高性能图像超分辨率方法的研究
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摘要
随着计算机技术与信息处理技术的飞速发展，人们越来越发现利用现有硬件技术，提高信息获取质量的重要性。如何通过软件的方式突破图像固有信息的限制，提高图像分辨率，从而获得更多图像的高频细节信息，具有重要的研究意义与应用价值。
在上述背景下，本文针对现有图像超分辨率重建方法在分辨率提升倍数较大时，算法复杂度高，重建效果不稳定的问题，研究并实现可针对通用图像的高性能超分辨率图像重建方法，主要研究成果包括：
提出了基于主元分析与高斯加权欧式距离的快速图像配准方法PCA-SIFT-Gaussian。首先分析了特征提取与特征匹配的常用方法及具有竞争力的传统SIFT方法的四个主要步骤：图像尺度空间的建立、精确定位极值点、关键点方向分配和SIFT特征描述子的生成，使提取的特征对图像间发生平移、旋转、仿射变换、视角变换、光照变换等具有较好的不变性。针对传统SIFT算法中128维特征向量占用存储空间大，匹配耗时多等问题，围绕关键点的41×41的邻域内形成3042维特征向量，引入主元分析法对多维数据进行降维，完成特征提取。在特征匹配过程中采用高斯加权欧式距离代替传统的欧式距离进行阈值判定。实验结果证明，本文算法在保持较高性能的同时，特征提取速度相比传统SIFT方法提升约40%。对高斯噪声、旋转与尺度变化、仿射变换及光照变化等具有更高的鲁棒性。
提出具有更快词典训练速度与重建精度的基于小波多分辨率分析的超分辨率图像重建方法。首先分析了稀疏表示法中三个重要步骤：建立图像降质模型、局部约束块稀疏表示、全局约束稀疏表示。针对稀疏表示法中训练过完备联合词典对计算量较大，算法耗时的问题，提出采用提升小波变换分解词典素材为个低频分量和三个高频分量，通过第二层和第三层提升小波变换后的高频分量估计出第层的高频分量，从而节约75%的像素数，降低训练词典的时间。在局部先验约束中特征提取算子F的选择上，采用PCA-SIFT-Gaussian代替传统维梯度高频滤波器以获得更多的高频细节。实验结果证明，本文算法与传统方法比较可缩短词典训练时间60%以上，且具有更高的重建精度。
提出同时具备填补矩阵丢失元素与修复受损元素功能的新方法。首先通过比较不同矩阵填充与矩阵恢复主流方法，引入具有优越的收敛性及求解精度的增广拉格朗日乘子法，提出同时具备矩阵填充与矩阵恢复功能的新方法——双非精确增广拉格朗日乘子法（Dual-IALM）。实验结果表明，该方法具有迭代次数少、速度快、精度高的特点及较强的抗噪能力，通过该方法可较好地解决图像去噪与图像融合问题等实际应用问题。
实现了由个或多个摄像头捕捉的具有亚像素位移的连续多帧低分辨率图像序列的高性能图像超分辨率重建系统。首先通过多帧图像配准方法PCA-SIFT-Gaussian对齐LR观测图像，然后采用第三章提出的改进的稀疏表示法训练联合词典对，并建立块稀疏表示和全局约束稀疏表示，生成初步重建的HR图像序列。最后采用Dual-IALM对图像序列构造的观测矩阵进行矩阵填充与矩阵恢复，将输出的低秩矩阵按照光栅扫描顺序重构为最终的HR图像。为了进
步优化软件系统，预先保存配准后的特征向量，直接在特征提取算子F中使用。此外，本文引入Ring-Jacobi排序法取代传统的Round-Robin排序法减少并行算法中奇异值分解的迭代次数。实验结果证明，本文提出的新方法SRMCR相比当前其它主流超分辨率重建方法，在分辨率提升四倍以上时，仍保留丰富的图像细节，重建HR图像的峰值信噪比平均值高于其它方法5.04dB至6.28dB，且不易受词典训练素材选择范围的影响，能有效处理针对通用图像的高性能超分辨率重建问题，可应用于遥感图像超分辨率重建等机器视觉领域。
With the rapid development of computer technology and information processingtechnology, people are increasingly found the importance of improving the quality ofthe information by using existing hardware technology. How to enhance the imageresolution through limit of the inherent information of the image, thereby obtainingmore high-frequency image details, which has important significance researching andapplication value.
Based on the abovementioned background, to solve the complexity of thecomputation and unstable reconstruction effect in traditional super resolution methods,one high performance super resolution general-purpose images reconstruction methodis achieved in this paper in the following aspects:
A fast image registration method, namely PCA-SIFT-Gaussian is proposed basedon Principal Component Analysis and Gaussian weighted Euclidean distance. Firstly,we introduced the most popular methods of feature extraction and matching. There arefour main steps to extract features by SIFT, Establishment of scale space, detection ofextrema, orientation assignment and generation of SIFT descriptor. To solve the largestorage space and matching time-consuming issues, we introduced3042dimensionalfeature vector surrounding the41×41pixels’ neighborhood. Then, PCA is achieved toreduce the multi-dimensional data instead of old128dimensional feature vectors. Inthe process of feature matching, we used Gaussian weighted Euclidean to replacetraditional Euclidean distance, which will meet the human visual characteristics better.Experimental results show that the proposed algorithm is more effective with fasterapproximately40%speed of feature extraction and matching compared to othermainstream image registration methods. It has higher robustness to Gaussian noise,rotation, and scale changes, affine transformation and illumination variation.
An effective super resolution image reconstruction method with faster speed oftraining joint dictionary pair is proposed. This method is based on Lifting WaveletTransform and sparse representation. According to the three main steps of sparse representation, which are image degradation model, local constraints with patchessparse representation, and global constraints, we improved the process of trainingjoint dictionary pair. High-frequency components of the image can be estimated bycalculating only25%pixels in the whole image. That means this presented methodsave up to75%time to train dictionary. On the other hand, PCA-SIFT-Gaussianpresented before is used to achieve the feature extraction factor F instead oftraditional one-dimensional gradient high-pass filter. Experimental results show thatthe proposed algorithm can effectively shorten the dictionary training time by morethan60%, and has higher reconstruction accuracy.
A new compressed sensing method, namely Dual-IALM, is proposed to achievematrix completion and matrix recovery simultaneously. After comparing allmainstream methods of matrix completion and matrix recovery, we introduced theAugmented Lagrangian Multiplier method, which has superior convergence andaccuracy and present a new method with this two matrix functions——Dual InexactAugmented Lagrangian Multiplier, abbreviated as Dual-IALM. Experimental resultsshow that this method has fewer iterations times, higher accuracy and strongeranti-noise ability, this method can solve the practical application of image denoisingand image fusion effectively.
A high performance image super resolution reconstruction system is achieved formulti-frame sub-pixel displacement low-resolution image sequences captured by oneor more sensors. Super-resolved reconstruction of images can yield poor results in theabsence of extensively-trained related dictionaries. A super-resolution algorithm ispresented which remedies this problem by exploiting recent results from the work onsparse representation and matrix completion. An over-complete dictionary pair istrained using natural image data. Sparse coefficients of low-resolution image patchesare estimated using local prior constraints. In multi-frame images, sparse coefficientsare similar across frames, and the Inexact Augmented Lagrange Multiplier method isemployed to achieve matrix completion and recovery in the process of imposingglobal constraints. Furthermore, we optimize the system with keeping thePCA-SIFT-Gaussian descriptor and introducing Ring-Jacobi ordering to accelerate the singular value decomposition. The final high-resolution image is generated from theoutput low-rank matrix. Experiments reveal that the method yields higher PSNR value(from5.04dB to6.28dB)than other mainstream SR algorithms, produces perceptiblysuperior edges and details, and is more robust to dictionary insufficiency which can becan be applied to the field of remote sensing and machine vision.
在上述背景下，本文针对现有图像超分辨率重建方法在分辨率提升倍数较大时，算法复杂度高，重建效果不稳定的问题，研究并实现可针对通用图像的高性能超分辨率图像重建方法，主要研究成果包括：
提出了基于主元分析与高斯加权欧式距离的快速图像配准方法PCA-SIFT-Gaussian。首先分析了特征提取与特征匹配的常用方法及具有竞争力的传统SIFT方法的四个主要步骤：图像尺度空间的建立、精确定位极值点、关键点方向分配和SIFT特征描述子的生成，使提取的特征对图像间发生平移、旋转、仿射变换、视角变换、光照变换等具有较好的不变性。针对传统SIFT算法中128维特征向量占用存储空间大，匹配耗时多等问题，围绕关键点的41×41的邻域内形成3042维特征向量，引入主元分析法对多维数据进行降维，完成特征提取。在特征匹配过程中采用高斯加权欧式距离代替传统的欧式距离进行阈值判定。实验结果证明，本文算法在保持较高性能的同时，特征提取速度相比传统SIFT方法提升约40%。对高斯噪声、旋转与尺度变化、仿射变换及光照变化等具有更高的鲁棒性。
提出具有更快词典训练速度与重建精度的基于小波多分辨率分析的超分辨率图像重建方法。首先分析了稀疏表示法中三个重要步骤：建立图像降质模型、局部约束块稀疏表示、全局约束稀疏表示。针对稀疏表示法中训练过完备联合词典对计算量较大，算法耗时的问题，提出采用提升小波变换分解词典素材为个低频分量和三个高频分量，通过第二层和第三层提升小波变换后的高频分量估计出第层的高频分量，从而节约75%的像素数，降低训练词典的时间。在局部先验约束中特征提取算子F的选择上，采用PCA-SIFT-Gaussian代替传统维梯度高频滤波器以获得更多的高频细节。实验结果证明，本文算法与传统方法比较可缩短词典训练时间60%以上，且具有更高的重建精度。
提出同时具备填补矩阵丢失元素与修复受损元素功能的新方法。首先通过比较不同矩阵填充与矩阵恢复主流方法，引入具有优越的收敛性及求解精度的增广拉格朗日乘子法，提出同时具备矩阵填充与矩阵恢复功能的新方法——双非精确增广拉格朗日乘子法（Dual-IALM）。实验结果表明，该方法具有迭代次数少、速度快、精度高的特点及较强的抗噪能力，通过该方法可较好地解决图像去噪与图像融合问题等实际应用问题。
实现了由个或多个摄像头捕捉的具有亚像素位移的连续多帧低分辨率图像序列的高性能图像超分辨率重建系统。首先通过多帧图像配准方法PCA-SIFT-Gaussian对齐LR观测图像，然后采用第三章提出的改进的稀疏表示法训练联合词典对，并建立块稀疏表示和全局约束稀疏表示，生成初步重建的HR图像序列。最后采用Dual-IALM对图像序列构造的观测矩阵进行矩阵填充与矩阵恢复，将输出的低秩矩阵按照光栅扫描顺序重构为最终的HR图像。为了进
步优化软件系统，预先保存配准后的特征向量，直接在特征提取算子F中使用。此外，本文引入Ring-Jacobi排序法取代传统的Round-Robin排序法减少并行算法中奇异值分解的迭代次数。实验结果证明，本文提出的新方法SRMCR相比当前其它主流超分辨率重建方法，在分辨率提升四倍以上时，仍保留丰富的图像细节，重建HR图像的峰值信噪比平均值高于其它方法5.04dB至6.28dB，且不易受词典训练素材选择范围的影响，能有效处理针对通用图像的高性能超分辨率重建问题，可应用于遥感图像超分辨率重建等机器视觉领域。
With the rapid development of computer technology and information processingtechnology, people are increasingly found the importance of improving the quality ofthe information by using existing hardware technology. How to enhance the imageresolution through limit of the inherent information of the image, thereby obtainingmore high-frequency image details, which has important significance researching andapplication value.
