在对图像结构组进行稀疏表示的过程中能够显式地在一个统一的框架下同时刻画自然图像固有的局部稀疏性和非局部自相似性。在正则化框架下，提出一个新颖的具有一般性的求解图像复原逆问题的基于图像结构组稀疏表示模型的L0范数目标函数，并且对于每一个结构组，设计了一个高效且低复杂度的自适应稀疏表示字典。在图像修补、图像去模糊和图像压缩感知重建三个应用中，实验结果表明提出的基于结构组稀疏表示模型的图像复原技术取得较目前许多主流算法更好的性能。
第三，提出了一种基于L0范数自适应学习稀疏基的图像压缩感知重建算法。目前存在的压缩感知重建算法中大都采用固定的基函数，也就是在确定的域中对信号进行分解，比如：DCT域、小波域和梯度域，但这些域都忽略了自然信号的非平稳特性，缺乏自适应能力，从而不能够将图像分解得足够稀疏，也就使得压缩感知重建的效果很差，限制了压缩感知在图像方面的应用。针对以上问题，本文将刻画整幅自然图像稀疏性的基于块的冗余稀疏表示模型引入到图像压缩感知重建问题中，提出了基于L0范数自适应学习稀疏基的图像压缩感知重建框架。在此框架中，基于L0范数自适应学习稀疏基的作用是能够获得更好的自适应性和更高的稀疏度，进而极大缩小压缩感知解空间，得到稳定解；而基于块的冗余稀疏表示模型作用则是能够减少重建图像的块效应，获得更高质量的视觉重建效果。实验结果证明提出的方法取得了较目前主流算法相当甚至更好的性能。
第四，提出了一种基于双重字典学习和稀疏表示的图像超分辨率算法。传统基于字典学习和稀疏表示的图像超分辨率算法存在高、低分辨率图像具有较大频谱差异的问题，从而造成在图像超分辨率过程中损失很多高频信息。针对以上问题，本文提出将需要重建的图像高频信息分解为主要高频信息和残差高频信息两部分。对于以上两种类型的高频信息，利用训练图像基于稀疏表示模型分别逐次设计训练出双重字典，即第一重主要字典和第二重残差字典。在图像超分辨率过程中，采用渐进式的方式运用双重字典和稀疏表示进行高分辨率图像重建。实验结果表明提出的算法能够缩小高、低分辨率图像的频谱差异，获得更丰富的图像细节和更高质量的高分辨率图像。
With the rapid development of information technology, mobile internet, solocial network, and the boom of Big Data, digitized media technology has been found everywhere and been widely applied in various fields of human society. Image and Video are becoming the main carriers of visual signals for digital multimedia content. The quality of digtal images plays a significant role in the process of visual perception and communication. The degradations of digital im-ages are inevitablly caused by many factors during the period of image acquisi-tion, storage, transmission and processing. Therefore, image restoration technol-ogy, which infers the recovery of the original image from the observed degraded version, has been a hot and basic topic in the field of image processing. The re-search of image restoration has a theoretical and practical significance. Nowa-days, image restoration has evolved into an energetic field at the intersection of image processing, computer vision, and computational imaging. Due to the in-formation loss in the process of image degradation, image restoration as an in-verse linear problem is usually ill-posed. The prior models of natural images have important impact for solving the problems of image restoration. The utiliza-tion of natural image prior models is able to constrain the solution space, and enable the inverse problem well-posed, achieving the restored images that are coincident with the characteristics of human visual perception. In this thesis, based on the sparse representation prior modeling of natural images, we mainly focus on the research topics on five image restoration problems: image inpainting, image deblurring, image noise removal, image super-resolution, and image com-pressive sensing recovery. The contents of the thesis can be divided into four sections that are detailed as follows.
First, a novel image restoration algorithm based on a joint sparse statistical modeling in space-transform domain is proposed. Traditional image prior models regularized image restoration algorithms usually have two shortcomings. On one hand, only one image property used in regularization-based framework is not enough to obtain satisfying restoration results. On the other hand, the image property of nonlocal self-similarity should be characterized by a more powerful manner, rather than by the traditional weighted graph. To rectify the above prob-lems, from the perspective of image statistics, we first establish two sparse statis-tical models by characterizing image local smoothness in two-dimensional space domain at pixel level, and image nonlocal self-similarity in three-dimensional transform domain at patch level, respectively, and then merge the two models into a novel joint sparse statistical modeling in hybrid space-transform domain, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Under the regularization-based framework, a new form of minimization func-tional for solving image inverse problem using the joint sparse statistical model-ing is formulated, which is accompanied by an effective choice for the corre-sponding regularization parameters. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal appli-cations verify the effectiveness of the proposed algorithm.
Second, a novel image restoration algorithm based on structural group sparse representation (SGSR) is proposed. Traditional patch-based sparse repre-sentation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational com-plexity in dictionary learning. Second, each patch is considered independently in dictionary learning and sparse coding, which ignores the relationship among patches, resulting in inaccurate sparse coding coefficients. To rectify the above problems, instead of using patch as the basic unit of sparse representation, this thesis exploits the concept of structural group as the basic unit of sparse repre-sentation, which is composed of nonlocal patches with similar structures, and es-tablishs a novel sparse representation modeling of natural images, called struc-tural group sparse representation (SGSR). The proposed SGSR is able to sparsely represent natural images in the domain of structural group, which enforces the intrinsic local sparsity and nonlocal self-similarity of images simultaneously in a unified framework. Under the regularization-based framework, a new form of minimization functional for solving image inverse problem via SGSR in the form of L0norm is formulated, associated with an effective self-adaptive dictionary learning method for each structural group with low complexity. Extensive ex- periments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed SGSR modeling outperforms many current state-of-the-art schemes in both PSNR and visual perception.
Third, a new algorithm for image compressive sensing recovery using adap-tively learned sparsifying basis via L0minimization is proposed. Most of the conventional CS recovery approaches exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are irrespective of the non-stationarity of natural signals and cannot achieve high enough degree of sparsity, thus resulting in poor CS recovery performance and restricting the CS application in natural images. This thesis introduces the patch-based redundant sparse representation model that is used to characterize the intrinsic sparsity of the whole image into the problem of image compressive sensing recovery, and develops a framework for image compressive sensing recovery using the adap-tively learned sparsifying basis in the form of L0norm. The role of the adaptive learned sparsifying basis in the form of L0is to achieve high enough degree of adaptability and sparsity, thus greatly confining the CS solution. The role of the patch-based redundant sparse representation model is to reduce blocking artifacts and obtain the CS results with high visual quality. Experimental results on a wide range of natural images for CS recovery have shown that the proposed algorithm achieves significant performance improvements over many current state-of-the-art schemes.
Fourth, a novel image super-resolution algorithm via dual-dictionary learn-ing and sparse representation is proposed. Aiming at reducing the large gap of the frequency in the low and high resolution images exhibited in the traditional dictionary learning and sparse representation based image super-resolution methods and recovering more image high-frequency information, in this thesis, the high-frequency (HF) to be estimated in super-solution is considered as a combination of two components: main high-frequency (MHF) and residual high-frequency (RHF). As for above two types of high-frequency, two corre-sponding dictionaries are successively learned by making use of training images via sparse representation, i.e., the main dictionary and the residual dictionary. In the process of image super-resolution, the input low resolution image is first magnified and added the reconstructed main high-frequency information by vir- tue of the main dictionary, thus generating a temporary image. Then, by pre-forming the same reconstruction scheme with the temporary image and the re-sidual dictionary, the reconstructed residual high-frequency information is recon-structed, leading to the final high-resolution image. Extensive experimental re-sults on test images validate that by employing the proposed two-layer progres-sive scheme, more image details can be recovered and much better results can be achieved.
第一，提出了一种基于空间-变换域上联合稀疏统计模型的图像复原算法。传统的基于图像先验模型正则化图像复原算法存在着两个缺陷。一方面，通常是只利用一个图像的先验特性，不能得到令人满意的复原效果；另一方面，在刻画图像的非局部自相似性时大多数都是利用一种加权的方式，没能够充分利用这一特性。针对以上问题，本文从图像统计的角度出发，分别在图像二维空间域上建立了刻画图像局部平滑特性的像素级稀疏统计模型和在图像三维变换域上建立了刻画图像非局部自相似特性的图像块级稀疏统计模型，并将以上两种稀疏统计模型合并，构成了一个混合空间-变换域上能够同时刻画图像局部平滑特性和非局部自相似性的联合稀疏统计模型。将联合稀疏统计模型嵌入正则化框架中，提出了一个新颖的求解一般图像复原逆问题的目标函数。通过图像修补、图像去模糊和图像混合高斯和脉冲噪声去除三种应用验证了提出算法的有效性、鲁棒性和收敛性。
第二，提出了一种基于图像结构组稀疏表示模型的图像复原算法。传统的基于自然图像块的稀疏表示通常面临两个问题。一是在字典学习的过程中需要求解一个具有非常高计算复杂度的大规模优化问题；二是在稀疏编码和字典的学习过程中，每一个图像块都是独立考虑，忽略了块与块之间的相关性，从而导致了稀疏编码系数不够准确。为了解决以上两个问题，本文打破了传统的基于图像块为图像稀疏表示基本单位的束缚，提出了一个新颖的以结构组为像稀疏表示基本单位的图像结构组稀疏表示模型。图像结构组是由具有相似结构的图像块组合，从而在对图像结构组进行稀疏表示的过程中能够显式地在一个统一的框架下同时刻画自然图像固有的局部稀疏性和非局部自相似性。在正则化框架下，提出一个新颖的具有一般性的求解图像复原逆问题的基于图像结构组稀疏表示模型的L0范数目标函数，并且对于每一个结构组，设计了一个高效且低复杂度的自适应稀疏表示字典。在图像修补、图像去模糊和图像压缩感知重建三个应用中，实验结果表明提出的基于结构组稀疏表示模型的图像复原技术取得较目前许多主流算法更好的性能。
第三，提出了一种基于L0范数自适应学习稀疏基的图像压缩感知重建算法。目前存在的压缩感知重建算法中大都采用固定的基函数，也就是在确定的域中对信号进行分解，比如：DCT域、小波域和梯度域，但这些域都忽略了自然信号的非平稳特性，缺乏自适应能力，从而不能够将图像分解得足够稀疏，也就使得压缩感知重建的效果很差，限制了压缩感知在图像方面的应用。针对以上问题，本文将刻画整幅自然图像稀疏性的基于块的冗余稀疏表示模型引入到图像压缩感知重建问题中，提出了基于L0范数自适应学习稀疏基的图像压缩感知重建框架。在此框架中，基于L0范数自适应学习稀疏基的作用是能够获得更好的自适应性和更高的稀疏度，进而极大缩小压缩感知解空间，得到稳定解；而基于块的冗余稀疏表示模型作用则是能够减少重建图像的块效应，获得更高质量的视觉重建效果。实验结果证明提出的方法取得了较目前主流算法相当甚至更好的性能。
第四，提出了一种基于双重字典学习和稀疏表示的图像超分辨率算法。传统基于字典学习和稀疏表示的图像超分辨率算法存在高、低分辨率图像具有较大频谱差异的问题，从而造成在图像超分辨率过程中损失很多高频信息。针对以上问题，本文提出将需要重建的图像高频信息分解为主要高频信息和残差高频信息两部分。对于以上两种类型的高频信息，利用训练图像基于稀疏表示模型分别逐次设计训练出双重字典，即第一重主要字典和第二重残差字典。在图像超分辨率过程中，采用渐进式的方式运用双重字典和稀疏表示进行高分辨率图像重建。实验结果表明提出的算法能够缩小高、低分辨率图像的频谱差异，获得更丰富的图像细节和更高质量的高分辨率图像。
With the rapid development of information technology, mobile internet, solocial network, and the boom of Big Data, digitized media technology has been found everywhere and been widely applied in various fields of human society. Image and Video are becoming the main carriers of visual signals for digital multimedia content. The quality of digtal images plays a significant role in the process of visual perception and communication. The degradations of digital im-ages are inevitablly caused by many factors during the period of image acquisi-tion, storage, transmission and processing. Therefore, image restoration technol-ogy, which infers the recovery of the original image from the observed degraded version, has been a hot and basic topic in the field of image processing. The re-search of image restoration has a theoretical and practical significance. Nowa-days, image restoration has evolved into an energetic field at the intersection of image processing, computer vision, and computational imaging. Due to the in-formation loss in the process of image degradation, image restoration as an in-verse linear problem is usually ill-posed. The prior models of natural images have important impact for solving the problems of image restoration. The utiliza-tion of natural image prior models is able to constrain the solution space, and enable the inverse problem well-posed, achieving the restored images that are coincident with the characteristics of human visual perception. In this thesis, based on the sparse representation prior modeling of natural images, we mainly focus on the research topics on five image restoration problems: image inpainting, image deblurring, image noise removal, image super-resolution, and image com-pressive sensing recovery. The contents of the thesis can be divided into four sections that are detailed as follows.
