Multimedia Tools and Applications

, Volume 76, Issue 6, pp 8859–8880 | Cite as

Robust structured sparse representation via half-quadratic optimization for face recognition

Article

Abstract

By representing a test sample with a linear combination of training samples, sparse representation-based classification (SRC) has shown promising performance in many applications such as computer vision and signal processing. However, there are several shortcomings in SRC such as 1) the l2-norm employed by SRC to measure the reconstruction fidelity is noise sensitive and 2) the l1-norm induced sparsity does not consider the correlation among the training samples. Furthermore, in real applications, face images with similar variations, such as illumination or expression, often have higher correlation than those from the same subject. Therefore, we correspondingly propose to improve the performance of SRC from two aspects by: 1) replacing the noise-sensitive l2-norm with an M-estimator to enhance its robustness and 2) emphasizing the sparsity in terms of the number of classes instead of the number of training samples, which leads to the structured sparsity. The formulated robust structured sparse representation (RGSR) model can be efficiently optimized via alternating minimization method under the half-quadratic (HQ) optimization framework. Extensive experiments on representative face data sets show that RGSR can achieve competitive performance in face recognition and outperforms several state-of-the-art methods in dealing with various types of noise such as corruption, occlusion and disguise.

Keywords

Sparse representation Structured sparsity Robustness Half-quadratic optimization Face recognition 