Based on the abovementioned background, to solve the complexity of thecomputation and unstable reconstruction effect in traditional super resolution methods,one high performance super resolution general-purpose images reconstruction methodis achieved in this paper in the following aspects:
A fast image registration method, namely PCA-SIFT-Gaussian is proposed basedon Principal Component Analysis and Gaussian weighted Euclidean distance. Firstly,we introduced the most popular methods of feature extraction and matching. There arefour main steps to extract features by SIFT, Establishment of scale space, detection ofextrema, orientation assignment and generation of SIFT descriptor. To solve the largestorage space and matching time-consuming issues, we introduced3042dimensionalfeature vector surrounding the41×41pixels’ neighborhood. Then, PCA is achieved toreduce the multi-dimensional data instead of old128dimensional feature vectors. Inthe process of feature matching, we used Gaussian weighted Euclidean to replacetraditional Euclidean distance, which will meet the human visual characteristics better.Experimental results show that the proposed algorithm is more effective with fasterapproximately40%speed of feature extraction and matching compared to othermainstream image registration methods. It has higher robustness to Gaussian noise,rotation, and scale changes, affine transformation and illumination variation.
An effective super resolution image reconstruction method with faster speed oftraining joint dictionary pair is proposed. This method is based on Lifting WaveletTransform and sparse representation. According to the three main steps of sparse representation, which are image degradation model, local constraints with patchessparse representation, and global constraints, we improved the process of trainingjoint dictionary pair. High-frequency components of the image can be estimated bycalculating only25%pixels in the whole image. That means this presented methodsave up to75%time to train dictionary. On the other hand, PCA-SIFT-Gaussianpresented before is used to achieve the feature extraction factor F instead oftraditional one-dimensional gradient high-pass filter. Experimental results show thatthe proposed algorithm can effectively shorten the dictionary training time by morethan60%, and has higher reconstruction accuracy.
A new compressed sensing method, namely Dual-IALM, is proposed to achievematrix completion and matrix recovery simultaneously. After comparing allmainstream methods of matrix completion and matrix recovery, we introduced theAugmented Lagrangian Multiplier method, which has superior convergence andaccuracy and present a new method with this two matrix functions——Dual InexactAugmented Lagrangian Multiplier, abbreviated as Dual-IALM. Experimental resultsshow that this method has fewer iterations times, higher accuracy and strongeranti-noise ability, this method can solve the practical application of image denoisingand image fusion effectively.
A high performance image super resolution reconstruction system is achieved formulti-frame sub-pixel displacement low-resolution image sequences captured by oneor more sensors. Super-resolved reconstruction of images can yield poor results in theabsence of extensively-trained related dictionaries. A super-resolution algorithm ispresented which remedies this problem by exploiting recent results from the work onsparse representation and matrix completion. An over-complete dictionary pair istrained using natural image data. Sparse coefficients of low-resolution image patchesare estimated using local prior constraints. In multi-frame images, sparse coefficientsare similar across frames, and the Inexact Augmented Lagrange Multiplier method isemployed to achieve matrix completion and recovery in the process of imposingglobal constraints. Furthermore, we optimize the system with keeping thePCA-SIFT-Gaussian descriptor and introducing Ring-Jacobi ordering to accelerate the singular value decomposition. The final high-resolution image is generated from theoutput low-rank matrix. Experiments reveal that the method yields higher PSNR value(from5.04dB to6.28dB)than other mainstream SR algorithms, produces perceptiblysuperior edges and details, and is more robust to dictionary insufficiency which can becan be applied to the field of remote sensing and machine vision.
引文
[1] Park S C, Park M K, Kang M G. Super-resolution image reconstruction: a technical overview.IEEE Signal Processing Magazine.2003,20(3):21-36.
[2]张良培,沈焕锋,张洪艳等.图像超分辨率重建.科学出版社.2012.
[3] Tsai R Y, Huang T S. Multipleframe image restoration and registration. In Advances inComputer Vision and Image Processing.1984,1:317-339.
[4] Patti A J, Sezan M I, Tekalp A M. High-resolution Standards Conversion of Low ResolutionVideo. In Proceedings of IEEE International Conference of ASSP, Detroit, USA.1995:2197~2200.
[5] Elad M, Feuer A. Restoration of a Single Superresolution Image from Several Blurred, Noisy,and Undersampled Measured Images. IEEE Trans IP.1997,6(12):1646~1658.
[6]赵进创，傅文利，胡强，等．电容层析成像系统成像质量的实验分析．自动化仪表．2003，24(10):18-20.
[7] Harris J L. Diffraction and Resolving Power. Journal of the Optical Society of America.1964,54(7):931-936.
[8] Keren D, Peleg S, Brada R. Image sequence enhancement using subpixel displacements. InProceedings of IEEE International Conference of CVPR, Ann Arbor, USA.1988:742-746.
[9] Ur H, Gross D. Improved resolution from subpixel shifted pictures. CVGIP: GraphicalModels and Image Processing.1992,54(2):181-186.
[10] Yen L J. On non-uniform sampling of bandwidth limited signals. IRE Transactions onCircuits Theory.1956,3(4):251-257.
[11] Nguyen N, Milanfar P. An efficient wavelet-based algorithm for image super-resolution. InProceedings of International Conference on Image Processing, Canada.2000:351-354.
[12] Alam M S, Bognar J G, Hardie R C, et al. Infrared image registration and high-resolutionreconstruction using multiple translationally shifted aliased video frames. IEEE Transactionson Instrumentation and Measurement.2000,49(5):915-923.
[13] Elad M, Hel-Or Y. A fast super-resolution reconstruction algorithm for pure translationalmotion and common space-invariant blur. IEEE Transactions on Image Processing.2001,10(8):1187-1193.
[14] Takeda H, Farsiu S, Milanfar P. Kernel regression for image processing and reconstruction.IEEE Transactions on Image Processing.2007,16(2):349-366.
[15] Kim T R, Yang J S W, Shin S, et al. Statistical torsion angle potential (STAP) energyfunctions for protein structure modeling: A bicubic interpolation approach. Proteins: Structure,Function, and Bioinformatics,2013.
[16] Irani M, Peleg S. Super Resolution From Image Sequences. In Proceedings of InternationalConference of PR, Atlantic City, USA.1990:115-120.
[17] Irani M, Peleg S. Improving resolution by image registration. CVGIP: Graphical Models andImage Processing.1991:53(3):231-239.
[18] Stark H, Oskoui P. High-resolution image recovery from image-plane arrays, using convexprojections. Journal of the Optical Society of America A.1989,6(11):1715-1726.
[19] Schultz R R, Stevenson R L. Extraction of high-resolution frames from video sequences.IEEE Transactions on Image Processing.1996,5(6):996-1011.
[20] Hardie R C, Barnard K J, and Armstrong E E. Join MAP registration and high resolutionimage estimation using a sequence of undersampled images. IEEE Transactions on ImageProcessing.1997,6(12):1621-1633.
[21] Elad M, Feuer A. Super-resolution reconstruction of an image. In Proceedings ofInternational Conference of Electrical and Electronics Engineers, Israel.1996:391-394.
[22] Elad M, Feuer A. Restoration of a single superresolution image from several blurred, noisy,and undersampled measured images. IEEE Transactions on Image Processing.1997,6(12):1646-1658.
[23] Patti A J, Sezan M I, Tekalp A M. Superresolution Video Reconstruction with ArbitrarySampling Lattices and Nonzero Aperture Time. IEEE Transactions on Image Processing.1997,6(8):1064~1076.
[24] Patti A J, Sezan M I, Tekalp A M. Robust Methods for High-quality Stills from InterlacedVideo in the Presence of Dominant Motion. IEEE Transactions on Circuits and Systems forVideo Technology.1997,7(2):328~342.
[25] Eren P E, Sezan M I, Tekalp A M. Robust, object-based high-resolution image reconstructionfrom low-resolution video. IEEE Transactions on Image Processing.1997,6(10):1446~1451.
[26] Freeman W T, Jones T R, Pasztor E C. Example-based super resolution. IEEE ComputerGraphics and Applications.2002,22(2):56-65.
[27] Chang H, Yeung D Y, Xiong Y. Super-resolution through neighbor embedding. Proceedingsof IEEE Computer Society Conference on Computer Vision and Pattern Recognition,Washington DC., USA.2004,1:275-282.
[28] Ni K S, Nguyen T Q. Image super resolution using support vector regression. IEEETransactions on Image Processing.2007,16(6):1596-1610.
[29] Liu C, Shum H Y, Freeman W T. Face hallucination: theory and practice. InternationalJournal of Computer Vision.2007,75(1):115-134.
[30] Yang J C, Wright J, Ma Y. Image Super-Resolution via Sparse Representation. IEEETransactions on Image Processing.2010,19(11):2861-2873.
[31] Zeyde R, Elad M, Protter M. On single image scale-up using sparse-representations.Proceedings of the7th international conference on Curves and Surfaces, Avignon, France.2010:711-730.
[32] Shum H Y, Szeliski R. Panoramic image mosaicing. Technical Report MSR-TR-97-23,Microsoft Research,1997.
[33] Zoghlami I, Faugeras O, Deriche R. Using geometric corners to build a2D mosaic from a setof images. In Proceedings of IEEE International Conference of CVPR, Los Alamitos, USA.1997:420-425.
[34] Harris C, Stephens M J. A combined corner and edge detector. Proceedings of The FourthAlvey Vision Conference, UK.1988:147-152.
[35] Faille F. A fast method to improve the stability of interest point detection under illuminationchanges. In Proceedings of International Conference of IP, Singapore.2004:2673-2676.
[36] Sunil A, David M M, Nathan S N, et al. An optimal algorithm for approximate nearestneighbor searching fixed dimensions. Journal of the ACM.1998,45(6):891-923.
[37] Lowe D G. Distinctive image features from scale-invariant keypoints. International Journal ofComputer Vision.2004,60(2):91-110.
[38] Mikolajczyk K, Schmid C. A performance evaluation of local descriptors. IEEE Trans PatternAnalysis and Machine Intelligence.2005,27(10):1615-1630.
[39] Bay H, Ess A, Tuytelaars T, et al. SURF: Speeded Up Robust Features. Computer Vision andImage Understanding.2008,110(3):346-359.
[40] Lowe D G. Object recognition m local scale-invariant features. Proceedings of IEEEInternational Conference on CV, Kerkyra, Greece.1999,2:1150-1157.
[41] Brown M, Lowe D G. Invariant features from interest point groups. Proceedings of BritishMachine Vision Conference, Wales.2002:656-665.
[42] Wold S, Esbensen K, Geladi P. Principal component analysis. Chemometrics and IntelligentLaboratory Systems.1987,2(1-3):37-52.
[43]陆欢,吴庆宪,姜长生.基于PCA与小波变换的彩色图像融合算法.计算机仿真.2007,24(9):202~205.
[44] Smith L I. A tutorial on Principal Components Analysis. Systems Neurobiology.2002.
[45] Wall M E, Rechtsteiner A, Rocha L M. Singular Value Decomposition and PrincipalComponent Analysis. A Practical Approach to Microarray Data Analysis.2003:91-109.
[46] Helen M, Virtanen T. Query by Example of Audio Signals using Euclidean Distance BetweenGaussian Mixture Models. Proceedings of IEEE International Conference on ASSP, Honolulu,USA.2007,1:225-228.
[47] Juan L, Gwon O. A Comparison of SIFT, PCA-SIFT and SURF. International Journal ofImage Processing.2009,3(4):143-152.
[48] He X, Niyogo P. Locality preserving projections. Advances in Neural Information ProcessingSystems.2003,16:153-160.
[49] Dagum P, Luby M. Approximating probabilistic inference in Bayesian belief networks isNP-hard. Artificial Intelligence.1993,60(1):141-153.
[50] Donoho D L. For most large underdetermined systems of linear equations the minimal1-norm solution is also the sparsest solution. Communications on Pure and AppliedMathematics.2006,59(6):797–829.
[51] Donoho D L. For most large underdetermined systems of equations, the minimal1-normnear-solution approximates the sparsest near-solution. Communications on Pure and AppliedMathematics.2006,59(7):907–934.
[52] Grossmann A, Morlet J. Decomposition of Hardy Functions into Square Integrable Waveletsof Constant Shape. SIAM Journal on Mathematical Analysis.1984,15(4):723-736.
[53]李建平,杨万年译.小波十讲.国防工业出版社,2004.
[54] Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in AppliedMathematics, Philadelphia, USA.1992,61.
[55] Gabor D. Theory of communication. Part1: The analysis of information. Journal of theInstitution of Electrical Engineers.1946,93(26):429-441.
[56] Nyquist H. Certain topics in telegraph transmission theory. Proceedings of the IEEE.2002,90(2):280-305.
[57] Liu C. A tutorial of the wavelet transform.2010.
[58] Sweldens W. The lifting scheme: a const ruction of second generation wavelets. SIAM J.Math. Anal.1997,29(2):511-546.
[59]罗少鹏,卢洵.基于提升小波和人眼视觉特性的自反馈彩色图像融合.红外技术.2008,30(1):31-34.
[60] Shapiro J M. Embedded image coding using zerotrees of wavelet coefficients. IEEETransactions on Signal Processing.1993,41(12):3445-3462.
[61] Candes E J, Romberg J K, Tao T. Stable signal recovery from incomplete and inaccuratemeasurements. Communications on Pure and Applied Mathematics.2006,59(8):1207-1223.
[62] Candes E J, Recht B. Exact matrix completion via convex optimization. Foundations ofComputational Mathematics.2009,9(6):717-772.
[63] Candes E J, Plan Y. Matrix Completion with Noise. Proceedings of the IEEE.2010,98(6):925-936.
[64] Cai J, Candes E J, Shen Z. A Singular Value Thresholding Algorithm for Matrix Completion.SIAM J. Optim.2010,20(4):1956-1982.
[65] Toh K C, Yun S W. An accelerated proximal gradient algorithm for nuclear norm regularizedleast squares problems. Eprints for The Optimization Community.2009.
[66] Candes E J, Li X, Ma Y. Robust principal component analysis. Journal of the ACM.2011,58(3): Article No.11.
[67] Hu Y, Zhang D, Liu J, et al. Accelerated singular value thresholding for matrix completion. InProceedings of the18th ACM SIGKDD International Conference on KDD, Beijing, China.2012:298-306.
[68] Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverseproblems. SIAM Journal on Imaging Sciences.2008,2(1):183-202.
[69] Bertsekas D P. Constrained Optimization and Lagrange Multiplier Method. Academic Press.1982.
[70] Sorensen D C. The Q-Superlinear Convergence of a Collinear Scaling Algorithm forUnconstrained Optimization. SIAM J. Numer. Anal.1980,17(1):84-114.
[71] Wright J, Ganesh A, Rao S, et al. Robust principal component analysis: Exact recovery ofcorrupted low-rank matrices via convex optimization. In Advances in Neural InformationProcessing Systems22.2009.
[72] Ganesh A, Lin Z, Wright J, et al. Fast algorithms for recovering a corrupted low-rank matrix.IEEE International Workshop on CAMSAP, Netherlands.2009:213-216.
[73] Cho K, Reyhani N. An iterative algorithm for singular value decomposition on noisyincomplete matrices. The2012International Joint Conference on Neural Networks, Australia.2012:1-6.
[74] Lin Z, Chen M, Ma Y. An accelerated proximal gradient algorithm for frame-Based imagerestoration via the balanced approach. SIAM Journal on Imaging Sciences.2011,4(2):573–596.
[75] Kenney C S, Laub A J. The matrix sign function. IEEE Transactions on Automatic Control.1995,40(8):1330-1348.
[76]夏明革,何友,唐小明等.多传感器图像融合综述.电光与控制.2002,9(4):1-7.
[77] Johnson J L. PCNN models and applications. IEEE Transactions on Neural Networks.1999,10(3):480-498.
[78]李建锋,邹北冀,辛国江等.种自适应PCNN图像融合方法.中南大学学报（自然科学版）.2011,42(7):2004-2010.
[79]牛晓晖,贾克斌.基于PCA和自适应区域方差的图像融合方法.计算机应用研究.2010,27(8):3179-3181.
[80] Wang Z, Jia K, Liu W. Different Frequency Processing of Image Fusion Based on LiftingWavelet Transform. Journal of Computational Information Systems.2012,8(20):8463-8470.
[81] Qu G, Zhang D, Yan P. Information measure for performance of image fusion. ElectronicsLetters.2002,38(7):313-315.
[82]阳方林,郭红阳,杨风暴.像素级图像融合效果的评价方法研究.测试技术学报.2002,16(4):276-279.
[83] Gonzalez-Audicana M, Saleta J L, Catalan R G. Fusion of multispectral and panchromaticimages using improved IHS and PCA mergers based on wavelet decomposition. IEEETransactions on Geoscience and Remote Sensing.2004,42(6):1291-1299.
[84] Yin H, Li S, Fang L. Simultaneous image fusion and super-resolution using sparserepresentation. Information Fusion.2013,14(3):229-240.
[85] Xydeas C S, Petrovic V. Objective image fusion performance measure. Electronics Letters.2000,36(4):308-309.
[86] Li H, Chai Y, Yin H, et al. Multifocus image fusion and denoising scheme based onhomogeneity similarity. Optics Communications.2012,285(2):91-100.
[87] Hwang H, Haddad R A. Adaptive median filters: new algorithms and results. IEEE Trans. onImage Processing.1995,4(4):499-502.
[88] Gelado I, Kelm J H, Ryoo S, et al. CUBA: an architecture for efficient CPU/co-processordata communication. In Proceedings of the22nd annual international conference onSupercomputing, Greece.2008:299-308.
[89] Businger P A, Golub G H. Algorithm358: singular value decomposition of a complex matrix[F1,4,5]. Communications of the ACM.1969,12(10):564-565.
[90] Demmel J W, Kahan W. Accurate singular values of bidiagoanl matrices. SIAM: SIAMJournal on Scientific Computing.1990,11(5):873-912.
[91] Gu M, Eisenstat S C. A divide-and-conquer algorithm for the bidiagonal SVD. SIAM Journalon Matrix Analysis and Applications.1995,16(1):79-92.
[92] Becka M, Oksa G, Vajtersic M. Dynamic ordering for a parallel block-Jacobi SVD algorithm.Parallel Computing.2002,28(2):243-262.
[93] Becka M, Oksa G. On variable blocking factor in a parallel dynamic block-Jacobi SVDalgorithm. Parallel Computing.2003,29(9):1153-1174.
[94] Hahne E L, AT&T Bell Lab. Round-robin scheduling for max-min fairness in data networks.IEEE Journal on Selected Areas in Communications.1991,9(7):1024-1039.
[95] Zhou B B, Brent R P. A parallel ring ordering algorithm for efficient one-sided Jacobi SVDcomputations. Journal of Parallel and Distributed Computing.1997,42(1):1-10.