First, a novel image restoration algorithm based on a joint sparse statistical modeling in space-transform domain is proposed. Traditional image prior models regularized image restoration algorithms usually have two shortcomings. On one hand, only one image property used in regularization-based framework is not enough to obtain satisfying restoration results. On the other hand, the image property of nonlocal self-similarity should be characterized by a more powerful manner, rather than by the traditional weighted graph. To rectify the above prob-lems, from the perspective of image statistics, we first establish two sparse statis-tical models by characterizing image local smoothness in two-dimensional space domain at pixel level, and image nonlocal self-similarity in three-dimensional transform domain at patch level, respectively, and then merge the two models into a novel joint sparse statistical modeling in hybrid space-transform domain, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Under the regularization-based framework, a new form of minimization func-tional for solving image inverse problem using the joint sparse statistical model-ing is formulated, which is accompanied by an effective choice for the corre-sponding regularization parameters. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal appli-cations verify the effectiveness of the proposed algorithm.
Second, a novel image restoration algorithm based on structural group sparse representation (SGSR) is proposed. Traditional patch-based sparse repre-sentation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational com-plexity in dictionary learning. Second, each patch is considered independently in dictionary learning and sparse coding, which ignores the relationship among patches, resulting in inaccurate sparse coding coefficients. To rectify the above problems, instead of using patch as the basic unit of sparse representation, this thesis exploits the concept of structural group as the basic unit of sparse repre-sentation, which is composed of nonlocal patches with similar structures, and es-tablishs a novel sparse representation modeling of natural images, called struc-tural group sparse representation (SGSR). The proposed SGSR is able to sparsely represent natural images in the domain of structural group, which enforces the intrinsic local sparsity and nonlocal self-similarity of images simultaneously in a unified framework. Under the regularization-based framework, a new form of minimization functional for solving image inverse problem via SGSR in the form of L0norm is formulated, associated with an effective self-adaptive dictionary learning method for each structural group with low complexity. Extensive ex- periments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed SGSR modeling outperforms many current state-of-the-art schemes in both PSNR and visual perception.
Third, a new algorithm for image compressive sensing recovery using adap-tively learned sparsifying basis via L0minimization is proposed. Most of the conventional CS recovery approaches exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are irrespective of the non-stationarity of natural signals and cannot achieve high enough degree of sparsity, thus resulting in poor CS recovery performance and restricting the CS application in natural images. This thesis introduces the patch-based redundant sparse representation model that is used to characterize the intrinsic sparsity of the whole image into the problem of image compressive sensing recovery, and develops a framework for image compressive sensing recovery using the adap-tively learned sparsifying basis in the form of L0norm. The role of the adaptive learned sparsifying basis in the form of L0is to achieve high enough degree of adaptability and sparsity, thus greatly confining the CS solution. The role of the patch-based redundant sparse representation model is to reduce blocking artifacts and obtain the CS results with high visual quality. Experimental results on a wide range of natural images for CS recovery have shown that the proposed algorithm achieves significant performance improvements over many current state-of-the-art schemes.
Fourth, a novel image super-resolution algorithm via dual-dictionary learn-ing and sparse representation is proposed. Aiming at reducing the large gap of the frequency in the low and high resolution images exhibited in the traditional dictionary learning and sparse representation based image super-resolution methods and recovering more image high-frequency information, in this thesis, the high-frequency (HF) to be estimated in super-solution is considered as a combination of two components: main high-frequency (MHF) and residual high-frequency (RHF). As for above two types of high-frequency, two corre-sponding dictionaries are successively learned by making use of training images via sparse representation, i.e., the main dictionary and the residual dictionary. In the process of image super-resolution, the input low resolution image is first magnified and added the reconstructed main high-frequency information by vir- tue of the main dictionary, thus generating a temporary image. Then, by pre-forming the same reconstruction scheme with the temporary image and the re-sidual dictionary, the reconstructed residual high-frequency information is recon-structed, leading to the final high-resolution image. Extensive experimental re-sults on test images validate that by employing the proposed two-layer progres-sive scheme, more image details can be recovered and much better results can be achieved.
引文
[1] B. Gunturk and X. Li, Image Restoration: Fundamentals and Advances. CRC Press,2012.
[2] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli,“Image quality assessment:From error visibility to structural similarity,” IEEE Trans.on Image Processing, vol.13, no.4, pp.600–612, Apr.2004.
[3] L. Zhang, L. Zhang, X. Mou and D. Zhang,“FSIM: A Feature SIMilarity index forimage quality assessment,” IEEE Trans. Image Processing, vol.20, no.8, pp.2378–2386, Aug.2011.
[4] M. R. Banham and A. K. Katsaggelos,“Digital image restoration,” IEEE Trans. Sig-nal Processing Mag., vol.14, no.2, pp.24–41, Mar.1997.
[5] R. Fergus, B. Singh, A. Hertzmann, S. T. Roweis, and W. T. Freeman,“Removingcamera shake from a single photograph,”ACM Transactions on Graphics, vol.25, no.3, pp.787–794, July2006.
[6] Q. Shan, J. Jia, and A. Agarwala,“High-quality motion deblurring from a single im-age,”ACM Transactions on Graphics, vol.27, no.3, pp.73:1–73:10, Aug.2008.
[7] S. Park, M. Park, and M. Kang,“Super resolution image reconstruction: A technicaloverview,”IEEE Transaction on Signal Processing,, vol.20, no.3, pp.21–36, Mar.2003.
[8] R. Schultz and R. Stevenson,“Extraction of high-resolution frames from video se-quences,” IEEE Transactions on Image Processing, vol.5, pp.996–1011, June1996.
[9] J. Lee,“Digital image enhancement and noise filtering by use of local statistics,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.2no.2, pp.165–168, Feb.1980
[10] G. Pok, J. C. Liu and A. S. Nair,“Selective removal of impulse noise based on ho-mogeneity level information,” IEEE Trans. on Image Process., vol.12, no.1, pp.85–92,2003.
[11] A. Foi, V. Katkovnik, K. Egiazarian. Pointwise Shape-Adaptive DCT forHigh-Quality De-noising and Deblocking of Grayscale and Color Images. IEEETransactions on Image Processing., vol.16, no.5, pp.1395–1411, May2007.
[12]高文，赵德斌，马思伟，“数字视频编码技术原理”北京：科学出版社，2010.
[13] H. Takeda, S. Farsiu, and P. Milanfar,“Kernel regression for image processing andreconstruction,” IEEE Trans. on Image Process., vol.16, no.2, pp.349–366, Feb.2007.
[14] S. Roth and M. J. Black,“Fields of experts,” International Journal of Computer Vi-sion, vol.82, no.2, pp.205–229,2009.
[15] N. Joshi, S. B. Kang, C. L. Zitnick, and R. Szeliski,“Image deblurring using inertialmeasurement sensors,”ACM Transactions on Graphics, vol.29, pp.30:1–30:9, July2010.
[16] A. Agrawal, Y. Xu, and R. Raskar,“Invertible motion blur in video,” ACM Transac-tions on Graphics, vol.28, no.3, pp.1–8,2009.
[17] J. Chan, J. Ma, P. Kempeneers, and F. Canters,“Superresolution enhancement of hy-perspectral CHRIS/Proba images with a thin-plate spline nonrigid transform model,”IEEE Transactions on Geoscience and Remote Sensing, vol.48, no.6, pp.2569–2579,2010.
[18] R. Liu, Z. Li, and J. Jia,“Image partial blur detection and classification,” in IEEEConference on Computer Vision and Pattern Recognition (CVPR), pp.1–8, June2008.
[19] X. Zhu and P. Milanfar,“Removing Atmospheric Turbulence via Space-InvariantDeconvolution,” IEEE Trans. on Pattern Analysis and Machine Intelligence vol.35,no.1, pp.157-170, Jan.2013
[20] J. Yang, Y. Zhang, W. Yin,“A fast alternating direction method for TVL1-L2signalreconstruction from partial fourier data,” IEEE J. Sel. Top. Signal Process. vol.4, no.2, pp.288–297,2010.
[21] J. Huang, S. Zhang, H. Li, D. Metaxas,"Composite Splitting Algorithms for ConvexOptimization", Computer Vision and Image Understanding, vol115, no.12, pp.1610-1622, Dec.2011
[22] V. Katkovnik, A. Foi, K. Egiazarian and J. Astola,“From local kernel to nonlocalmultiple-model image denoising,” International Journal of Computer Vision, vol.86,no.1, pp.1–32, Jan.2010.
[23] Z. Xu and J. Sun,“Image inpainting by patch propagation using patch sparsity,” IEEETrans. on Image Process., vol.19, no.5, pp.1153–1165, May2010.
[24] Z. Xiong, X. Sun, and F. Wu,“Image hallucination with feature enhancement,” Proc.of IEEE Conference on Computer Vision and Pattern Classification (CVPR),2009.
[25] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian,“Image restoration by sparse3Dtransform-domain collaborative filtering,” Proc. of SPIE Conference Series,2008.
[26] J. Zhang, D. Zhao, C. Zhao, R. Xiong, S. Ma and W. Gao,"Compressed Sensing Re-covery via Collaborative Sparsity", Proc. of IEEE Data Compression Conference, pp.287–296, Snowbird, Utah, USA, Apr.2012.
