Robust Image Recovery via Mask Matrix

  • Mengying Jin
  • Yunjie ChenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11935)


This paper studies the problem of recovering an unknown image matrix from noisy observations. Existed works, such as Robust Principal Component Analysis (RPCA), are under the case where the image component and error component are additive, but in real world applications, the components are often non-additive. Especially an image may consist of a foreground object overlaid on a background, where each pixel either belongs to the foreground or the background. To separate image components robustly in such a situation, this paper employs a binary mask matrix which shows the location of each component, and proposes a novel image recovery model, called Masked Robust Principal Component Analysis (MaskRPCA). On one hand, the image component and error component are measured by rank function and sparse function, separately. On another hand, the non-additive between components is characterized by mask matrix. Then we develop an iterative scheme based on alternating direction method of multipliers. Extensive experiments on face images and videos demonstrate the effectiveness of the proposed algorithm.


Non-additive signal Low rank Sparse Robust image recovery 



The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. This work was supported in part by the National Nature Science Foundation of China 61672291 and Six talent peaks project in Jiangsu Province SWYY-034.


  1. 1.
    Jolliffe, I.T.: Principal Component Analysis, 2nd edn. Springer-Verlag, New York (2002). Scholar
  2. 2.
    Candès, E., Li, X., Ma, Y., Wright, J.: Robust principal component analysis. J. ACM 58(3), 1–37 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Wright, J., Ganesh, A., Rao, S., Ma, Y.: Robust principal component analysis: exact recovery of corrupted low-rank matrices by convex optimization. In: Proceedings of the 22nd International Conference on Neural Information Processing Systems, pp. 2080–2088. MIT Press, Vancouver (2009)Google Scholar
  4. 4.
    Bao, B.K., Liu, G., Xu, C., Yan, S.: Inductive robust principal component analysis. IEEE Trans. Image Process. 21(8), 3794–3800 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhang, F., Yang, J., Tai, Y., Tang, J.: Double nuclear norm-based matrix decomposition for occluded image recovery and background modeling. IEEE Trans. Image Process. 24(6), 1956–1966 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Nie, F., Wang, H., Huang, H., Ding, C.: Joint schatten p-norm and lp-norm robust matrix completion for missing value recovery. Knowl. Inf. Syst. 42(3), 525–544 (2015)CrossRefGoogle Scholar
  7. 7.
    Bouwmans, T., Sobral, A., Javed, S., Jung, S., Zahzah, E.: Decomposition into low-rank plus additive matrices for background/foreground separation: a review for a comparative evaluation with a large-scale dataset. Comput. Sci. Rev. 23, 1–71 (2017)CrossRefGoogle Scholar
  8. 8.
    Zhou, Z., Jin, Z.: Double nuclear norm-based robust principal component analysis for image disocclusion and object detection. Neurocomputing 205, 481–489 (2016)CrossRefGoogle Scholar
  9. 9.
    Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 171–184 (2013)CrossRefGoogle Scholar
  10. 10.
    Gao, G., Jing, X.-Y., Huang, P., Zhou, Q., Wu, S., Yue, D.: Locality-constrained double low-rank representation for effective face hallucination. IEEE Access 4, 8775–8786 (2016)CrossRefGoogle Scholar
  11. 11.
    Li, J., Kong, Y., Zhao, H., Yang, J., Fu, Y.: Learning fast low-rank projection for image classification. IEEE Trans. Image Process. 25(10), 4803–4814 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Goldstein, T., O’Donoghue, B., Setzer, S., Baraniuk, R.: Fast alternating direction optimization methods. SIAM J. Imaging Sci. 7(3), 1588–1623 (2014)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Yi, X., Park, D., Chen, Y., Caramanis, C.: Fast algorithms for robust PCA via gradient descent. In: International Conference on Neural Information Processing Systems, pp. 4152–4160. MIT Press, Barcelona (2016)Google Scholar
  14. 14.
    Tan, B., Liu, B.: Acceleration for proximal stochastic dual coordinate ascent algorithm in solving regularised loss minimisation with l2 norm. Electron. Lett. 54(5), 315–317 (2018)CrossRefGoogle Scholar
  15. 15.
    Mohammadreza, S., Hegde, C.: Fast algorithms for demixing sparse signals from nonlinear observations. IEEE Trans. Signal Process. 65(16), 4209–4222 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Lin, Z.C., Chen, M.M., Ma, Y.: The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrix. Technical Report UILU-ENG-09–2215, UIUC, October 2009Google Scholar
  17. 17.
    Cai, J., Candès, E., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Nie, F., Yuan, J., Huang, H.: Optimal mean robust principal component analysis. In: 31st International Conference on Machine Learning, pp. 1062–1070. MIT Press, Beijing (2014)Google Scholar
  19. 19.
    Netrapalli, P., Niranjan, U.N., Sanghavi, S.: Provable non-convex robust PCA. In: International Conference on Neural Information Processing Systems, pp. 1107–1115. MIT Press, Montreal (2014)Google Scholar
  20. 20.
    Zhou, P., Feng, J.: Outlier-robust tensor PCA. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 3938–3946. IEEE, Honolulu (2017)Google Scholar
  21. 21.
    Li, L., Huang, W., Gu, I., Tian, Q.: Statistical modeling of complex backgrounds for foreground objects detection. IEEE Trans. Image Process. 13(11), 1459–1472 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Nanjing University of Information Science and TechnologyNanjingChina

Personalised recommendations