[96] Drma Z, Veseli K. New Fast and Accurate Jacobi SVD Algorithm. I. SIAM. J. Matrix Anal.&Appl.2008,29(4):1322-1342.
[97] Kerr A, Campbell D, Richards M. QR decomposition on GPUs. In Proceedings of2ndWorkshop on General Purpose Processing on Graphics Processing Units, Washington, DC,USA.2009:71-78.
[98] Farrell J, Shapiro C, Nelson R R, et al. Standard setting in high-definition television.Brookings Papers on Economic Activity. Microeconomics.1992,1992:1-93.
[99] Fadaifard H, Wolberg G, Haralickc R. Multiscale3D feature extraction and matching with anapplication to3D face recognition. Graphical Models.2013,75(4):157-176.
[100] Lippert A. NVIDIA GPU Architecture for General Purpose Computing.2009.
[101]毕文元,陈志强,张丽等.基于CUDA的三维重建过程实时可视化方法. CT理论与应用研究.2010,19(2):1-8.
[102] Liang X, Ren X, Zhang Z, et al. Repairing sparse low-rank texture. In Proceedings ofthe12th European conference on Computer Vision, Italy.2012:482-495.
[103] Waqas J, Yi Z, Zhang L. Collaborative neighbor representation based classificationusing L2-minimization approach. Pattern Recognition Letters.2013,34(2):201-208.
[104] Candes E J, Eldar Y C, Strohmer T. Phase Retrieval via Matrix Completion. SIAM J.Imaging Sci.2013,6(1):199-255.
[2]张良培,沈焕锋,张洪艳等.图像超分辨率重建.科学出版社.2012.
[3] Tsai R Y, Huang T S. Multipleframe image restoration and registration. In Advances inComputer Vision and Image Processing.1984,1:317-339.
[4] Patti A J, Sezan M I, Tekalp A M. High-resolution Standards Conversion of Low ResolutionVideo. In Proceedings of IEEE International Conference of ASSP, Detroit, USA.1995:2197~2200.
[5] Elad M, Feuer A. Restoration of a Single Superresolution Image from Several Blurred, Noisy,and Undersampled Measured Images. IEEE Trans IP.1997,6(12):1646~1658.
[6]赵进创，傅文利，胡强，等．电容层析成像系统成像质量的实验分析．自动化仪表．2003，24(10):18-20.
[7] Harris J L. Diffraction and Resolving Power. Journal of the Optical Society of America.1964,54(7):931-936.
[8] Keren D, Peleg S, Brada R. Image sequence enhancement using subpixel displacements. InProceedings of IEEE International Conference of CVPR, Ann Arbor, USA.1988:742-746.
[9] Ur H, Gross D. Improved resolution from subpixel shifted pictures. CVGIP: GraphicalModels and Image Processing.1992,54(2):181-186.
[10] Yen L J. On non-uniform sampling of bandwidth limited signals. IRE Transactions onCircuits Theory.1956,3(4):251-257.
[11] Nguyen N, Milanfar P. An efficient wavelet-based algorithm for image super-resolution. InProceedings of International Conference on Image Processing, Canada.2000:351-354.
[12] Alam M S, Bognar J G, Hardie R C, et al. Infrared image registration and high-resolutionreconstruction using multiple translationally shifted aliased video frames. IEEE Transactionson Instrumentation and Measurement.2000,49(5):915-923.
[13] Elad M, Hel-Or Y. A fast super-resolution reconstruction algorithm for pure translationalmotion and common space-invariant blur. IEEE Transactions on Image Processing.2001,10(8):1187-1193.
[14] Takeda H, Farsiu S, Milanfar P. Kernel regression for image processing and reconstruction.IEEE Transactions on Image Processing.2007,16(2):349-366.
[15] Kim T R, Yang J S W, Shin S, et al. Statistical torsion angle potential (STAP) energyfunctions for protein structure modeling: A bicubic interpolation approach. Proteins: Structure,Function, and Bioinformatics,2013.
[16] Irani M, Peleg S. Super Resolution From Image Sequences. In Proceedings of InternationalConference of PR, Atlantic City, USA.1990:115-120.
[17] Irani M, Peleg S. Improving resolution by image registration. CVGIP: Graphical Models andImage Processing.1991:53(3):231-239.
[18] Stark H, Oskoui P. High-resolution image recovery from image-plane arrays, using convexprojections. Journal of the Optical Society of America A.1989,6(11):1715-1726.
[19] Schultz R R, Stevenson R L. Extraction of high-resolution frames from video sequences.IEEE Transactions on Image Processing.1996,5(6):996-1011.
[20] Hardie R C, Barnard K J, and Armstrong E E. Join MAP registration and high resolutionimage estimation using a sequence of undersampled images. IEEE Transactions on ImageProcessing.1997,6(12):1621-1633.
[21] Elad M, Feuer A. Super-resolution reconstruction of an image. In Proceedings ofInternational Conference of Electrical and Electronics Engineers, Israel.1996:391-394.
[22] Elad M, Feuer A. Restoration of a single superresolution image from several blurred, noisy,and undersampled measured images. IEEE Transactions on Image Processing.1997,6(12):1646-1658.
[23] Patti A J, Sezan M I, Tekalp A M. Superresolution Video Reconstruction with ArbitrarySampling Lattices and Nonzero Aperture Time. IEEE Transactions on Image Processing.1997,6(8):1064~1076.
[24] Patti A J, Sezan M I, Tekalp A M. Robust Methods for High-quality Stills from InterlacedVideo in the Presence of Dominant Motion. IEEE Transactions on Circuits and Systems forVideo Technology.1997,7(2):328~342.
[25] Eren P E, Sezan M I, Tekalp A M. Robust, object-based high-resolution image reconstructionfrom low-resolution video. IEEE Transactions on Image Processing.1997,6(10):1446~1451.
[26] Freeman W T, Jones T R, Pasztor E C. Example-based super resolution. IEEE ComputerGraphics and Applications.2002,22(2):56-65.
[27] Chang H, Yeung D Y, Xiong Y. Super-resolution through neighbor embedding. Proceedingsof IEEE Computer Society Conference on Computer Vision and Pattern Recognition,Washington DC., USA.2004,1:275-282.
[28] Ni K S, Nguyen T Q. Image super resolution using support vector regression. IEEETransactions on Image Processing.2007,16(6):1596-1610.
[29] Liu C, Shum H Y, Freeman W T. Face hallucination: theory and practice. InternationalJournal of Computer Vision.2007,75(1):115-134.
[30] Yang J C, Wright J, Ma Y. Image Super-Resolution via Sparse Representation. IEEETransactions on Image Processing.2010,19(11):2861-2873.
[31] Zeyde R, Elad M, Protter M. On single image scale-up using sparse-representations.Proceedings of the7th international conference on Curves and Surfaces, Avignon, France.2010:711-730.
[32] Shum H Y, Szeliski R. Panoramic image mosaicing. Technical Report MSR-TR-97-23,Microsoft Research,1997.
[33] Zoghlami I, Faugeras O, Deriche R. Using geometric corners to build a2D mosaic from a setof images. In Proceedings of IEEE International Conference of CVPR, Los Alamitos, USA.1997:420-425.
[34] Harris C, Stephens M J. A combined corner and edge detector. Proceedings of The FourthAlvey Vision Conference, UK.1988:147-152.
[35] Faille F. A fast method to improve the stability of interest point detection under illuminationchanges. In Proceedings of International Conference of IP, Singapore.2004:2673-2676.
[36] Sunil A, David M M, Nathan S N, et al. An optimal algorithm for approximate nearestneighbor searching fixed dimensions. Journal of the ACM.1998,45(6):891-923.
[37] Lowe D G. Distinctive image features from scale-invariant keypoints. International Journal ofComputer Vision.2004,60(2):91-110.
[38] Mikolajczyk K, Schmid C. A performance evaluation of local descriptors. IEEE Trans PatternAnalysis and Machine Intelligence.2005,27(10):1615-1630.
[39] Bay H, Ess A, Tuytelaars T, et al. SURF: Speeded Up Robust Features. Computer Vision andImage Understanding.2008,110(3):346-359.
[40] Lowe D G. Object recognition m local scale-invariant features. Proceedings of IEEEInternational Conference on CV, Kerkyra, Greece.1999,2:1150-1157.
[41] Brown M, Lowe D G. Invariant features from interest point groups. Proceedings of BritishMachine Vision Conference, Wales.2002:656-665.
[42] Wold S, Esbensen K, Geladi P. Principal component analysis. Chemometrics and IntelligentLaboratory Systems.1987,2(1-3):37-52.
[43]陆欢,吴庆宪,姜长生.基于PCA与小波变换的彩色图像融合算法.计算机仿真.2007,24(9):202~205.
[44] Smith L I. A tutorial on Principal Components Analysis. Systems Neurobiology.2002.
[45] Wall M E, Rechtsteiner A, Rocha L M. Singular Value Decomposition and PrincipalComponent Analysis. A Practical Approach to Microarray Data Analysis.2003:91-109.
[46] Helen M, Virtanen T. Query by Example of Audio Signals using Euclidean Distance BetweenGaussian Mixture Models. Proceedings of IEEE International Conference on ASSP, Honolulu,USA.2007,1:225-228.
[47] Juan L, Gwon O. A Comparison of SIFT, PCA-SIFT and SURF. International Journal ofImage Processing.2009,3(4):143-152.
[48] He X, Niyogo P. Locality preserving projections. Advances in Neural Information ProcessingSystems.2003,16:153-160.
[49] Dagum P, Luby M. Approximating probabilistic inference in Bayesian belief networks isNP-hard. Artificial Intelligence.1993,60(1):141-153.
[50] Donoho D L. For most large underdetermined systems of linear equations the minimal1-norm solution is also the sparsest solution. Communications on Pure and AppliedMathematics.2006,59(6):797–829.
[51] Donoho D L. For most large underdetermined systems of equations, the minimal1-normnear-solution approximates the sparsest near-solution. Communications on Pure and AppliedMathematics.2006,59(7):907–934.
[52] Grossmann A, Morlet J. Decomposition of Hardy Functions into Square Integrable Waveletsof Constant Shape. SIAM Journal on Mathematical Analysis.1984,15(4):723-736.
[53]李建平,杨万年译.小波十讲.国防工业出版社,2004.
[54] Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in AppliedMathematics, Philadelphia, USA.1992,61.
[55] Gabor D. Theory of communication. Part1: The analysis of information. Journal of theInstitution of Electrical Engineers.1946,93(26):429-441.
[56] Nyquist H. Certain topics in telegraph transmission theory. Proceedings of the IEEE.2002,90(2):280-305.
[57] Liu C. A tutorial of the wavelet transform.2010.
[58] Sweldens W. The lifting scheme: a const ruction of second generation wavelets. SIAM J.Math. Anal.1997,29(2):511-546.
[59]罗少鹏,卢洵.基于提升小波和人眼视觉特性的自反馈彩色图像融合.红外技术.2008,30(1):31-34.
[60] Shapiro J M. Embedded image coding using zerotrees of wavelet coefficients. IEEETransactions on Signal Processing.1993,41(12):3445-3462.
[61] Candes E J, Romberg J K, Tao T. Stable signal recovery from incomplete and inaccuratemeasurements. Communications on Pure and Applied Mathematics.2006,59(8):1207-1223.
[62] Candes E J, Recht B. Exact matrix completion via convex optimization. Foundations ofComputational Mathematics.2009,9(6):717-772.
[63] Candes E J, Plan Y. Matrix Completion with Noise. Proceedings of the IEEE.2010,98(6):925-936.
[64] Cai J, Candes E J, Shen Z. A Singular Value Thresholding Algorithm for Matrix Completion.SIAM J. Optim.2010,20(4):1956-1982.
[65] Toh K C, Yun S W. An accelerated proximal gradient algorithm for nuclear norm regularizedleast squares problems. Eprints for The Optimization Community.2009.
[66] Candes E J, Li X, Ma Y. Robust principal component analysis. Journal of the ACM.2011,58(3): Article No.11.
[67] Hu Y, Zhang D, Liu J, et al. Accelerated singular value thresholding for matrix completion. InProceedings of the18th ACM SIGKDD International Conference on KDD, Beijing, China.2012:298-306.
[68] Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverseproblems. SIAM Journal on Imaging Sciences.2008,2(1):183-202.
[69] Bertsekas D P. Constrained Optimization and Lagrange Multiplier Method. Academic Press.1982.
[70] Sorensen D C. The Q-Superlinear Convergence of a Collinear Scaling Algorithm forUnconstrained Optimization. SIAM J. Numer. Anal.1980,17(1):84-114.
[71] Wright J, Ganesh A, Rao S, et al. Robust principal component analysis: Exact recovery ofcorrupted low-rank matrices via convex optimization. In Advances in Neural InformationProcessing Systems22.2009.
[72] Ganesh A, Lin Z, Wright J, et al. Fast algorithms for recovering a corrupted low-rank matrix.IEEE International Workshop on CAMSAP, Netherlands.2009:213-216.
[73] Cho K, Reyhani N. An iterative algorithm for singular value decomposition on noisyincomplete matrices. The2012International Joint Conference on Neural Networks, Australia.2012:1-6.
[74] Lin Z, Chen M, Ma Y. An accelerated proximal gradient algorithm for frame-Based imagerestoration via the balanced approach. SIAM Journal on Imaging Sciences.2011,4(2):573–596.
[75] Kenney C S, Laub A J. The matrix sign function. IEEE Transactions on Automatic Control.1995,40(8):1330-1348.
[76]夏明革,何友,唐小明等.多传感器图像融合综述.电光与控制.2002,9(4):1-7.
[77] Johnson J L. PCNN models and applications. IEEE Transactions on Neural Networks.1999,10(3):480-498.
[78]李建锋,邹北冀,辛国江等.种自适应PCNN图像融合方法.中南大学学报（自然科学版）.2011,42(7):2004-2010.
[79]牛晓晖,贾克斌.基于PCA和自适应区域方差的图像融合方法.计算机应用研究.2010,27(8):3179-3181.
[80] Wang Z, Jia K, Liu W. Different Frequency Processing of Image Fusion Based on LiftingWavelet Transform. Journal of Computational Information Systems.2012,8(20):8463-8470.
[81] Qu G, Zhang D, Yan P. Information measure for performance of image fusion. ElectronicsLetters.2002,38(7):313-315.
[82]阳方林,郭红阳,杨风暴.像素级图像融合效果的评价方法研究.测试技术学报.2002,16(4):276-279.
[83] Gonzalez-Audicana M, Saleta J L, Catalan R G. Fusion of multispectral and panchromaticimages using improved IHS and PCA mergers based on wavelet decomposition. IEEETransactions on Geoscience and Remote Sensing.2004,42(6):1291-1299.
[84] Yin H, Li S, Fang L. Simultaneous image fusion and super-resolution using sparserepresentation. Information Fusion.2013,14(3):229-240.
[85] Xydeas C S, Petrovic V. Objective image fusion performance measure. Electronics Letters.2000,36(4):308-309.
[86] Li H, Chai Y, Yin H, et al. Multifocus image fusion and denoising scheme based onhomogeneity similarity. Optics Communications.2012,285(2):91-100.
[87] Hwang H, Haddad R A. Adaptive median filters: new algorithms and results. IEEE Trans. onImage Processing.1995,4(4):499-502.
[88] Gelado I, Kelm J H, Ryoo S, et al. CUBA: an architecture for efficient CPU/co-processordata communication. In Proceedings of the22nd annual international conference onSupercomputing, Greece.2008:299-308.
[89] Businger P A, Golub G H. Algorithm358: singular value decomposition of a complex matrix[F1,4,5]. Communications of the ACM.1969,12(10):564-565.
[90] Demmel J W, Kahan W. Accurate singular values of bidiagoanl matrices. SIAM: SIAMJournal on Scientific Computing.1990,11(5):873-912.
[91] Gu M, Eisenstat S C. A divide-and-conquer algorithm for the bidiagonal SVD. SIAM Journalon Matrix Analysis and Applications.1995,16(1):79-92.
[92] Becka M, Oksa G, Vajtersic M. Dynamic ordering for a parallel block-Jacobi SVD algorithm.Parallel Computing.2002,28(2):243-262.
[93] Becka M, Oksa G. On variable blocking factor in a parallel dynamic block-Jacobi SVDalgorithm. Parallel Computing.2003,29(9):1153-1174.
[94] Hahne E L, AT&T Bell Lab. Round-robin scheduling for max-min fairness in data networks.IEEE Journal on Selected Areas in Communications.1991,9(7):1024-1039.
[95] Zhou B B, Brent R P. A parallel ring ordering algorithm for efficient one-sided Jacobi SVDcomputations. Journal of Parallel and Distributed Computing.1997,42(1):1-10.
[96] Drma Z, Veseli K. New Fast and Accurate Jacobi SVD Algorithm. I. SIAM. J. Matrix Anal.&Appl.2008,29(4):1322-1342.
[97] Kerr A, Campbell D, Richards M. QR decomposition on GPUs. In Proceedings of2ndWorkshop on General Purpose Processing on Graphics Processing Units, Washington, DC,USA.2009:71-78.
[98] Farrell J, Shapiro C, Nelson R R, et al. Standard setting in high-definition television.Brookings Papers on Economic Activity. Microeconomics.1992,1992:1-93.
[99] Fadaifard H, Wolberg G, Haralickc R. Multiscale3D feature extraction and matching with anapplication to3D face recognition. Graphical Models.2013,75(4):157-176.
[100] Lippert A. NVIDIA GPU Architecture for General Purpose Computing.2009.
[101]毕文元,陈志强,张丽等.基于CUDA的三维重建过程实时可视化方法. CT理论与应用研究.2010,19(2):1-8.
[102] Liang X, Ren X, Zhang Z, et al. Repairing sparse low-rank texture. In Proceedings ofthe12th European conference on Computer Vision, Italy.2012:482-495.
[103] Waqas J, Yi Z, Zhang L. Collaborative neighbor representation based classificationusing L2-minimization approach. Pattern Recognition Letters.2013,34(2):201-208.
[104] Candes E J, Eldar Y C, Strohmer T. Phase Retrieval via Matrix Completion. SIAM J.Imaging Sci.2013,6(1):199-255.
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