[27] J. Koloda, J. stergaard, S. H. Jensen, A.M. Peinado and V. Sánchez,“SequentialError Concealment for Video/Images by Sparse Linear Prediction,” IEEE Transac-tions on Multimedia, vol.15, no.4, pp.957–969, June2013.
[28] X. Zhang, R. Xiong, X. Fan, S. Ma and W. Gao,“Compression artifact reduction byoverlapped-block transform coefficient estimation with block similarity,” IEEE Trans.on Image Process., vol.22, no.12, pp.4613–4626, Dec.2013.
[29] H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems. Dor-drecht: Kluwer Academic Publishers,2000.
[30] W. Dong, L. Zhang, G. Shi, and X. Wu,“Image deblurring and super-resolution byadaptive sparse domain selection and adaptive regularization,” IEEE Trans. on ImageProcessing, vol.20, no.7, pp.1838–1857, Jul.2011.
[31] J. Zhang, R. Xiong, S. Ma, D. Zhao,“High-quality image resto-ration from partialrandom samples in spatial domain,” Proc. of IEEE Visual Commun. and Image Pro-cess., pp.1–4, Taiwan, Nov.2011.
[32] A. Elmoataz, O. Lezoray, and S. Bougleux,“Nonlocal discrete regularization onweighted graphs: a framework for image and manifold processing,” IEEE Trans. Im-age Processing, vol.17, no.7, pp.1047–1060, Jul.2008.
[33] W. Dong, L. Zhang, and G. Shi,“Centralized sparse representation for image restora-tion,” in Proc. IEEE Int. Conf. Comput. Vis.(ICCV), Nov.2011.
[34] X. Li.“Image recovery from hybrid sparse representation: a deterministic annealingapproach,” IEEE J. of Selected Topics in Signal Processing, vol.5, no.6, pp.953–962,Sep.2011.
[35] L. Rudin, S. Osher, and E. Fatemi,“Nonlinear total variation based noise removalalgorithms,” Phys. D., vol.60, pp.259–268,1992.
[36] A. Chambolle,“An algorithm for total variation minimization and applications,” J.Math. Imaging Vis., vol.20, pp.89–97,2004.
[37]刘贤明，基于自适应模型的图像超分辨率技术：算法和应用，哈尔滨工业大学博士学位论文，2012.7。
[38] X. Li and M. Orchard,“New edge-directed interpolation,” IEEE Trans. on ImageProcessing, vol.10, no.10, pp.1521–1527, Oct2001.
[39] A. Buades, B. Coll and J. M. Morel,“Image enhancement by non-local reverse heatequation,” CMLA, Tech, Rep.22,2006.
[40] J. Zhang, S. Liu, R. Xiong, S. Ma, D. Zhao,"Improved total variation based imagecompressive sensing recovery by nonlocal regularization", Proc. of IEEE Int. Sym.of Circuits and Systems, May2013.
[41] X. Zhang, M. Burger, X. Bresson and S. Osher,“Bregmanized nonlocal regularizationfor deconvolution and sparse reconstruction,” SIAM J. Imaging Sci., vol.3, no.3, pp.253–276,2010.
[42] H. Zhang, J. Yang, Y. Zhang, and Thomas Huang,“Non-local Kernel Regression forImage and Video Restoration,” ECCV2010.
[43] M. Aharon, M. Elad, and A. Bruckstein,“K-SVD: An algorithm for designing over-complete dictionaries for sparse representation,” IEEE Trans. on Signal Process., vol.54, no.11, pp.4311–4322,2006.
[44] M. Bruckstein, D.L. Donoho, and M. Elad,“From sparse solutions of systems ofequations to sparse modeling of signals and images,” SIAM Review, vol.51, no.1, pp.34–81,2009.
[45] D. Mumford and J. Shah,“Optimal approximation by piecewise smooth functions andassociated variational problems,” Comm. on Pure and Appl. Math., vol.42, pp.577–685,1989.
[46] J. Besag,“Spatial Interaction and the Statistical Analysis of Lattice Systems,” Journalof the Royal Statistical Society, Series B (Methodological), vol.36, no.2, pp.192–236,1974.
[47] A. Beck and M. Teboulle,“Fast gradient-based algorithms for constrained total varia-tion image denoising and deblurring problems,” IEEE Trans. on Image Process., vol.18, no.11, pp.2419–2434, Nov.2009.
[48] J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen,“Algorithms and Software forTotal Variation Image Reconstruction via First-Order Methods,” Numerical Algo-rithms, vol.53, pp.67–92,2010.
[49] G. Chantas, N. P. Galatsanos, R. Molina, A. K. Katsaggelos,“Variational Bayesianimage restoration with a product of spatially weighted total variation image priors,”IEEE Trans. Image Process., vol.19, no.2, pp.351–362, Feb.2010.
[50] L. Xu, C. Lu, Y. Xu, and J. Jia,“Image smoothing via L0gradient minimization,”ACM Trans. on Graphics, vol.30, no.6, Dec.2011.
[51] L. Amborsio and V. M. Tortorelli,“Approximation of functionals depending onjumps by elliptic functionals via γ convergence,” Comm. on Pure and Appl. Math.,vol. XLIII, pp.999–1036,1990.
[52] A. Speis, G. Healey,“An analytical and experimental study of the performanceof Markov Random Fields applied to texture images using small samples,” IEEETrans. on Image Processing, vol.5, no.3, pp.447–458, Mar.1996.
[53] X. Zhang and X. Wu,“Image Interpolation by Adaptive2-D Autoregressive Modelingand Soft-Decision Estimation,” IEEE Trans. on Image Processing, vol.17, no.6, pp.887-896, Jun.2008.
[54] Y. Zhang, D. Zhao, S. Ma, R. Wang and W. Gao,“A Motion Aligned Auto-regressiveModel for Frame Rate up Conversion,” IEEE Trans. on Image Processing, vol19, No.5, pp.1248-1258, May.2010.
[55] Y. Zhang, D. Zhao, X. Ji, R. Wang and W. Gao,“A Spatio-temporal Auto-regressiveModel for Frame Rate up Conversion,” IEEE Trans. on Circuits and System VideoTechnology, vol.19, No.9, pp.1289-1301, Sep.2009.
[56] A. A. Efros and T. K. Leung,“Texture synthesis by non-parametric sampling,” Proc.of Int. Conf. Computer Vision, vol.2, pp.1022–1038,1999.
[57] A. Buades, B. Coll, and J. M. Morel,“A non-local algorithm for image denoising,”Proc. of Int. Conf. on Computer Vision and Pattern Recognition,2005.
[58] M. Protter, M. Elad, H. Takeda, and P. Milanfar,“Generalizing the nonlocal-means tosuper-resolution reconstruction,” IEEE Trans. On Image Process., vol.18, no.1, pp.36–51, Jan.2009.
[59] S. Kindermann, S. Osher, and P.W. Jones,“Deblurring and denoising of images bynonlocal functionals,” Multiscale Model. Simul., vol.4, no.4, pp.1091–1115,2005.
[60] F. R. K. Chung. Spectral graph theory, pp.1–212. American Mathematical Society,1997.
[61] G. Gilboa and S. Osher,“Nonlocal operators with applications to image processing,”Multiscale Modeling and Simulation, vol.7, no.3, pp.1005–1028,2008.
[62] G. Peyré, S. Bougleux, and L. Cohen,“Non-local regularization of inverse problems,”Proc. of European Conference on Computer Vision, Marseille-France, Oct.2008.
[63] M. Jung, X. Bresson, T. F. Chan, and L. A. Vese,“Nonlocal Mumford-Shah regular-izers for color image restoration”, IEEE Trans. Image Process., vol.20, no.6, pp.1583–1598, Jun.2011.
[64] J. Sun, M.Tappen. Learning Non-Local Range Markov Random Field for Image Res-toration. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), Colorado,USA,2011.
[65] X. Gao, J. Zhang, F. Jiang, S. Ma, D. Zhao,“Image Interpolation via Local Auto-regressive and Nonlocal3-D Sparse Regularization,” IEEE Visual Communicationsand Image Processing (VCIP2012),2012.
[66] X Zhang, S Ma, Y Zhang, L Zhang, W Gao,“Nonlocal edge-directed interpolation,”Advances in Multimedia Information Processing PCM2009.
[67] T. Peleg, Y.C. Eldar, M. Eladm,“Exploiting Statistical Dependencies in Sparse Rep-resentations for Signal Recovery,” IEEE Transactions on Signal Processing, vol.60,no.5, pp.2286–2303May2012.
[68] M. Elad and M. Aharon,“Image denoising via sparse and redundant representationsover learned dictionaries,” IEEE Trans. Image Process., vol.15, no.12, pp.3736–3745, Dec.2006.
[69] J. Yang, J. Wright, T. Huang, and Y. Ma,“Image super-resolution via sparse repre-sentation,” IEEE Trans. Image Process., vol.19, no.11, pp.2861–2873, Nov.2010.
[70] J. Yang, K. Yu, Y. Gong, and T. Huang,“Linear spatial pyramid matching uisngsparse coding for image classification,” Proc. of IEEE Conference on Computer Vi-sion and Pattern Recognition (CVPR),2009.
[71] J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, S. Yan,"Sparse Representation forComputer Vision and Pattern Recognition,” Proceedings of the IEEE, vol.98, no.6, pp.1031–1044, Jun.2010.
[72] D. L. Donoho and J. M. Johnstone,“Ideal spatial adaptation by wavelet shrink-age,”Biometrika, vol.81, no.3, pp.425–455, September1994.
[73] M. A. T. Figueiredo and R. D. Nowak,“An EM algorithm for wavelet-based imagerestoration,” IEEE Transactions on Image Processing, vol.12, no.8, pp.906–916,August2003.
[74] E. Candès, L. Demanet, D. Donoho, and L. Ying,“Fast discrete curvelet transforms,”Multiscale Model. Sim., vol.5, pp.861–899,2005.
[75] H. Lee, A. Battle, R. Raina, and A. Y. Ng,“Efficient sparse coding algorithms,” inAdvances in Neural Information Processing Systems (NIPS),2007.
[76] K. Engan, S. O. Aase, and J. H. Hakon-Husoy,“Method of optimal directions forframe design,” Proc. of IEEE Int. Conf. Acoust., Speech, Signal Process., vol.5, pp.2443–2446,1999.
[77] Joel A. Tropp and Anna C. Gilbert,“Signal recovery from random measurements viaorthogonal matching pursuit,” IEEE Transactions on Information Theory, vol.53, no.12, pp.4655–4666, Dec.2007.
[78] A. Iusem,“Augmented Lagrangian methods and proximal pointmethods for convexoptimization,” Investigación Operativa, vol.8, pp.11–49,1999
[79] P. Combettes and J.-C. Pesquet,“A Douglas-Rachford splitting approach to non-smooth convex variational signal recovery,” IEEE J. Sel.Topics Signal Process., vol.1, no.4, pp.564–574, Dec.2007.
[80] J. Bioucas-Dias and M. Figueiredo,“A new TwIST: two-step iterative shrink-age/thresholding algorithms for image restoration,” IEEE Trans. on Image Process.,vol.16, no.12, pp.2992–3004, Dec.2007.
[81] J. Eckstein and D. Bertsekas,“On the Douglas–Rachford splitting method and theproximal point algorithm for maximal monotone operators,” Math. Program., vol.5,pp.293–318,1992.
[82] M. Afonso, J. Bioucas-Dias and M. Figueiredo,“Fast image recovery using variablesplitting and constrained optimization,” IEEE Trans. on Image Process., vol.19, no.9,pp.2345–2356, Sep.2010.
[83] S. Chen, D. Donoho, M. Saunders,“Atomic decompositions by basis pursuit,” SIAMReview, vol.43, pp.129–159,2001.
[84] T. Goldstein and S. Osher,“The split Bregman algorithm for L1regularized prob-lems,” SIAM J. Imaging Sci., vol.2, pp.323–343,2009.
[85] J. F. Cai, S. Osher, and Z. W. Shen,“Split Bregman methods and frame based imagerestoration,” Multiscale Model. Simul., vol.8. pp.5057–5071,2009.
[86] W. Yin, S. Osher, D. Goldfarb, and J. Darbon,“Bregman iterative algorithms for L1minimization with applications to compressed sensing,” SIAM J. Imag. Sci., vol.1,pp.143–168,2008
[87] L. Zhang, W. Dong, D. Zhang, G. Shi,“Two-stage image denoising by principlecomponent analysis with local pixel grouping,” Pattern Recognition, vol.43,pp.1531–5549, Apr.2010.
[88] J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman,“Non-local sparse modelsfor image restoration,” Proc. IEEE Int. Conf. Comput. Vis., Tokyo, Japan, Sep.2009.
[89] W. Dong, L. Zhang, G. Shi and X. Li,“Nonlocally Centralized Sparse Representationfor Image Restoration,” IEEE Trans. on Image Processing, vol.22, no.4, pp.1620-1630, Apr.2013.
[90] M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester,“Image in-painting,” Proc. ofSIGGRAPH, pp.417–424,2000.
[91] M. Bertalmio, A. L. Bertozzi, and G. Sapiro,“Navier–Strokes, fluid dynamics, andimage and video inpainting,” Proc. of IEEE Computer Society Conf. Computer Visionand Pattern Recognition,2001.
[92] T. Chan and J. Shen,“Local inpainting models and tv inpainting,” SIAM J. Appl.Math., vol.62, no.3, pp.1019–1043,2001.
[93] T. Chan and J. Shen,“Non-texture inpainting by curvature-driven diffusions,” J. Vis.Commun. Image Represent., vol.4, no.12, pp.436–449,2001.
[94] C. Bertalmio, M. Bertalmio, V. Caselles, G. Sapiro, and J. Verdera,“Filling-in byjoint interpolation of vector fields and gray levels,” IEEE Trans. Image Process., vol.10, no.8, pp.1200–1211, Aug.2001.
[95] A. Levin, A. Zomet, and Y. Weiss,“Learning how to inpaint from global image sta-tistics,” in Proc. of Int. Conf. Comp. Vision, pp.305–312,2003.
[96] S. Roth and M. J. Black,“Fields of experts: A framework for learning image priors,”in Proc. IEEE Computer Society Conf. Computer Vision and Pattern Recognition,2005.
[97] S. Roth and M. J. Black,“Steerable random fields,” in Proc. of IEEE Computer Soci-ety Conf. Computer Vision and Pattern Recognition,2007.
[98] A. Efros and T. Leung,“Texture synthesis by non-parametric sam-pling,” in Proc. ofInt. Conf. Comp. Vision,1999.
[99] M. Bertalmio, L. Vese, G. Sapiro, and S. Osher,“Simultaneous structure and textureimage inpainting,” IEEE Trans. Image Process., vol.12, no.8, pp.882–889, Aug.2003.
[100] A. Criminisi, P. Perez, and K. Toyama,“Object removal by examplar-based imageinpainting,” in of Proc. Int. Conf. Comp. Vision,2003.
[101] J. Wu and Q. Ruan,“Object removal by cross isophotes examplar-based imageinpainting,” in Proc. of Int. Conf. Pattern Recognition,2006.
[102] A. Wong and J. Orchard,“A nonlocal-means approach to examplar-based inpainting,”Proc. of IEEE Int. Conf. Image Processing,2008.
[103] G. T. N. Komodakis,“Image completion using efficient belief propagation via priori-ty scheduling and dynamic pruning,” IEEE Trans. Image Process., vol.16, no.11, pp.2649–2661, Nov.2007.
[104] J. Jia and C. K. Tang,“Image repairing: Robust image synthesis by adaptive nd tensorvoting,” in Proc. of IEEE Computer Society Conf. Computer Vision and PatternRecogition,2003.
[105] I. Drori, D. CohenOr, and H. Yeshurun,“Fragment-based image completion,” ACMTrans. Graph., vol.22, no.3, pp.303–312, Jul.2003.
[106] M. Elad, J. L. Starck, P. Querre, and D. L. Donoho,“Simultaneous cartoon and tex-ture image inpainting using morphological component analysis,” Appl. Comput.Harmon. Anal., vol.19, no.3, pp.340–358, Nov.2005.
[107] O. G. Guleryuz,“Nonlinear approximation based image recovery using adaptivesparse reconstructures and iterated denoising-part i: Theory,” IEEE Trans. ImageProcess., vol.15, no.3, pp.539–554, Mar.2006.
[108] O. G. Guleryuz,“Nonlinear approximation based image recovery using adaptivesparse reconstructures and iterated denoising-part ii: Adaptive algorithms,” IEEETrans. Image Process., vol.15, no.3, pp.555–571, Mar.2006.
[109] M. J. Fadili, J. L. Starck, and F. Murtagh,“Inpainting and zooming using sparse rep-resentations,” The Comput. J., vol.52, no.1, pp.64–79,2009
[110] S. Kaczmarz,“Angenherte auflsung von systemen linearer gleichungen,” Bull. Int.Acad. Polon. Sci. A, vol.355, p.357,1937.
[111] H. Andrews and B. Hunt, Digital Image Restoration. Prentice-Hall,1977.
[112] L. Landweber,“An iteration formula for Fredholm integral equations of the firstkind,” American Journal of Mathematics, pp.615–624,1951.
[113] S. F. Gull and G. J. Daniell,“Image reconstruction from incomplete and noisy da-ta,”Nature, vol.272, pp.686–690, Apr.1978.
[114] L. B. Lucy,“An iterative technique for the rectification of observed distribu-tions,”Astronomical Journal, vol.79, no.6, pp.745–754, Jun.1974.
[115] J. Biemond, R. Lagendijk, and R. Mersereau,“Iterative methods for image deblur-ring,” Proceedings of the IEEE, vol.78, no.5, pp.856–883,1990.
[116] D. Youla,“Generalized image restoration by the method of alternating orthogonalprojections,” IEEE Transactions on Circuits and System, vol.25, no.9, pp.694–702,Sep.1978.
[117] H. Trussell and M. Civanlar,“The feasible solution in signal restoration,” IEEETransactions on Acoustics, Speech and Signal Processing, vol.32, no.2, pp.201–212,Apr1984.
[118] H. Trussell and M. Civanlar,“The landweber iteration and projection onto convexsets,” IEEE Trans. on Acoustics, Speech, and Signal Processing, vol.33, no.6, pp.1632–1634, Dec.1985.
[119] A. Tikhonov and V. Arsenin, Solutions of Ill-posed Problems. New York: Wiley,1977.
[120] G. Aubert and L. Vese,“A variational method in image recovery,”SIAM Journal onNumerical Analysis, vol.34, no.5, pp.1948–1979,1997.
[121] J. M. Bioucas-Dias, M. A. T. Figueiredo, and J. P. Oliveira,“Total variation-basedimage deconvolution: a majorization-minimization approach,” Proc. of Int.. Conf. onAcoustics, Speech and Signal Processing,2006.
[122] S. Babacan, R. Molina, and A. Katsaggelos,“Parameter estimation in TV image res-toration using variational distribution approximation,” IEEE Transactions on ImageProcessing, vol.17, no.3, pp.326–339, Mar.2008.
[123] M. Banham and A. Katsaggelos,“Spatially adaptive wavelet-based multiscale imagerestoration,” IEEE Trans. on Image Proc., vol.5, no.4, pp.619–634, Apr.1996.
[124] R. Neelamani, H. Choi, and R. Baraniuk,“Forward: Fourier-wavelet regularized de-convolution for ill-conditioned systems,”IEEE Transactions on Signal Processing, vol.52, no.2, pp.418–433,2004.
[125] A. Chambolle, R. DeVore, N.-Y. Lee, and B. Lucier,“Nonlinear wavelet image pro-cessing: variational problems, compression, and noise removal through waveletshrinkage,” IEEE Trans. on Image Processing, vol.7, pp.319–335,1998.
[126] G. Steidl, J. Weickert, T. Brox, P. Mrazek, and M. Welk,“On the equivalence of softwavelet shrinkage, total variation diffusion, total variation regularization, andsides,”SIAM J. Numer. Anal., vol.42, no.2, pp.686–713,2004.
[127] A. Danielyan, V. Katkovnik, and K. Egiazarian,“BM3D frames and variational imagedeblurring,” IEEE Trans. Image Process., vol.21, no.4, pp.1715–1728, Apr.2012.
[128] S. M. Smith, J. M. Brady. SUSAN―A New Approach to Low Level Image Pro-cessing. International Journal of Computer Vision. vol.23, no.1, pp.45–78,1997.
[129] C. Tomasi, R. Manduchi. Bilateral filtering for gray and color images. Proc. of IEEEInternational Conference on Computer Vision (ICCV),1998.
[130] D. L. Donoho,“De-noising by soft-thresholding,” IEEE Transactions on InformationTheory, vol41, no.3, pp.613–627,1995.
[131] S. Mallat, S. Zhong,“Characterization of signals from multiscale edges,” IEEETransactions on Pattern Analysis and Machine Intelligence, vol.14, no.7, pp.710–732,1992.
[132] A. P. Witkin,“Scale-Space Filtering,” Proc. of International Joint Conference on Ar-tificial Intelligence (IJCAI),1983.
[133] M. Elad, M.A.T. Figueiredo, Yi Ma,“On the Role of Sparse and Redundant Repre-sentations in Image Processing,” Proceedings of the IEEE, vol98, no.6, pp.972–982,Jun.2010.
[134] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian,“Image denoising by sparse3Dtransform-domain collaborative filtering,” IEEE Trans. on Image Process., vol.16, no.8, pp.2080–2095, Aug.2007.
[135] Y. Dong and S. Xu,“A new directional weighted median filter for removal of ran-dom-valued impulse noise,” IEEE Signal Process. Letters, vol.14, no.3, pp.193–196,2007.
[136] H. Hwang and R. Haddad,“Adaptive median filters: new algorithms and results,”IEEE Trans. on Image Process., vol.4, no.4, pp.499–502,1995.
[137] S. J. Ko and Y. H. Lee,“Center weighted median filters and their applications to im-age enhancement,” IEEE Transactions on Circuits and Systems, vol.39, no.9, pp.984–993,1991.
