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Nuclear-\(L_1\) Norm Joint Regression for Face Reconstruction and Recognition

  • Lei Luo
  • Jian YangEmail author
  • Jianjun Qian
  • Ying Tai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9004)

Abstract

Recognizing a face with significant lighting, disguise and occlusion variations is an interesting and challenging problem in pattern recognition. To address this problem, many regression based methods, represented by sparse representation classifier (SRC), are presented recently. SRC uses the \(L_1\)-norm to characterize the pixel-level sparse noise but ignore the spatial information of noise. In this paper, we find that nuclear-norm is good for characterizing image-wise structural noise, and thus we use the nuclear norm and \(L_1\)-norm to jointly characterize the error image in regression model. Our experimental results demonstrate that the proposed method is more effective than state-of-the-art regression methods for face reconstruction and recognition.

Keywords

Singular Value Decomposition Face Image Sparse Representation Structural Noise Nuclear Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Wright, J., Yang, A., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE PAMI 31, 210–227 (2009)CrossRefGoogle Scholar
  2. 2.
    Cover, T., Hart, P.: Nearest neighbor pattern classification. IEEE Trans. Inf. Theory 13, 21–27 (1967)CrossRefzbMATHGoogle Scholar
  3. 3.
    Li, S., Lu, J.: Face recognition using the nearest feature line method. IEEE Trans. Neural Networks 10, 439–443 (1999)CrossRefGoogle Scholar
  4. 4.
    Lu, C.Y., Min, H., Gui, J., Zhu, L., Lei, Y.K.: Face recognition via weighted sparse representation. J. Vis. Commun. Image Represent 24, 111–116 (2003)CrossRefGoogle Scholar
  5. 5.
    Daubechies, I., Devore, R., Fornasier, M., Gunturk, C.: Iteratively re-weighted least squares minimization for sparse recovery. arXiv: 0807.0575 (2008)
  6. 6.
    Cands, E., Wakin, M., Boydg, S.: Enhancing sparsity by reweighted l1 minimization. J. Fourier Anal. Appl. 14, 877–905 (2008)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Zhang, L., Yang, M., Feng, X.: Sparse representation or collaborative representation: which helps face recognition? In: ICCV (2011)Google Scholar
  8. 8.
    Yang, J., Zhang, L., Xu, Y., Yang, J.Y.: Beyond sparsity: the role of l1-optimizer in pattern classification. Pattern Recognit. 45, 1104–1118 (2012)CrossRefzbMATHGoogle Scholar
  9. 9.
    Yang, J., Chu, D., Zhang, L., Xu, Y.: Sparse representation classifier steered discriminative projection with applications to face recognition. IEEE Trans. Neural Networks. Learn. Syst. 24, 1023–1035 (2013)CrossRefGoogle Scholar
  10. 10.
    Zheng, Z., Zhang, H., Jia, J., Zhao, J., Guo, L., Fu, F., Yu, M.: Low-rank matrix recovery with discriminant regularization. In: Pei, J., Tseng, V.S., Cao, L., Motoda, H., Xu, G. (eds.) PAKDD 2013, Part II. LNCS, vol. 7819, pp. 437–448. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  11. 11.
    Naseem, I., Togneri, R., Bennamoun, M.: Linear regression for face recognition. IEEE PAMI 32, 2106–2112 (2010)CrossRefGoogle Scholar
  12. 12.
    Yang, M., Zhang, L., Yang, J., Zhang, D.: Robust sparse coding for face recognition. In: CVPR (2011)Google Scholar
  13. 13.
    He, R., Zheng, W.S., Hu, B.G.: Maximum correntropy criterion for robust face recognition. IEEE PAMI 22, 1753–1766 (2011)Google Scholar
  14. 14.
    Li, X.X., Dai, D.Q., Zhang, X.F., Ren, C.X.: Structured sparse error coding for face recognition with occlusion. IEEE Trans. Image Process. 22, 1889–1990 (2013)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Jia, K., Chan, T.-H., Ma, Y.: Robust and practical face recognition via structured sparsity. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part IV. LNCS, vol. 7575, pp. 331–344. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  16. 16.
    Yang, J., Qian, J.J., Luo, L., Zhang, F.L., Gao, Y.C.: Nuclear norm based matrix regression with applications to face recognition with occlusion and illumination changes. arXiv:1405.1207 (2014)
  17. 17.
    Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximations. IEEE Trans. Image Process. 22, 17–140 (1976)Google Scholar
  18. 18.
    Gabay, D.: Applications of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R. (eds.) Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, pp. 299–331. North-Holland, Amsterdam (1983)CrossRefGoogle Scholar
  19. 19.
    Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statisticallearning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3, 1–112 (2011)CrossRefGoogle Scholar
  20. 20.
    Hansson, A., Liu, Z., Vandenberghe, L.: Subspace system identification via weighted nuclear norm optimization. In: CDC, pp. 3439–3444 (2012)Google Scholar
  21. 21.
    Lin, Z., Chen, M., Ma, Y.: Multiplier method for exact recovery of corrupted low-rank matrices. UIUC Technical Report UILU-ENG-09-2215 (2009)Google Scholar
  22. 22.
    Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Trans. Patt. Anal. Mach. Intell. 35, 171–184 (2013)CrossRefGoogle Scholar
  23. 23.
    He, B., Tao, M., Yuan, X.: Alternating direction method with gaussian back substitution for separable convex programming. SIAM J. Optim. 22, 313–340 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Luan, X., Liu, B., Yang, L., Qian, J.: Extracting sparse error of robust pca for face recognition in the presence of varying illumination and occlusion. Pattern Recognit. 47, 495–508 (2014)CrossRefGoogle Scholar
  25. 25.
    Li, J., Lu, C.Y.: A new decision rule for sparse representation based classification for face recognition. Neurocomputing 116, 265–271 (2013)CrossRefGoogle Scholar
  26. 26.
    Gu, Z.H., Shao, M., Li, L.Y.: Discriminative metric: schatten norm vs. vector norm. In: ICPR 2012, Tsukuba, JapanGoogle Scholar
  27. 27.
    Martinez, A., benavente, R.: The ar face database. Tech-nical Report 24, CVC (1998)Google Scholar
  28. 28.
    Lee, K., Ho, J., Kriegman, D.: Acquiring linear subspaces for face recognition under variable lighting. IEEE PAMI 27, 684–698 (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Nanjing University of Science and TechnologyNanjingPeople’s Republic of China

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