Supervised Online Dictionary Learning for Image Separation Using OMP

  • Yuxin Zhang
  • Bo Yuan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9772)


In this paper, we propose a new algorithm to perform single image separation based on online dictionary learning and orthogonal matching pursuit (OMP). This method consists of two separate processes: dictionary training for representing morphologically different components and the separation stage. The training process takes advantage of the prior knowledge of the components by adding component recovery error control penalties. The learned dictionaries have lower coherence with each other and better separation ability, which can benefit the separation process in two ways. Firstly, simple sparse coding methods such as OMP can be used to efficiently obtain superior performance. Secondly, well trained dictionaries can lead to satisfactory separation results even when the components are similar. The dictionaries obtained can also serve as good initial inputs for other models using dictionary learning and sparse representation. Experiments on complex images confirm that better results can be achieved efficiently by our method compared to other state-of-the-art algorithms.


Online dictionary learning Image separation Morphological component analysis OMP 


  1. 1.
    Luo, Y., Xu, Y., Ji, H.: Removing rain from a single image via discriminative sparse coding. In: IEEE International Conference on Computer Vision, pp. 3397–3405 (2015)Google Scholar
  2. 2.
    Kong, N., Tai, Y., Shin, J.: A physically-based approach to reflection separation: from physical modeling to constrained optimization. IEEE Trans. Pattern Anal. Mach. Intell. 36(2), 209–221 (2014)CrossRefGoogle Scholar
  3. 3.
    King, B., Atlas, L.: Single-channel source separation using complex matrix factorization. IEEE Trans. Audio Speech Lang. Process. 19(8), 2591–2597 (2011)CrossRefGoogle Scholar
  4. 4.
    Hao, Y., Xu, J., Bai, J., Han, Y.: Image decomposition combining a total variational filter and a Tikhonov quadratic filter. Multidimension. Syst. Signal Process. 26(3), 739–751 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Wang, G., Pan, Z., Zhao, Z., Sun, X.: The split Bregman method of image decomposition model for ultrasound image denoising. In: 3rd International Conference on Image and Signal Processing, pp. 2870–2875 (2010)Google Scholar
  6. 6.
    Bobin, J., Starck, J., Fadili, J.M., Moudden, Y., Donoho, D.L.: Morphological component analysis: an adaptive thresholding strategy. IEEE Trans. Image Process. 16(11), 2675–2681 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kutyniok, G.: Data separation by sparse representations. In: Eldar, Y., Kutyniok, G. (eds.) Compressed Sensing: Theory and Applications, pp. 485–517. Cambridge University Press, Cambridge (2012)CrossRefGoogle Scholar
  8. 8.
    Elad, M.: Sparse and Redundant Representations. Springer, New York (2010)CrossRefzbMATHGoogle Scholar
  9. 9.
    Liu, S., Hu, S., Xiao, Y.: Image separation using wavelet-complex Shearlet dictionary. J. Syst. Eng. Electron. 25(2), 314–321 (2014)CrossRefGoogle Scholar
  10. 10.
    Engan, K., Aase, S.O., Husoy, J.H.: Method of optimal directions for frame design. In: 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 2443–2446 (1999)Google Scholar
  11. 11.
    Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)CrossRefGoogle Scholar
  12. 12.
    Mairal, J., Bach, F., Ponce, J., Sapio, G.: Online dictionary learning for sparse coding. In: 26th Annual International Conference on Machine Learning, pp. 689–696 (2009)Google Scholar
  13. 13.
    Shoham, N., Elad, M.: Algorithms for signal separation exploiting sparse representations, with applications to texture image separation. In: 2008 IEEE Convention of Electrical and Electronics Engineers, pp. 538–542 (2008)Google Scholar
  14. 14.
    Peyr, G., Fadili, J.M., Starck, J.: Learning the morphological diversity. Soc. Ind. Appl. Math. Imaging Sci. 3(3), 646–669 (2010)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Li, Y., Feng, X.: Image decomposition via learning the morphological diversity. Pattern Recogn. Lett. 33(2), 111–120 (2012)CrossRefGoogle Scholar
  16. 16.
    Liu, Q., Liu, J., Liang, D.: Adaptive image decomposition via dictionary learning with structural incoherence. In: 2013 IEEE International Conference on Image Processing, pp. 280–284 (2013)Google Scholar
  17. 17.
    Rezaiifar, R.: Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: 27th Asilomar Conference on Signals, Systems and Computers, pp. 40–44 (1993)Google Scholar
  18. 18.
    Studer, C., Baraniuk, R.G.: Stable restoration and separation of approximately sparse signals. Appl. Comput. Harm. Anal. 37(1), 12–35 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Studer, C., Kuppinger, P., Pope, G., Bölcskei, H.: Recovery of sparsely corrupted signals. IEEE Trans. Inf. Theory 58(5), 3115–3130 (2012)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zhang, L., Zhang, L., Mou, X., Zhang, D.: FSIM: a fast feature similarity index for image quality assessment. IEEE Trans. Image Process. 20(8), 2378–2386 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Intelligent Computing Lab, Division of Informatics, Graduate School at ShenzhenTsinghua UniversityShenzhenPeople’s Republic of China

Personalised recommendations