[138] J. F. Cai, R. Chan, M. Nikolova,“Two-phase methods for deblurring images corrupt-ed by impulse plus Gaussian noise,” Inverse Problem Imaging, vol.2, no.2, pp.187–204,2008.
[139] Y. Huang, M. Ng and Y. Wen,“Fast image restoration methods for impulse andGaussian noise removal,” IEEE Signal Process. Letters, vol.16, no.6, pp.457–460,2009.
[140] Y. Li, L. X. Shen, D. Dai, and B. Suter,“Framelet algorithms for de-blurring imagescorrupted by impulse plus Gaussian noise,” IEEE Trans. on Image Process., vol.20,no.7, pp.1822–1837, Jul.2011.
[141] M. Nikolova,“A variational approach to remove outliers and impulse noise,” Journalof Mathematical Imaging and Vision, vol.20, pp.99–120,2004.
[142] J. F. Cai, R. Chan and M. Nikolova,“Fast two-phase image deblurring under impulsenoise,” Journal of Mathematical Imaging and Vision, vol.36, no.1, pp.46–53,2010.
[143] R. Chan, C. Hu and M. Nikolova,“An iterative procedure for removing ran-dom-valued impulse noise,” IEEE Signal Process. Letters, vol.11, no.12, pp.921–924,2004.
[144] Y. Xiao, T. Zeng, J. Yu and M. Ng,“Restoration of images corrupted by mixedGaussian-impulse noise via L1-L0minimization,” Pattern Recongnition, vol.44, pp.1708–1720,2011.
[145] M. Irani, S. Peleg,“Improving resolution by image registration,” CVGIP: GraphModels Image Process, vol.53, no.3, pp.231–239,1991.
[146] H. Stark, P. Oskoui,“High-resolution image recovery from image-plane arrays, usingconvex projections,” J Opt Soc Am A., vol.6, no.11, pp.1715–1726,1989.
[147] A. M. Tekalp, M. K. Ozkan, M. I. Sezan,“High-resolution image reconstruction fromlower-resolution image sequences and space-varying image restoration,” Proc. IEEEInterna-tional Conference on Acoustics, Speech, and Signal Processing,1992.
[148] R. C. Hardie, K.J. Barnard, E.E. Armstrong,“Joint MAP registration andhigh-resolution image estimation using a sequence of undersampled images,” IEEETransactions on Image Processing, vol.6, no.12, pp.1621–1633, Dec.1997.
[149] H. Shen, L. Zhang, B. Huang, and P. Li,“A MAP Approach for Joint Motion Estima-tion, Segmentation, and Super Resolution,” IEEE Transactions on Image Processing,vol.16, no.2, pp.479–490, Feb.2007.
[150] Y. He, K. Yap, L. Chen, L. Chau,“A nonlinear least square technique for simultane-ous image registration and super-resolution,” IEEE Transactions on Image Processing,vol.16, no.11, pp.2830–2841, Nov.2007.
[151] M. K. Ng, H. Shen, E. Y. Lam, L. Zhang,“A Total Variation Regularization BasedSuper-Resolution Reconstruction Algorithm for Digital Video,” EURASIP J. on Ad-vances in Signal Processing,2007.
[152] Q. Yuan, L. Zhang, H. Shen,“Multi-frame Super-resolution Employing a SpatiallyWeighted Total Variation Model,” IEEE Trans Circuits Syst Video Technol, vol.22.no.3, pp.379–392, Mar.2011.
[153] J. Sun, J. Sun, Z. Xu, H. Shum,“Image super-resolution using gradient profile prior,”Proc. of Computer Vision and Pattern Recognition,2008.
[154] T. Katsuki, A. Torii, M. Inoue,“Posterior-Mean Super-Resolution With a CausalGaussian Markov Random Field Prior,” IEEE Trans Image Processing, vol.21. no.7,pp.3182–3193, Jul.2012.
[155] J. Sun, N. Zheng, H. Tao, H. Shum,“Image hallucination with primal sketch priors,”Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recog-nition (CVPR),2003.
[156] W. T. Freeman, E.C. Pasztor, O.T. Carmichael,“Learning Low-Level Vision,” Inter-national Journal of Computer Vision, vol.40, no.1, pp.25–47,2000.
[157] W.T. Freeman, E.C. Pasztor,“Learning low-level vision,” Proc. IEEE InternationalConference on Computer Vision (ICCV),1999.
[158] H. Chang, D. Yeung, Y. Xiong,“Super-resolution through neighbor embedding,”Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recogni-tion (CVPR),2004.
[159] D. Capel, A. Zisserman,“Super-resolution from multiple views using learnt imagemodels,” Proc. IEEE Computer Society Conference on Computer Vision and PatternRecognition (CVPR).2001,
[160] R. Zeyde, M. Elad, and M. Protter,“On Single Image Scale-Up usingSparse-Representations,” Curves&Surfaces, Avignon France, June,2010.
[161] D. L. Donoho,“Compressed sensing,” IEEE Trans. Inform. Theory, vol.52, no.4, pp.1289–1306,2006.
[162] E. Candès, J. Romberg, and T. Tao,“Robust uncertainty principles: Exact signal re-construction from highly incomplete frequency information,” IEEE Trans. Inform.Theory, vol.52, pp.489–509,2006.
[163] M. Davenport, M. F. Duarte, Y. C. Eldar and G. Kutyniok, Compressed Sensing:Theory and Applications, Cam-bridge University Press,2011.
[164] M. Duarte, M. Davenport, D. Takhar, J. Laska, and T. Sun,“Single-pixel imaging viacompressive sampling,” IEEE Signal Processing Magazine, vol.25, no.2, pp.83–91,2008.
[165]李树涛,魏丹,“压缩传感综述,”自动化学报，vol.35, no.11, pp.1369–1137,2009.
[166]刘丹华，石光明，周佳社，高大化，吴家骥,“基于Compressed Sensing框架的图像多描述编码方法,”红外与毫米波学报, vol.28, no.4, pp.298-302, Aug.2009.
[167] S. Mun and J. E. Fowler,“Block compressive sensing of images using directionaltransforms,” Proc. of IEEE Int. Conf. Image Process.,2009.
[168] L. He, H. Chen and L. Carin,“Tree-structured compressive sensing with variationalBayesian analysis,” IEEE Signal Processing Letter, vol.17, no.3, pp.233–236,2010.
[169] l1-Magic Toolbox available at http://users.ece.gatech.edu/~justin/l1magic/.
[170] C. Li, W. Yin, and Y. Zhang,“TVAL3: TV Minimization by Augmented Lagrangianand Alternating Direction Algorithm,”2009.
[171] L. He and L. Carin,“Exploiting structure in wavelet-based Bayesian compressivesensing,” IEEE Trans. Signal Process., vol.57, no.9, pp.3488–3497,2009.
[172] Y. Kim, M. S. Nadar and A. Bilgin,“Compressive sensing using a Gaussian scalemixtures model in wavelet do-main,” Proc. of IEEE Int. Conf. Image Process., pp.3365–3368,2010.
[173] X. Wu, X. Zhang and J. Wang,“Model-guided adaptive recovery of compressivesensing,” Proc. of IEEE Data Compression Conf.,2009.
[174] C. Chen, E. W. Tramel, and J. E. Fowler,“Compressed-sensing recovery of imagesand video using multihy-pothesis predictions,” Proc. of the45th Asilomar Conferenceon Signals, Systems, and Computers, Pacific Grove, CA, pp.1193–1198, Nov.2011.
[175] J. Zhang, D. Zhao, C. Zhao, R. Xiong, S. Ma and W. Gao,“Image compressive sens-ing recovery via collaborative sparsity,” IEEE Journal on Emerging and SelectedTopics in Circuits and Systems, vol.2, no.3, pp.380–391, Sep.2012.
[176] M. K. Varanasi, B. Aazhang,“Parametric generalized Gaussian density estimation,” J.Acoust. Soc. Amer., vol.86, no.4, pp.1404–1415,1989.
[177] M. Zhou, H. Chen, J. Paisley, L. Ren, L. Li, Z. Xing, D. Dunson, G. Sapiro and L.Carin,“Nonparametric Bayesian dictionary learning for analysis of noisy and incom-plete images,” IEEE Trans. Image Processing, vol.21, no.1, pp.130–144, Jan.2012.
[178] J. Portilla,“Image restoration through l0analysis-based sparse optimization in tightframes,” IEEE Int. conf. Image Process., pp.3909-3912, Nov.2009.
[179] H. Takeda, S. Farsiu, P. Milanfar,“Deblurring using regularized locally-adaptivekernel regression,” IEEE Transactions on Image Processing, vol.17, no.4, pp.550–563, Apr.2008.
[2] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli,“Image quality assessment:From error visibility to structural similarity,” IEEE Trans.on Image Processing, vol.13, no.4, pp.600–612, Apr.2004.
[3] L. Zhang, L. Zhang, X. Mou and D. Zhang,“FSIM: A Feature SIMilarity index forimage quality assessment,” IEEE Trans. Image Processing, vol.20, no.8, pp.2378–2386, Aug.2011.
[4] M. R. Banham and A. K. Katsaggelos,“Digital image restoration,” IEEE Trans. Sig-nal Processing Mag., vol.14, no.2, pp.24–41, Mar.1997.
[5] R. Fergus, B. Singh, A. Hertzmann, S. T. Roweis, and W. T. Freeman,“Removingcamera shake from a single photograph,”ACM Transactions on Graphics, vol.25, no.3, pp.787–794, July2006.
[6] Q. Shan, J. Jia, and A. Agarwala,“High-quality motion deblurring from a single im-age,”ACM Transactions on Graphics, vol.27, no.3, pp.73:1–73:10, Aug.2008.
[7] S. Park, M. Park, and M. Kang,“Super resolution image reconstruction: A technicaloverview,”IEEE Transaction on Signal Processing,, vol.20, no.3, pp.21–36, Mar.2003.
[8] R. Schultz and R. Stevenson,“Extraction of high-resolution frames from video se-quences,” IEEE Transactions on Image Processing, vol.5, pp.996–1011, June1996.
[9] J. Lee,“Digital image enhancement and noise filtering by use of local statistics,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.2no.2, pp.165–168, Feb.1980
[10] G. Pok, J. C. Liu and A. S. Nair,“Selective removal of impulse noise based on ho-mogeneity level information,” IEEE Trans. on Image Process., vol.12, no.1, pp.85–92,2003.
[11] A. Foi, V. Katkovnik, K. Egiazarian. Pointwise Shape-Adaptive DCT forHigh-Quality De-noising and Deblocking of Grayscale and Color Images. IEEETransactions on Image Processing., vol.16, no.5, pp.1395–1411, May2007.
[12]高文，赵德斌，马思伟，“数字视频编码技术原理”北京：科学出版社，2010.
[13] H. Takeda, S. Farsiu, and P. Milanfar,“Kernel regression for image processing andreconstruction,” IEEE Trans. on Image Process., vol.16, no.2, pp.349–366, Feb.2007.
[14] S. Roth and M. J. Black,“Fields of experts,” International Journal of Computer Vi-sion, vol.82, no.2, pp.205–229,2009.
[15] N. Joshi, S. B. Kang, C. L. Zitnick, and R. Szeliski,“Image deblurring using inertialmeasurement sensors,”ACM Transactions on Graphics, vol.29, pp.30:1–30:9, July2010.