References

  1. 1.
    Bickel PJ, Ritov Y, Tsybakov AB (2009) Simultaneous analysis of Lasso and Dantzig selector. Ann Stat 37(4):1705–1732MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bioucas-Dias JM, Figueiredo MA (2007) A new twist: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans Image Process 16(12):2992–3004MathSciNetCrossRefGoogle Scholar
  3. 3.
    Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University PressGoogle Scholar
  4. 4.
    Combettes PL, Wajs VR (2005) Signal recovery by proximal forward-backward splitting. Multiscale Model Simul 4(4):1168–1200MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Ding C, Zhou D, He X, Zha H (2006) R1-PCA: rotational invariant L1-norm principal component for robust subspace factorization. Proc Int Conf Mach Learn 281–288Google Scholar
  6. 6.
    Donoho DL, Elad M (2003) Optimally sparse representation in general (nonorthogonal) dictionaries via l 1 minimization. Proc Natl Acad Sci 100(5):2197–2202MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Du L, Li X, Shen Y-D (2012) Robust nonnegative matrix factorization via half-quadratic minimization. Proc IEEE Int Conf Data Min 201–210Google Scholar
  8. 8.
    Elhamifar E, Vidal R (2009) Sparse subspace clustering. Proc IEEE Conf Comput Vis Pattern Recognit 2790–2797Google Scholar
  9. 9.
    Geman D, Reynolds G (1992) Constrained restoration and the recovery of discontinuities. IEEE Trans Pattern Anal Mach Intell 14(3):367–383CrossRefGoogle Scholar
  10. 10.
    Geman D, Yang C (1995) Nonlinear image recovery with half-quadratic regularization. IEEE Trans Image Process 4(7):932–946CrossRefGoogle Scholar
  11. 11.
    Georghiades AS, Belhumeur PN, Kriegman D (2001) From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans Pattern Anal Mach Intell 23(6):643–660CrossRefGoogle Scholar
  12. 12.
    Grave E, Obozinski GR, Bach FR (2011) Trace Lasso: a trace norm regularization for correlated designs. Proc Adv Neural Inf Proces Syst 2187–2195Google Scholar
  13. 13.
    Gross R, Matthews I, Cohn J, Kanade T, Baker S (2010) Multi-PIE. Image Vis Comput 28:807–813CrossRefGoogle Scholar
  14. 14.
    He R, Sun Z, Tan T, Zheng W-S (2011) Recovery of corrupted low-rank matrices via half-quadratic based nonconvex minimization. Proc IEEE Conf Comput Vis Pattern Recognit 2889–2896Google Scholar
  15. 15.
    He R, Zheng W-S, Hu B-G (2011) Maximum correntropy criterion for robust face recognition. IEEE Trans Pattern Anal Mach Intell 33(8):1561–1576CrossRefGoogle Scholar
  16. 16.
    He R, Zheng W-S, Tan T, Sun Z (2014) Half-quadratic-based iterative minimization for robust sparse representation. IEEE Trans Pattern Anal Mach Intell 36(2):261–275CrossRefGoogle Scholar
  17. 17.
    Huber PJ (2011) Robust statistics. SpringerGoogle Scholar
  18. 18.
    Lai J, Jiang X (2014) Supervised trace lasso for robust face recognition. Proc IEEE Int Conf. Multimedia Expo 1–6Google Scholar
  19. 19.
    Lee HY, Hoo WL, Chan CS (2015) Color video denoising using epitome and sparse coding. Expert Syst Appl 42(2):751–759CrossRefGoogle Scholar
  20. 20.
    Lee K-C, Ho J, Kriegman D (2005) Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans Pattern Anal Mach Intell 27(5):684–698CrossRefGoogle Scholar
  21. 21.
    Liu W, Pokharel PP, Principe JC (2007) Correntropy: properties and applications in non-gaussian signal processing. IEEE Trans Signal Process 55(11):5286–5298MathSciNetCrossRefGoogle Scholar
  22. 22.
    Lu C, Tang J, Lin M, Lin L, Yan S, Lin Z (2013) Correntropy induced l2 graph for robust subspace clustering. Proc IEEE Int Conf Comput Vis 1801–1808Google Scholar
  23. 23.
    Martinez AM (1998) The AR face database, CVC Technical ReportGoogle Scholar
  24. 24.
    Nie F, Huang H, Cai X, Ding CH (2010) Efficient and robust feature selection via joint l2, 1-norms minimization. Proc Adv Neural Inf Proces Syst 1813–1821Google Scholar
  25. 25.
    Nikolova M, Ng MK (2005) Analysis of half-quadratic minimization methods for signal and image recovery. SIAM J Sci Comput 27(3):937–966MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Rosas-Romero R, Tagare HD (2014) Segmentation of endocardium in ultrasound images based on sparse representation over learned redundant dictionaries. Eng Appl Artif Intell 29:201–210CrossRefGoogle Scholar
  27. 27.
    Tibshirani R (1996) Regression shrinkage and selection via the Lasso. J R Statist Soc B 58(1):267–288MathSciNetMATHGoogle Scholar
  28. 28.
    Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86CrossRefGoogle Scholar
  29. 29.
    Wagner A, Wright J, Ganesh A, Zhou Z, Ma Y (2009) Towards a practical face recognition system: robust registration and illumination by sparse representation. Proc IEEE Conf Comput Vis Pattern Recognit 597–604Google Scholar
  30. 30.
    Wright J, Yang AY, Ganesh A, Sastry SS, Ma Y (2009) Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell 31(2):210–227CrossRefGoogle Scholar
  31. 31.
    Yang AY, Zhou Z, Balasubramanian, Sastry SS, Ma Y (2013) Fast l1-minimization algorithms for robust face recognition. IEEE Trans Image Process 22(8):3234–3246CrossRefGoogle Scholar
  32. 32.
    Yang M, Zhang L (2010) Gabor feature based sparse representation for face recognition with Gabor occlusion dictionary. Proc Eur Conf Comput Vis 448–461Google Scholar
  33. 33.
    Yang M, Zhang L, Yang J, Zhang D (2010) Metaface learning for sparse representation based face recognition. Proc Int Conf Image Proces 1601–1604Google Scholar
  34. 34.
    Yang M, Zhang L, Yang J, Zhang D (2011) Robust sparse coding for face recognition. Proc IEEE Conf Comput Vis Pattern Recognit 625–632Google Scholar
  35. 35.
    Yang S, Lv Y, Ren Y, Jiao L (2013) Superpixel-wise semi-supervised structural sparse coding classifier for image segmentation. Eng Appl Artif Intell 26(10):2608–2612CrossRefGoogle Scholar
  36. 36.
    Zhang L, Yang M, Feng X (2011) Sparse representation or collaborative representation: Which helps face recognition?. Proc IEEE Int Conf Comput Vis 471–478Google Scholar
  37. 37.
    Zhao P, Yu B (2006) On model selection consistency of Lasso. J Mach Learn Res 7:2541–2563MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyHangzhou Dianzi UniversityHangzhouChina
  2. 2.Key Laboratory of Complex Systems Modeling and SimulationMinistry of EducationHangzhouChina
  3. 3.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations