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摘要: 处理部分光照和遮挡等噪声的图像重构及分类问题因其极具挑战而备受关注，该问题的解决很大程度上取决于对误差的描述，常见的方法以向量形式存储误差矩阵且假定其服从于独立同分布，忽视了图像数据的内部结构信息.针对该问题，本文提出一种联合平滑矩阵多变量椭圆分布的稀疏表示算法（Sparse representation with smoothed matrix multivariate elliptical distribution，SMED）.该算法强调误差矩阵中各个像素间的依赖性并假定误差矩阵作为一个随机矩阵变量服从于矩阵多变量椭圆分布；之后，引入辅助变量光滑目标函数，使得模型易于获得全局最优解；最后，采用迭代加权最小二乘法优化求解模型.此外，文中对SMED算法的收敛性和复杂度进行了理论分析，并讨论了模型的参数敏感性.在AR、ExYaleB和PubFig三个公开数据集中的实验验证了所提算法具有鲁棒的鉴别力，且其综合性能明显优于经典算法.Abstract: As one of the most challerging problems, partial illumination or occlusion in image reconstruction and classification has recently received considerable attention. This problem heavily depends on the characterization of representation error, while most existing approaches ignore the internal structure information of image data for the error matrix needs to be stretched into a vector with each element being assumed independently corrupted. To improve the algorithms in this regard, a new sparse representation with smoothed matrix multivariate elliptical distribution (SMED) is proposed, which emphasizes the dependency between pixels of noise and assums that error matrix is a random matrix variate and follows a matrix multivariate elliptical distribution. Then, it introduces regularization terms to smooth the objective function, which makes the model easily to obtain a globally optimal solution. Finally, iteratively reweighted least square is adopted to solve the SMED model efficiently. Furthermore, comprehensive analyses are also performed including convergence behavior, computational complexity, together with parameter determination. Experimental results on the AR, ExYaleB and PubFig databases demonstrate that the proposed algorithm is a robust discriminative classifier with excellent performance, being superior to classical algorithms.1) 本文责任编委 黎铭
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图 1 多元分布比较图(常数取${C}_i=1$, $i=1, 2, 3$)
Fig. 1 The comparison chart of the multivariate distribution (where the constants are ${ C}_{i}=1$, $i=1, 2, 3$)
图 2 不同参数$\mu_{{c}}$和$\rho$值下的SMED$_{11}$算法收敛值曲线
Fig. 2 Convergence curves of SMED$_{11}$ algorithm on AR with different regularization parameters $\mu_{{c}}$ and $\rho$
图 3 不同光照影响及墨镜和围巾遮挡下的人脸重构性能对比
Fig. 3 The reconfiguration performance contrast of different algorithms under illuminition changes and sunglass or scraf occlusion
图 4 不同像素污损程度下的人脸识别率对比
Fig. 4 Comparison of recognition rates under the different pixel corruption levels
图 5 不同遮挡程度下的人脸识别率对比
Fig. 5 Comparison of recognition rates under the different occlusion levels
图 6 PubFig中1人的训练样本和测试样本示例图
Fig. 6 Sample images for one person from PubFig face database
表 1 AR人脸库真实影响下不同算法的识别率对比(%)
Table 1 Comparison of recognition rates on AR database (%)
算法 光照影响 墨镜遮挡 围巾遮挡 SMED$_{11}$ 95.83 74.66 67.64 SMED$_{1/21}$ 91.93 77.17 69.83 SMED$_{3/22}$ 93.16 72.67 60.33 SRC 90.50 68.83 55.83 CRC 95.33 69.67 63.50 RRC 88.17 71.16 69.83 FFS 83.00 65.50 50.83 HQ_A 87.83 70.00 44.50 HQ_M 93.51 75.83 48.93 
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表 2 AR数据库中各算法测试时间对比(s)
Table 2 Running time of competing algorithms on AR database (s)
分类器 测试时间 SMED$_{11}$ 0.1703 SMED$_{1/21}$ 0.1748 SMED$_{3/22}$ 0.1648 SRC 0.0917 CRC 0.0041 RRC 3.2165 FFS 0.1738 HQ_A 4.3898 HQ_M 13.2725
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表 3 ExYaleB、PubFig数据库中各算法测试时间对比(s)
Table 3 Running time of competing algorithms on ExYaleB, PubFig database (s)
分类器 测试时间 ExYaleB ExYaleB ExYaleB ExYaleB PubFig (白色遮挡) (黑色遮挡) (baboon遮挡) (鲜花遮挡) SMED$_{11}$ 0.2429 0.2508 0.2191 0.2376 1.6705 SMED$_{1/21}$ 0.3450 0.2452 0.2561 0.2445 1.7864 SMED$_{3/22}$ 0.2638 0.2435 0.2318 0.2186 1.6425 CRC 0.0037 0.0045 0.0031 0.0035 0.0152 RRC 0.2510 0.2370 0.2426 0.2375 2.5819 CESR 0.3244 0.1276 0.2966 0.2240 2.3499 HQ_M 12.2049 11.7532 12.3732 11.6457 6.8705
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[1] Jalali S, Poor H V. Universal compressed sensing for almost lossless recovery. IEEE Transactions on Information Theory, 2017, 63(5): 2933-2953 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=bf10e8c14dfa411302b59ddd62239924 [2] Hyder M, Mahata K. An approximate L0 norm minimization algorithm for compressed sensing. In: Proceedings of the 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing. Taipei, China: IEEE, 2009. 3365-3368 https://www.researchgate.net/publication/224461335_An_approximate_L0_norm_minimization_algorithm_for_compressed_sensing [3] Wright J, Yang A Y, Ganesh A, Sastry S S, Ma Y. Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(2): 210-227 doi: 10.1109/TPAMI.2008.79 [4] Yang J, Zhang L, Xu Y, Yang J Y. Beyond sparsity: the role of L1-optimizer in pattern classification. Pattern Recognition, 2012, 45(3): 1104-1118 doi: 10.1016/j.patcog.2011.08.022 [5] Zhang L, Yang M, Feng X C. Sparse representation or collaborative representation: which helps face recognition? In: Proceedings of the 2011 IEEE International Conference on Computer Vision (ICCV). Barcelona, Spain: IEEE, 2011. 471-478 https://www.researchgate.net/publication/221111435_Sparse_Representation_or_Collaborative_Representation_Which_Helps_Face_Recognition [6] Zhang H M, Yang J, Xie J C, Qian J J, Zhang B. Weighted sparse coding regularized nonconvex matrix regression for robust face recognition. Information Sciences, 2017, 394-395: 1-17 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=c078613f1e6f52a08b1bba4b4f4be933 [7] Yang G, Wang Y, Guo L. A sparser reduced set density estimator by introducing weighted l1 penalty term. Pattern Recognition Letters, 2015, 58: 15-22 doi: 10.1016/j.patrec.2015.01.016 [8] Liu C L, Hsaio W H, Xiao B, Chen C Y, Wu W L. Maximum-margin sparse coding. Neurocomputing, 2017, 238: 340-350 doi: 10.1016/j.neucom.2017.01.071 [9] Lu C W, Shi J P, Jia J Y. Online robust dictionary learning. In: Proceedings of the 2013 IEEE Conference on Computer Vision and Pattern Recognition. Portland, OR, USA: IEEE, 2013. 415-422 https://www.researchgate.net/publication/261479300_Online_Robust_Dictionary_Learning [10] Naseem I, Togneri R, Bennamoun M. Linear regression for face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(11): 2106-2112 doi: 10.1109/TPAMI.2010.128 [11] Naseem I, Togneri R, Bennamoun M. Robust regression for face recognition. Pattern Recognition, 2012, 45(1): 104-118 http://d.old.wanfangdata.com.cn/OAPaper/oai_pubmedcentral.nih.gov_3413675 [12] Yang M, Zhang L, Yang J, Zhang D. Robust sparse coding for face recognition. In: Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Colorado Springs, CO, USA: IEEE, 2011. 625-632 https://www.researchgate.net/publication/224254772_Robust_sparse_coding_for_face_recognition [13] Yang M, Zhang L, Yang J, Zhang D. Regularized robust coding for face recognition. IEEE Transactions on Image Processing, 2013, 22(5): 1753-1766 doi: 10.1109/TIP.2012.2235849 [14] He R, Zheng W S, Hu B G. Maximum correntropy criterion for robust face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33(8): 1561-1576 doi: 10.1109/TPAMI.2010.220 [15] He R, Zheng W S, Tan T N, Sun Z N. Half-quadratic-based iterative minimization for robust sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014, 36(2): 261-275 doi: 10.1109/TPAMI.2013.102 [16] He R, Zheng W S, Hu B G, Kong X W. Two-stage nonnegative sparse representation for large-scale face recognition. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(1): 35-46 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=b50eb274beaffb3f9113cf3d0d7c964d [17] Kibria B M G, Haq M S. The multivariate linear model with matric-T error variables. Journal of Applied Statistical Sciences, 2000, 9(4): 277-290 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1177/001316446202200205 [18] Basu S, Micchelli C A, Olsen P. Power exponential densities for the training and classification of acoustic feature vectors in speech recognition. Journal of Computational and Graphical Statistics, 2001, 10(1): 158-184 doi: 10.1198/10618600152418818 [19] Liu M H. Multivariate Nonnormal Regression Models, Information Complexity, and Genetic Algorithms: A Three Way Hybrid for Intelligent Data Mining [Ph. D. dissertation]. University of Tennessee, USA, 2006. [20] Balakrishnan N, Hashorva E. Scale mixtures of Kotz–dirichlet distributions. Journal of Multivariate Analysis, 2013, 113: 48-58 doi: 10.1016/j.jmva.2011.08.012 [21] Abdous B, Genest C, Rémillard B. Dependence properties of meta-elliptical distributions. Statistical Modeling and Analysis for Complex Data Problems. Boston, MA, USA: Springer, 2005. 1-15 [22] Long C, You D H, Hu J, Wang G, Dong M L. Quick and effective multiple contingency screening algorithm based on long-tailed distribution. IET Generation, Transmission and Distribution, 2016, 10(1): 257-262 doi: 10.1049/iet-gtd.2015.0885 [23] Chong C. Stochastic PDEs with heavy-tailed noise. Stochastic Processes and Their Applications, 2017, 127(7): 2262- 2280 doi: 10.1016/j.spa.2016.10.011 [24] Sun Y, Babu P, Palomar D P. Robust estimation of structured covariance matrix for heavy-tailed elliptical distributions. IEEE Transactions on Signal Processing, 2016, 64(14): 3576-3590 doi: 10.1109/TSP.2016.2546222 [25] Liu M H, Bozdogan H. Multivariate regression models with power exponential random errors and subset selection using genetic algorithms with information complexity. European Journal of Pure and Applied Mathematics, 2008, 1(1): 4-37 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=Open J-Gate000001561206 [26] Sun Y, Babu P, Palomar D P. Robust estimation of structured covariance matrix for heavy-tailed distributions. In: Proceedings of the 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). Brisbane, QLD, Australia: IEEE, 2015. 5693-5697 http://www.oalib.com/paper/4116400 [27] Fang K T, Anderson T W. Statistical Inference in Elliptically Contoured and Related Distributions. New York, USA: Allerton Press, 1990. [28] Zhao T, Liu H. Calibrated precision matrix estimation for high-dimensional elliptical distributions. IEEE Transactions on Information Theory, 2014, 60(12): 7874-7887 doi: 10.1109/TIT.2014.2360980 [29] Díaz-García J A, Gutiérrez-Jáimez R. Compound and scale mixture of matricvariate and matrix variate Kotz-type distributions. Journal of the Korean Statistical Society, 2010, 39(1): 75-82 doi: 10.1016/j.jkss.2009.04.004 [30] Wai P S, Kun S S, Ismail M T, Ariffin S, Karim A. Model performance between linear vector autoregressive and Markov switching vector autoregressive models on modelling structural change in time series data. In: Proceedings of the 2015 International Symposium on Mathematical Sciences and Computing Research (iSMSC). Ipon, Malaysia: IEEE, 2015. 379-383 https://ieeexplore.ieee.org/document/7594083/ [31] Hsu D, Kakade S M, Zhang T. Robust matrix decomposition with sparse corruptions. IEEE Transactions on Information Theory, 2011, 57(11): 7221-7234 doi: 10.1109/TIT.2011.2158250 [32] Lai M J, Xu Y Y, Yin W T. Improved iteratively reweighted least squares for unconstrained smoothed ℓq minimization. SIAM Journal on Numerical Analysis, 2013, 51(2): 927-957 doi: 10.1137/110840364 [33] Li W Y. Visualizing network communities with a semi-definite programming method. Information Sciences, 2015, 321: 1-13 doi: 10.1016/j.ins.2015.05.037 [34] Lin Q H, Xiao L. An adaptive accelerated proximal gradient method and its homotopy continuation for sparse optimization. Computational Optimization and Applications, 2015, 60(3): 633-674 doi: 10.1007/s10589-014-9694-4 [35] Goldstein T, O'Donoghue B, Setzer S, Baraniuk R. Fast alternating direction optimization methods. SIAM Journal on Imaging Sciences, 2014, 7(3): 1588-1623 doi: 10.1137/120896219 [36] 许凯, 吴小俊, 尹贺峰.基于分布式低秩表示的子空间聚类算法.计算机研究与发展, 2016, 53(7): 1605-1611 http://d.old.wanfangdata.com.cn/Periodical/jsjyjyfz201607018Xu Kai, Wu Xiao-Jun, Yin He-Feng. Distributed low rank representation-based subspace clustering algorithm. Journal of Computer Research and Development, 2016, 53(7): 1605 -1611 http://d.old.wanfangdata.com.cn/Periodical/jsjyjyfz201607018 [37] Barrah E M, Safi S, Malaoui A. New technique for face recognition based on singular value decomposition (SVD). In: Proceedings of the 2nd International Conference on Cloud Computing Technologies and Applications (CloudTech). Marrakech, Morocco: IEEE, 2016. 96-99 https://www.researchgate.net/publication/313545436_New_technique_for_face_recognition_based_on_Singular_Value_Decomposition_SVD [38] Chen K, Lv Q, Lu Y, Dou Y. Robust regularized extreme learning machine for regression using iteratively reweighted least squares. Neurocomputing, 2017, 230: 345-358 doi: 10.1016/j.neucom.2016.12.029 [39] 李波, 卢春园, 冷成财, 金连宝.基于局部图拉普拉斯约束的鲁棒低秩表示聚类方法.自动化学报, 2015, 41(11): 1971-1980 http://www.aas.net.cn/CN/abstract/abstract18771.shtmlLi Bo, Lu Chun-Yuan, Leng Cheng-Cai, Jin Lian-Bao. Robust low rank subspace clustering based on local graph Laplace constraint. Acta Automatica Sinica, 2015, 41(11): 1971-1980 http://www.aas.net.cn/CN/abstract/abstract18771.shtml [40] Benner P, Li R C, Truhar N. On the ADI method for Sylvester equations. Journal of Computational and Applied Mathematics, 2009, 233(4): 1035-1045 http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_1201.4779 [41] Boyd S, Vandenberghe L. Convex Optimization. Cambridge, UK: Cambridge University Press, 2009. [42] Marshall A W, Olkin I, Arnold B C. Inequalities: Theory of Majorization and Its Applications (2nd edition). New York: Springer, 2011. [43] Lee K C, Ho J, Kriegman D J. Acquiring linear subspaces for face recognition under variable lighting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(5): 684-698 doi: 10.1109/TPAMI.2005.92 [44] Kumar N, Berg A C, Belhumeur P N, Nayar S K. Attribute and simile classifiers for face verification. In: Proceedings of the 12th IEEE International Conference on Computer Vision. Kyoto, Japan: IEEE, 2009. 365-372 [45] Wu J X, Brubaker S C, Mullin M D, Rehg J M. Fast asymmetric learning for cascade face detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008, 30(3): 369-382 doi: 10.1109/TPAMI.2007.1181 [46] Gu J, Hu H, Li H. Local robust sparse representation for face recognition with single sample per person. IEEE/CAA Journal of Automatica Sinica, 2018, 5(2): 547-554 doi: 10.1109/JAS.2017.7510658 -
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