[16] A. Agrawal, Y. Xu, and R. Raskar,“Invertible motion blur in video,” ACM Transac-tions on Graphics, vol.28, no.3, pp.1–8,2009.
[17] J. Chan, J. Ma, P. Kempeneers, and F. Canters,“Superresolution enhancement of hy-perspectral CHRIS/Proba images with a thin-plate spline nonrigid transform model,”IEEE Transactions on Geoscience and Remote Sensing, vol.48, no.6, pp.2569–2579,2010.
[18] R. Liu, Z. Li, and J. Jia,“Image partial blur detection and classification,” in IEEEConference on Computer Vision and Pattern Recognition (CVPR), pp.1–8, June2008.
[19] X. Zhu and P. Milanfar,“Removing Atmospheric Turbulence via Space-InvariantDeconvolution,” IEEE Trans. on Pattern Analysis and Machine Intelligence vol.35,no.1, pp.157-170, Jan.2013
[20] J. Yang, Y. Zhang, W. Yin,“A fast alternating direction method for TVL1-L2signalreconstruction from partial fourier data,” IEEE J. Sel. Top. Signal Process. vol.4, no.2, pp.288–297,2010.
[21] J. Huang, S. Zhang, H. Li, D. Metaxas,"Composite Splitting Algorithms for ConvexOptimization", Computer Vision and Image Understanding, vol115, no.12, pp.1610-1622, Dec.2011
[22] V. Katkovnik, A. Foi, K. Egiazarian and J. Astola,“From local kernel to nonlocalmultiple-model image denoising,” International Journal of Computer Vision, vol.86,no.1, pp.1–32, Jan.2010.
[23] Z. Xu and J. Sun,“Image inpainting by patch propagation using patch sparsity,” IEEETrans. on Image Process., vol.19, no.5, pp.1153–1165, May2010.
[24] Z. Xiong, X. Sun, and F. Wu,“Image hallucination with feature enhancement,” Proc.of IEEE Conference on Computer Vision and Pattern Classification (CVPR),2009.
[25] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian,“Image restoration by sparse3Dtransform-domain collaborative filtering,” Proc. of SPIE Conference Series,2008.
[26] J. Zhang, D. Zhao, C. Zhao, R. Xiong, S. Ma and W. Gao,"Compressed Sensing Re-covery via Collaborative Sparsity", Proc. of IEEE Data Compression Conference, pp.287–296, Snowbird, Utah, USA, Apr.2012.
[27] J. Koloda, J. stergaard, S. H. Jensen, A.M. Peinado and V. Sánchez,“SequentialError Concealment for Video/Images by Sparse Linear Prediction,” IEEE Transac-tions on Multimedia, vol.15, no.4, pp.957–969, June2013.
[28] X. Zhang, R. Xiong, X. Fan, S. Ma and W. Gao,“Compression artifact reduction byoverlapped-block transform coefficient estimation with block similarity,” IEEE Trans.on Image Process., vol.22, no.12, pp.4613–4626, Dec.2013.
[29] H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems. Dor-drecht: Kluwer Academic Publishers,2000.
[30] W. Dong, L. Zhang, G. Shi, and X. Wu,“Image deblurring and super-resolution byadaptive sparse domain selection and adaptive regularization,” IEEE Trans. on ImageProcessing, vol.20, no.7, pp.1838–1857, Jul.2011.
[31] J. Zhang, R. Xiong, S. Ma, D. Zhao,“High-quality image resto-ration from partialrandom samples in spatial domain,” Proc. of IEEE Visual Commun. and Image Pro-cess., pp.1–4, Taiwan, Nov.2011.
[32] A. Elmoataz, O. Lezoray, and S. Bougleux,“Nonlocal discrete regularization onweighted graphs: a framework for image and manifold processing,” IEEE Trans. Im-age Processing, vol.17, no.7, pp.1047–1060, Jul.2008.
[33] W. Dong, L. Zhang, and G. Shi,“Centralized sparse representation for image restora-tion,” in Proc. IEEE Int. Conf. Comput. Vis.(ICCV), Nov.2011.
[34] X. Li.“Image recovery from hybrid sparse representation: a deterministic annealingapproach,” IEEE J. of Selected Topics in Signal Processing, vol.5, no.6, pp.953–962,Sep.2011.
[35] L. Rudin, S. Osher, and E. Fatemi,“Nonlinear total variation based noise removalalgorithms,” Phys. D., vol.60, pp.259–268,1992.
[36] A. Chambolle,“An algorithm for total variation minimization and applications,” J.Math. Imaging Vis., vol.20, pp.89–97,2004.
[37]刘贤明，基于自适应模型的图像超分辨率技术：算法和应用，哈尔滨工业大学博士学位论文，2012.7。
[38] X. Li and M. Orchard,“New edge-directed interpolation,” IEEE Trans. on ImageProcessing, vol.10, no.10, pp.1521–1527, Oct2001.
[39] A. Buades, B. Coll and J. M. Morel,“Image enhancement by non-local reverse heatequation,” CMLA, Tech, Rep.22,2006.
[40] J. Zhang, S. Liu, R. Xiong, S. Ma, D. Zhao,"Improved total variation based imagecompressive sensing recovery by nonlocal regularization", Proc. of IEEE Int. Sym.of Circuits and Systems, May2013.
[41] X. Zhang, M. Burger, X. Bresson and S. Osher,“Bregmanized nonlocal regularizationfor deconvolution and sparse reconstruction,” SIAM J. Imaging Sci., vol.3, no.3, pp.253–276,2010.
[42] H. Zhang, J. Yang, Y. Zhang, and Thomas Huang,“Non-local Kernel Regression forImage and Video Restoration,” ECCV2010.
[43] M. Aharon, M. Elad, and A. Bruckstein,“K-SVD: An algorithm for designing over-complete dictionaries for sparse representation,” IEEE Trans. on Signal Process., vol.54, no.11, pp.4311–4322,2006.
[44] M. Bruckstein, D.L. Donoho, and M. Elad,“From sparse solutions of systems ofequations to sparse modeling of signals and images,” SIAM Review, vol.51, no.1, pp.34–81,2009.
[45] D. Mumford and J. Shah,“Optimal approximation by piecewise smooth functions andassociated variational problems,” Comm. on Pure and Appl. Math., vol.42, pp.577–685,1989.
[46] J. Besag,“Spatial Interaction and the Statistical Analysis of Lattice Systems,” Journalof the Royal Statistical Society, Series B (Methodological), vol.36, no.2, pp.192–236,1974.
[47] A. Beck and M. Teboulle,“Fast gradient-based algorithms for constrained total varia-tion image denoising and deblurring problems,” IEEE Trans. on Image Process., vol.18, no.11, pp.2419–2434, Nov.2009.
[48] J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen,“Algorithms and Software forTotal Variation Image Reconstruction via First-Order Methods,” Numerical Algo-rithms, vol.53, pp.67–92,2010.
[49] G. Chantas, N. P. Galatsanos, R. Molina, A. K. Katsaggelos,“Variational Bayesianimage restoration with a product of spatially weighted total variation image priors,”IEEE Trans. Image Process., vol.19, no.2, pp.351–362, Feb.2010.
[50] L. Xu, C. Lu, Y. Xu, and J. Jia,“Image smoothing via L0gradient minimization,”ACM Trans. on Graphics, vol.30, no.6, Dec.2011.
[51] L. Amborsio and V. M. Tortorelli,“Approximation of functionals depending onjumps by elliptic functionals via γ convergence,” Comm. on Pure and Appl. Math.,vol. XLIII, pp.999–1036,1990.
[52] A. Speis, G. Healey,“An analytical and experimental study of the performanceof Markov Random Fields applied to texture images using small samples,” IEEETrans. on Image Processing, vol.5, no.3, pp.447–458, Mar.1996.
[53] X. Zhang and X. Wu,“Image Interpolation by Adaptive2-D Autoregressive Modelingand Soft-Decision Estimation,” IEEE Trans. on Image Processing, vol.17, no.6, pp.887-896, Jun.2008.
[54] Y. Zhang, D. Zhao, S. Ma, R. Wang and W. Gao,“A Motion Aligned Auto-regressiveModel for Frame Rate up Conversion,” IEEE Trans. on Image Processing, vol19, No.5, pp.1248-1258, May.2010.
[55] Y. Zhang, D. Zhao, X. Ji, R. Wang and W. Gao,“A Spatio-temporal Auto-regressiveModel for Frame Rate up Conversion,” IEEE Trans. on Circuits and System VideoTechnology, vol.19, No.9, pp.1289-1301, Sep.2009.
[56] A. A. Efros and T. K. Leung,“Texture synthesis by non-parametric sampling,” Proc.of Int. Conf. Computer Vision, vol.2, pp.1022–1038,1999.
[57] A. Buades, B. Coll, and J. M. Morel,“A non-local algorithm for image denoising,”Proc. of Int. Conf. on Computer Vision and Pattern Recognition,2005.
[58] M. Protter, M. Elad, H. Takeda, and P. Milanfar,“Generalizing the nonlocal-means tosuper-resolution reconstruction,” IEEE Trans. On Image Process., vol.18, no.1, pp.36–51, Jan.2009.
[59] S. Kindermann, S. Osher, and P.W. Jones,“Deblurring and denoising of images bynonlocal functionals,” Multiscale Model. Simul., vol.4, no.4, pp.1091–1115,2005.
[60] F. R. K. Chung. Spectral graph theory, pp.1–212. American Mathematical Society,1997.
[61] G. Gilboa and S. Osher,“Nonlocal operators with applications to image processing,”Multiscale Modeling and Simulation, vol.7, no.3, pp.1005–1028,2008.
[62] G. Peyré, S. Bougleux, and L. Cohen,“Non-local regularization of inverse problems,”Proc. of European Conference on Computer Vision, Marseille-France, Oct.2008.
[63] M. Jung, X. Bresson, T. F. Chan, and L. A. Vese,“Nonlocal Mumford-Shah regular-izers for color image restoration”, IEEE Trans. Image Process., vol.20, no.6, pp.1583–1598, Jun.2011.
[64] J. Sun, M.Tappen. Learning Non-Local Range Markov Random Field for Image Res-toration. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), Colorado,USA,2011.
[65] X. Gao, J. Zhang, F. Jiang, S. Ma, D. Zhao,“Image Interpolation via Local Auto-regressive and Nonlocal3-D Sparse Regularization,” IEEE Visual Communicationsand Image Processing (VCIP2012),2012.
[66] X Zhang, S Ma, Y Zhang, L Zhang, W Gao,“Nonlocal edge-directed interpolation,”Advances in Multimedia Information Processing PCM2009.
[67] T. Peleg, Y.C. Eldar, M. Eladm,“Exploiting Statistical Dependencies in Sparse Rep-resentations for Signal Recovery,” IEEE Transactions on Signal Processing, vol.60,no.5, pp.2286–2303May2012.
[68] M. Elad and M. Aharon,“Image denoising via sparse and redundant representationsover learned dictionaries,” IEEE Trans. Image Process., vol.15, no.12, pp.3736–3745, Dec.2006.
