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Mixed-Norm Projection-Based Iterative Algorithm for Face Recognition

  • Qingshan LiuEmail author
  • Jiang Xiong
  • Shaofu Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11555)

Abstract

In this paper, the mixed-norm optimization is investigated for sparse signal reconstruction. Furthermore, an iterative optimization algorithm based on the projection method is presented for face recognition. From the theoretical point of view, the optimality and convergence of the proposed algorithm is strictly proved. And from the application point of view, the mixed norm combines the \(L_1\) and \(L_2\) norms to give a sparse and collaborative representation for pattern recognition, which has higher recognition rate than sparse representation algorithms. The algorithm is designed by combining the projection operator onto a box set with the projection matrix, which is effective to guarantee the feasibility of the optimal solution. Moreover, numerical experiments on randomly generated signals and three face image data sets are presented to show that the mixed-norm minimization is a combination of sparse representation and collaborative representation for pattern classification.

Keywords

Mixed norm Projection method Iterative algorithm Face recognition 

References

  1. 1.
    Wright, J., Yang, A.Y., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009)Google Scholar
  2. 2.
    Liu, Q., Wang, J.: \({L}_1\)-minimization algorithms for sparse signal reconstruction based on a projection neural network. IEEE Trans. Neural Netw. Learn. Syst. 27, 698–707 (2016)Google Scholar
  3. 3.
    Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43, 129–159 (2001)Google Scholar
  4. 4.
    Elhamifar, E., Vidal, R.: Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 35, 2765–2781 (2013)Google Scholar
  5. 5.
    Mairal, J., Elad, M., Sapiro, G.: Sparse representation for color image restoration. IEEE Trans. Image Proc. 17, 53–69 (2008)Google Scholar
  6. 6.
    Wang, J., Yang, J., Yu, K., Lv, F., Huang, T., Gong, Y.: Locality-constrained linear coding for image classification. In: Proceeding IEEE Conference on Computer Vision and Pattern Recognition, pp. 3360–3367 (2010)Google Scholar
  7. 7.
    Cai, T.T., Wang, L.: Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Trans. Inf. Theor. 57, 4680–4688 (2011)Google Scholar
  8. 8.
    Figueiredo, M.A., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Sign. Proces. 1, 586–597 (2007)Google Scholar
  9. 9.
    Wright, S.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia (1997)Google Scholar
  10. 10.
    Xu, B., Liu, Q.: Iterative projection based sparse reconstruction for face recognition. Neurocomputing 284, 99–106 (2018)Google Scholar
  11. 11.
    Xu, B., Liu, Q., Huang, T.: A discrete-time projection neural network for sparse signal reconstruction with application to face recognition. IEEE Trans. Neural Netw. Learn. Syst. (2018).  https://doi.org/10.1109/TNNLS.2018.2836933Google Scholar
  12. 12.
    Tank, D., Hopfield, J.: Simple neural optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans. Circ. Syst. 33, 533–541 (1986)Google Scholar
  13. 13.
    Wang, J.: Analysis and design of a recurrent neural network for linear programming. IEEE Trans. Circ. Syst.-I 40, 613–618 (1993)Google Scholar
  14. 14.
    Xia, Y., Wang, J.: A general projection neural network for solving monotone variational inequalities and related optimization problems. IEEE Trans. Neural Netw. 15, 318–328 (2004)Google Scholar
  15. 15.
    Liu, Q., Wang, J.: A one-layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints. IEEE Trans. Neural Netw. Learn. Syst. 24, 812–824 (2013)Google Scholar
  16. 16.
    Liu, Q., Yang, S., Wang, J.: A collective neurodynamic approach to distributed constrained optimization. IEEE Trans. Neural Netw. Learn. Syst. 28, 1747–1758 (2017)Google Scholar
  17. 17.
    Liu, Q., Yang, S., Hong, Y.: Constrained consensus algorithms with fixed step size for distributed convex optimization over multiagent networks. IEEE Trans. Autom. Control 62, 4259–4265 (2017)Google Scholar
  18. 18.
    Xia, Y., Kamel, M.S.: Novel cooperative neural fusion algorithms for image restoration and image fusion. IEEE Trans. Image Process. 16, 367–381 (2007)Google Scholar
  19. 19.
    Xia, Y., Wang, J.: A one-layer recurrent neural network for support vector machine learning. IEEE Trans. Syst. Man Cybern.- Part B: Cybern. 34, 1261–1269 (2004)Google Scholar
  20. 20.
    Zhang, Y., Wang, J., Xu, Y.: A dual neural network for bi-criteria kinematic control of redundant manipulators. IEEE Trans. Robot. Autom. 18, 923–931 (2002)Google Scholar
  21. 21.
    Zhang, L., Yang, M., Feng, X.: Sparse representation or collaborative representation: which helps face recognition? In: Proceedings 2011 IEEE International Conference on Computer Vision, pp. 471–478 (2011)Google Scholar
  22. 22.
    Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic, New York (1982)Google Scholar
  23. 23.
    LaSalle, J.: The Stability of Dynamical Systems. SIAM, Philadelphia (1976)Google Scholar
  24. 24.
    Samaria, F.S., Harter, A.C.: Parameterisation of a stochastic model for human face identification. In: Proceedings of the Second IEEE Workshop on Applications of Computer Vision, pp. 138–142 (1994)Google Scholar
  25. 25.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, Hoboken (2012)Google Scholar
  26. 26.
    Georghiades, A.S., Belhumeur, P.N., Kriegman, D.J.: From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intell. 23, 643–660 (2001)Google Scholar
  27. 27.
    Sim, T., Baker, S., Bsat, M.: The CMU pose, illumination, and expression database. IEEE Trans. Pattern Anal. Mach. Intell. 25, 1615–1618 (2003)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of MathematicsSoutheast UniversityNanjingChina
  2. 2.Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher EducationChongqing Three Gorges UniversityChongqingChina
  3. 3.School of Computer Science and EngineeringSoutheast UniversityNanjingChina

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