[69] J. Yang, J. Wright, T. Huang, and Y. Ma,“Image super-resolution via sparse repre-sentation,” IEEE Trans. Image Process., vol.19, no.11, pp.2861–2873, Nov.2010.
[70] J. Yang, K. Yu, Y. Gong, and T. Huang,“Linear spatial pyramid matching uisngsparse coding for image classification,” Proc. of IEEE Conference on Computer Vi-sion and Pattern Recognition (CVPR),2009.
[71] J. Wright, Y. Ma, J. Mairal, G. Spairo, T. Huang, S. Yan,"Sparse Representation forComputer Vision and Pattern Recognition,” Proceedings of the IEEE, vol.98, no.6, pp.1031–1044, Jun.2010.
[72] D. L. Donoho and J. M. Johnstone,“Ideal spatial adaptation by wavelet shrink-age,”Biometrika, vol.81, no.3, pp.425–455, September1994.
[73] M. A. T. Figueiredo and R. D. Nowak,“An EM algorithm for wavelet-based imagerestoration,” IEEE Transactions on Image Processing, vol.12, no.8, pp.906–916,August2003.
[74] E. Candès, L. Demanet, D. Donoho, and L. Ying,“Fast discrete curvelet transforms,”Multiscale Model. Sim., vol.5, pp.861–899,2005.
[75] H. Lee, A. Battle, R. Raina, and A. Y. Ng,“Efficient sparse coding algorithms,” inAdvances in Neural Information Processing Systems (NIPS),2007.
[76] K. Engan, S. O. Aase, and J. H. Hakon-Husoy,“Method of optimal directions forframe design,” Proc. of IEEE Int. Conf. Acoust., Speech, Signal Process., vol.5, pp.2443–2446,1999.
[77] Joel A. Tropp and Anna C. Gilbert,“Signal recovery from random measurements viaorthogonal matching pursuit,” IEEE Transactions on Information Theory, vol.53, no.12, pp.4655–4666, Dec.2007.
[78] A. Iusem,“Augmented Lagrangian methods and proximal pointmethods for convexoptimization,” Investigación Operativa, vol.8, pp.11–49,1999
[79] P. Combettes and J.-C. Pesquet,“A Douglas-Rachford splitting approach to non-smooth convex variational signal recovery,” IEEE J. Sel.Topics Signal Process., vol.1, no.4, pp.564–574, Dec.2007.
[80] J. Bioucas-Dias and M. Figueiredo,“A new TwIST: two-step iterative shrink-age/thresholding algorithms for image restoration,” IEEE Trans. on Image Process.,vol.16, no.12, pp.2992–3004, Dec.2007.
[81] J. Eckstein and D. Bertsekas,“On the Douglas–Rachford splitting method and theproximal point algorithm for maximal monotone operators,” Math. Program., vol.5,pp.293–318,1992.
[82] M. Afonso, J. Bioucas-Dias and M. Figueiredo,“Fast image recovery using variablesplitting and constrained optimization,” IEEE Trans. on Image Process., vol.19, no.9,pp.2345–2356, Sep.2010.
[83] S. Chen, D. Donoho, M. Saunders,“Atomic decompositions by basis pursuit,” SIAMReview, vol.43, pp.129–159,2001.
[84] T. Goldstein and S. Osher,“The split Bregman algorithm for L1regularized prob-lems,” SIAM J. Imaging Sci., vol.2, pp.323–343,2009.
[85] J. F. Cai, S. Osher, and Z. W. Shen,“Split Bregman methods and frame based imagerestoration,” Multiscale Model. Simul., vol.8. pp.5057–5071,2009.
[86] W. Yin, S. Osher, D. Goldfarb, and J. Darbon,“Bregman iterative algorithms for L1minimization with applications to compressed sensing,” SIAM J. Imag. Sci., vol.1,pp.143–168,2008
[87] L. Zhang, W. Dong, D. Zhang, G. Shi,“Two-stage image denoising by principlecomponent analysis with local pixel grouping,” Pattern Recognition, vol.43,pp.1531–5549, Apr.2010.
[88] J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman,“Non-local sparse modelsfor image restoration,” Proc. IEEE Int. Conf. Comput. Vis., Tokyo, Japan, Sep.2009.
[89] W. Dong, L. Zhang, G. Shi and X. Li,“Nonlocally Centralized Sparse Representationfor Image Restoration,” IEEE Trans. on Image Processing, vol.22, no.4, pp.1620-1630, Apr.2013.
[90] M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester,“Image in-painting,” Proc. ofSIGGRAPH, pp.417–424,2000.
[91] M. Bertalmio, A. L. Bertozzi, and G. Sapiro,“Navier–Strokes, fluid dynamics, andimage and video inpainting,” Proc. of IEEE Computer Society Conf. Computer Visionand Pattern Recognition,2001.
[92] T. Chan and J. Shen,“Local inpainting models and tv inpainting,” SIAM J. Appl.Math., vol.62, no.3, pp.1019–1043,2001.
[93] T. Chan and J. Shen,“Non-texture inpainting by curvature-driven diffusions,” J. Vis.Commun. Image Represent., vol.4, no.12, pp.436–449,2001.
[94] C. Bertalmio, M. Bertalmio, V. Caselles, G. Sapiro, and J. Verdera,“Filling-in byjoint interpolation of vector fields and gray levels,” IEEE Trans. Image Process., vol.10, no.8, pp.1200–1211, Aug.2001.
[95] A. Levin, A. Zomet, and Y. Weiss,“Learning how to inpaint from global image sta-tistics,” in Proc. of Int. Conf. Comp. Vision, pp.305–312,2003.
[96] S. Roth and M. J. Black,“Fields of experts: A framework for learning image priors,”in Proc. IEEE Computer Society Conf. Computer Vision and Pattern Recognition,2005.
[97] S. Roth and M. J. Black,“Steerable random fields,” in Proc. of IEEE Computer Soci-ety Conf. Computer Vision and Pattern Recognition,2007.
[98] A. Efros and T. Leung,“Texture synthesis by non-parametric sam-pling,” in Proc. ofInt. Conf. Comp. Vision,1999.
[99] M. Bertalmio, L. Vese, G. Sapiro, and S. Osher,“Simultaneous structure and textureimage inpainting,” IEEE Trans. Image Process., vol.12, no.8, pp.882–889, Aug.2003.
[100] A. Criminisi, P. Perez, and K. Toyama,“Object removal by examplar-based imageinpainting,” in of Proc. Int. Conf. Comp. Vision,2003.
[101] J. Wu and Q. Ruan,“Object removal by cross isophotes examplar-based imageinpainting,” in Proc. of Int. Conf. Pattern Recognition,2006.
[102] A. Wong and J. Orchard,“A nonlocal-means approach to examplar-based inpainting,”Proc. of IEEE Int. Conf. Image Processing,2008.
[103] G. T. N. Komodakis,“Image completion using efficient belief propagation via priori-ty scheduling and dynamic pruning,” IEEE Trans. Image Process., vol.16, no.11, pp.2649–2661, Nov.2007.
[104] J. Jia and C. K. Tang,“Image repairing: Robust image synthesis by adaptive nd tensorvoting,” in Proc. of IEEE Computer Society Conf. Computer Vision and PatternRecogition,2003.
[105] I. Drori, D. CohenOr, and H. Yeshurun,“Fragment-based image completion,” ACMTrans. Graph., vol.22, no.3, pp.303–312, Jul.2003.
[106] M. Elad, J. L. Starck, P. Querre, and D. L. Donoho,“Simultaneous cartoon and tex-ture image inpainting using morphological component analysis,” Appl. Comput.Harmon. Anal., vol.19, no.3, pp.340–358, Nov.2005.
[107] O. G. Guleryuz,“Nonlinear approximation based image recovery using adaptivesparse reconstructures and iterated denoising-part i: Theory,” IEEE Trans. ImageProcess., vol.15, no.3, pp.539–554, Mar.2006.
[108] O. G. Guleryuz,“Nonlinear approximation based image recovery using adaptivesparse reconstructures and iterated denoising-part ii: Adaptive algorithms,” IEEETrans. Image Process., vol.15, no.3, pp.555–571, Mar.2006.
[109] M. J. Fadili, J. L. Starck, and F. Murtagh,“Inpainting and zooming using sparse rep-resentations,” The Comput. J., vol.52, no.1, pp.64–79,2009
[110] S. Kaczmarz,“Angenherte auflsung von systemen linearer gleichungen,” Bull. Int.Acad. Polon. Sci. A, vol.355, p.357,1937.
[111] H. Andrews and B. Hunt, Digital Image Restoration. Prentice-Hall,1977.
[112] L. Landweber,“An iteration formula for Fredholm integral equations of the firstkind,” American Journal of Mathematics, pp.615–624,1951.
[113] S. F. Gull and G. J. Daniell,“Image reconstruction from incomplete and noisy da-ta,”Nature, vol.272, pp.686–690, Apr.1978.
[114] L. B. Lucy,“An iterative technique for the rectification of observed distribu-tions,”Astronomical Journal, vol.79, no.6, pp.745–754, Jun.1974.
[115] J. Biemond, R. Lagendijk, and R. Mersereau,“Iterative methods for image deblur-ring,” Proceedings of the IEEE, vol.78, no.5, pp.856–883,1990.
[116] D. Youla,“Generalized image restoration by the method of alternating orthogonalprojections,” IEEE Transactions on Circuits and System, vol.25, no.9, pp.694–702,Sep.1978.
[117] H. Trussell and M. Civanlar,“The feasible solution in signal restoration,” IEEETransactions on Acoustics, Speech and Signal Processing, vol.32, no.2, pp.201–212,Apr1984.
[118] H. Trussell and M. Civanlar,“The landweber iteration and projection onto convexsets,” IEEE Trans. on Acoustics, Speech, and Signal Processing, vol.33, no.6, pp.1632–1634, Dec.1985.
[119] A. Tikhonov and V. Arsenin, Solutions of Ill-posed Problems. New York: Wiley,1977.
[120] G. Aubert and L. Vese,“A variational method in image recovery,”SIAM Journal onNumerical Analysis, vol.34, no.5, pp.1948–1979,1997.
[121] J. M. Bioucas-Dias, M. A. T. Figueiredo, and J. P. Oliveira,“Total variation-basedimage deconvolution: a majorization-minimization approach,” Proc. of Int.. Conf. onAcoustics, Speech and Signal Processing,2006.
[122] S. Babacan, R. Molina, and A. Katsaggelos,“Parameter estimation in TV image res-toration using variational distribution approximation,” IEEE Transactions on ImageProcessing, vol.17, no.3, pp.326–339, Mar.2008.
[123] M. Banham and A. Katsaggelos,“Spatially adaptive wavelet-based multiscale imagerestoration,” IEEE Trans. on Image Proc., vol.5, no.4, pp.619–634, Apr.1996.
[124] R. Neelamani, H. Choi, and R. Baraniuk,“Forward: Fourier-wavelet regularized de-convolution for ill-conditioned systems,”IEEE Transactions on Signal Processing, vol.52, no.2, pp.418–433,2004.
[125] A. Chambolle, R. DeVore, N.-Y. Lee, and B. Lucier,“Nonlinear wavelet image pro-cessing: variational problems, compression, and noise removal through waveletshrinkage,” IEEE Trans. on Image Processing, vol.7, pp.319–335,1998.
[126] G. Steidl, J. Weickert, T. Brox, P. Mrazek, and M. Welk,“On the equivalence of softwavelet shrinkage, total variation diffusion, total variation regularization, andsides,”SIAM J. Numer. Anal., vol.42, no.2, pp.686–713,2004.
[127] A. Danielyan, V. Katkovnik, and K. Egiazarian,“BM3D frames and variational imagedeblurring,” IEEE Trans. Image Process., vol.21, no.4, pp.1715–1728, Apr.2012.
[128] S. M. Smith, J. M. Brady. SUSAN―A New Approach to Low Level Image Pro-cessing. International Journal of Computer Vision. vol.23, no.1, pp.45–78,1997.
[129] C. Tomasi, R. Manduchi. Bilateral filtering for gray and color images. Proc. of IEEEInternational Conference on Computer Vision (ICCV),1998.
[130] D. L. Donoho,“De-noising by soft-thresholding,” IEEE Transactions on InformationTheory, vol41, no.3, pp.613–627,1995.
[131] S. Mallat, S. Zhong,“Characterization of signals from multiscale edges,” IEEETransactions on Pattern Analysis and Machine Intelligence, vol.14, no.7, pp.710–732,1992.
[132] A. P. Witkin,“Scale-Space Filtering,” Proc. of International Joint Conference on Ar-tificial Intelligence (IJCAI),1983.
[133] M. Elad, M.A.T. Figueiredo, Yi Ma,“On the Role of Sparse and Redundant Repre-sentations in Image Processing,” Proceedings of the IEEE, vol98, no.6, pp.972–982,Jun.2010.
[134] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian,“Image denoising by sparse3Dtransform-domain collaborative filtering,” IEEE Trans. on Image Process., vol.16, no.8, pp.2080–2095, Aug.2007.
[135] Y. Dong and S. Xu,“A new directional weighted median filter for removal of ran-dom-valued impulse noise,” IEEE Signal Process. Letters, vol.14, no.3, pp.193–196,2007.
[136] H. Hwang and R. Haddad,“Adaptive median filters: new algorithms and results,”IEEE Trans. on Image Process., vol.4, no.4, pp.499–502,1995.
[137] S. J. Ko and Y. H. Lee,“Center weighted median filters and their applications to im-age enhancement,” IEEE Transactions on Circuits and Systems, vol.39, no.9, pp.984–993,1991.
[138] J. F. Cai, R. Chan, M. Nikolova,“Two-phase methods for deblurring images corrupt-ed by impulse plus Gaussian noise,” Inverse Problem Imaging, vol.2, no.2, pp.187–204,2008.
[139] Y. Huang, M. Ng and Y. Wen,“Fast image restoration methods for impulse andGaussian noise removal,” IEEE Signal Process. Letters, vol.16, no.6, pp.457–460,2009.
[140] Y. Li, L. X. Shen, D. Dai, and B. Suter,“Framelet algorithms for de-blurring imagescorrupted by impulse plus Gaussian noise,” IEEE Trans. on Image Process., vol.20,no.7, pp.1822–1837, Jul.2011.
[141] M. Nikolova,“A variational approach to remove outliers and impulse noise,” Journalof Mathematical Imaging and Vision, vol.20, pp.99–120,2004.
[142] J. F. Cai, R. Chan and M. Nikolova,“Fast two-phase image deblurring under impulsenoise,” Journal of Mathematical Imaging and Vision, vol.36, no.1, pp.46–53,2010.
[143] R. Chan, C. Hu and M. Nikolova,“An iterative procedure for removing ran-dom-valued impulse noise,” IEEE Signal Process. Letters, vol.11, no.12, pp.921–924,2004.
[144] Y. Xiao, T. Zeng, J. Yu and M. Ng,“Restoration of images corrupted by mixedGaussian-impulse noise via L1-L0minimization,” Pattern Recongnition, vol.44, pp.1708–1720,2011.
[145] M. Irani, S. Peleg,“Improving resolution by image registration,” CVGIP: GraphModels Image Process, vol.53, no.3, pp.231–239,1991.
[146] H. Stark, P. Oskoui,“High-resolution image recovery from image-plane arrays, usingconvex projections,” J Opt Soc Am A., vol.6, no.11, pp.1715–1726,1989.
[147] A. M. Tekalp, M. K. Ozkan, M. I. Sezan,“High-resolution image reconstruction fromlower-resolution image sequences and space-varying image restoration,” Proc. IEEEInterna-tional Conference on Acoustics, Speech, and Signal Processing,1992.
[148] R. C. Hardie, K.J. Barnard, E.E. Armstrong,“Joint MAP registration andhigh-resolution image estimation using a sequence of undersampled images,” IEEETransactions on Image Processing, vol.6, no.12, pp.1621–1633, Dec.1997.
[149] H. Shen, L. Zhang, B. Huang, and P. Li,“A MAP Approach for Joint Motion Estima-tion, Segmentation, and Super Resolution,” IEEE Transactions on Image Processing,vol.16, no.2, pp.479–490, Feb.2007.
[150] Y. He, K. Yap, L. Chen, L. Chau,“A nonlinear least square technique for simultane-ous image registration and super-resolution,” IEEE Transactions on Image Processing,vol.16, no.11, pp.2830–2841, Nov.2007.
[151] M. K. Ng, H. Shen, E. Y. Lam, L. Zhang,“A Total Variation Regularization BasedSuper-Resolution Reconstruction Algorithm for Digital Video,” EURASIP J. on Ad-vances in Signal Processing,2007.
[152] Q. Yuan, L. Zhang, H. Shen,“Multi-frame Super-resolution Employing a SpatiallyWeighted Total Variation Model,” IEEE Trans Circuits Syst Video Technol, vol.22.no.3, pp.379–392, Mar.2011.
[153] J. Sun, J. Sun, Z. Xu, H. Shum,“Image super-resolution using gradient profile prior,”Proc. of Computer Vision and Pattern Recognition,2008.
[154] T. Katsuki, A. Torii, M. Inoue,“Posterior-Mean Super-Resolution With a CausalGaussian Markov Random Field Prior,” IEEE Trans Image Processing, vol.21. no.7,pp.3182–3193, Jul.2012.
[155] J. Sun, N. Zheng, H. Tao, H. Shum,“Image hallucination with primal sketch priors,”Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recog-nition (CVPR),2003.
[156] W. T. Freeman, E.C. Pasztor, O.T. Carmichael,“Learning Low-Level Vision,” Inter-national Journal of Computer Vision, vol.40, no.1, pp.25–47,2000.
[157] W.T. Freeman, E.C. Pasztor,“Learning low-level vision,” Proc. IEEE InternationalConference on Computer Vision (ICCV),1999.
[158] H. Chang, D. Yeung, Y. Xiong,“Super-resolution through neighbor embedding,”Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recogni-tion (CVPR),2004.
[159] D. Capel, A. Zisserman,“Super-resolution from multiple views using learnt imagemodels,” Proc. IEEE Computer Society Conference on Computer Vision and PatternRecognition (CVPR).2001,
[160] R. Zeyde, M. Elad, and M. Protter,“On Single Image Scale-Up usingSparse-Representations,” Curves&Surfaces, Avignon France, June,2010.
[161] D. L. Donoho,“Compressed sensing,” IEEE Trans. Inform. Theory, vol.52, no.4, pp.1289–1306,2006.
[162] E. Candès, J. Romberg, and T. Tao,“Robust uncertainty principles: Exact signal re-construction from highly incomplete frequency information,” IEEE Trans. Inform.Theory, vol.52, pp.489–509,2006.
[163] M. Davenport, M. F. Duarte, Y. C. Eldar and G. Kutyniok, Compressed Sensing:Theory and Applications, Cam-bridge University Press,2011.
[164] M. Duarte, M. Davenport, D. Takhar, J. Laska, and T. Sun,“Single-pixel imaging viacompressive sampling,” IEEE Signal Processing Magazine, vol.25, no.2, pp.83–91,2008.
[165]李树涛,魏丹,“压缩传感综述,”自动化学报，vol.35, no.11, pp.1369–1137,2009.
[166]刘丹华，石光明，周佳社，高大化，吴家骥,“基于Compressed Sensing框架的图像多描述编码方法,”红外与毫米波学报, vol.28, no.4, pp.298-302, Aug.2009.
[167] S. Mun and J. E. Fowler,“Block compressive sensing of images using directionaltransforms,” Proc. of IEEE Int. Conf. Image Process.,2009.
[168] L. He, H. Chen and L. Carin,“Tree-structured compressive sensing with variationalBayesian analysis,” IEEE Signal Processing Letter, vol.17, no.3, pp.233–236,2010.
[169] l1-Magic Toolbox available at http://users.ece.gatech.edu/~justin/l1magic/.
[170] C. Li, W. Yin, and Y. Zhang,“TVAL3: TV Minimization by Augmented Lagrangianand Alternating Direction Algorithm,”2009.
[171] L. He and L. Carin,“Exploiting structure in wavelet-based Bayesian compressivesensing,” IEEE Trans. Signal Process., vol.57, no.9, pp.3488–3497,2009.
[172] Y. Kim, M. S. Nadar and A. Bilgin,“Compressive sensing using a Gaussian scalemixtures model in wavelet do-main,” Proc. of IEEE Int. Conf. Image Process., pp.3365–3368,2010.
[173] X. Wu, X. Zhang and J. Wang,“Model-guided adaptive recovery of compressivesensing,” Proc. of IEEE Data Compression Conf.,2009.
[174] C. Chen, E. W. Tramel, and J. E. Fowler,“Compressed-sensing recovery of imagesand video using multihy-pothesis predictions,” Proc. of the45th Asilomar Conferenceon Signals, Systems, and Computers, Pacific Grove, CA, pp.1193–1198, Nov.2011.
[175] J. Zhang, D. Zhao, C. Zhao, R. Xiong, S. Ma and W. Gao,“Image compressive sens-ing recovery via collaborative sparsity,” IEEE Journal on Emerging and SelectedTopics in Circuits and Systems, vol.2, no.3, pp.380–391, Sep.2012.
[176] M. K. Varanasi, B. Aazhang,“Parametric generalized Gaussian density estimation,” J.Acoust. Soc. Amer., vol.86, no.4, pp.1404–1415,1989.
[177] M. Zhou, H. Chen, J. Paisley, L. Ren, L. Li, Z. Xing, D. Dunson, G. Sapiro and L.Carin,“Nonparametric Bayesian dictionary learning for analysis of noisy and incom-plete images,” IEEE Trans. Image Processing, vol.21, no.1, pp.130–144, Jan.2012.
[178] J. Portilla,“Image restoration through l0analysis-based sparse optimization in tightframes,” IEEE Int. conf. Image Process., pp.3909-3912, Nov.2009.
[179] H. Takeda, S. Farsiu, P. Milanfar,“Deblurring using regularized locally-adaptivekernel regression,” IEEE Transactions on Image Processing, vol.17, no.4, pp.550–563, Apr.2008.