An AK-BRP dictionary learning algorithm for video frame sparse representation in compressed sensing



Sparsifying transform is an important prerequisite in compressed sensing. And it is practically significant to research the fast and efficient signal sparse representation methods. In this paper, we propose an adaptive K-BRP (AK-BRP) dictionary learning algorithm. The bilateral random projection (BRP), a method of low rank approximation, is used to update the dictionary atoms. Furthermore, in the sparse coding stage, an adaptive sparsity constraint is utilized to obtain sparse representation coefficient and helps to improve the efficiency of the dictionary update stage further. Finally, for video frame sparse representation, our adaptive dictionary learning algorithm achieves better performance than K-SVD dictionary learning algorithm in terms of computation cost. And our method produces smaller reconstruction error as well.


Bilateral random projections (BRP) Adaptive K-BRP algorithm Dictionary learning Sparse representation K-SVD algorithm 


  1. 1.
    Aharon M, Elad M, Bruckstein A (2006) K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54(11):4311–4322CrossRefGoogle Scholar
  2. 2.
    Anaraki PF, Hughes SM (2013) Compressive K-SVD. In: Proceedings of the 2013 I.E. International Conference on Acoustics, Speech, and Signal Processing. Vancouver, Canada: IEEE, 5469–5473Google Scholar
  3. 3.
    Bahrampour S, Nasrabadi NM, Ray A, and Jenkins WK (2015) “Multimodal task-driven dictionary learning for image classification,” arXiv: 1502.01094Google Scholar
  4. 4.
    Candès E, Tao T (2006) Near optional signal recovery from random projections: universal encoding strategies [J]. IEEE Trans Inf Theory 52(12):5406–5425CrossRefMATHGoogle Scholar
  5. 5.
    Candès EJ, Wakin MB (2008) An intoduction to compressive sampling. IEEE Signal Process Mag 25(2):21–30CrossRefGoogle Scholar
  6. 6.
    Tianyi Zhou and Dacheng Tao (2012) Bilateral random projections, Proceedings of the 2012 I.E. International Symposium on Information Theory, pp. 1286–1290Google Scholar
  7. 7.
    Tianyi Zhou and Dacheng Zhao (2011) GoDec: Randomized low-rank and sparse matrix decomposition in noisy case, Proceedings of the 28th International Conference on Machine Learning, pp. 33–40Google Scholar
  8. 8.
    Delgado KK, Murray JF, Rao BD (2003) Dictionary learning algorithms for sparse representation. Neural Comput 15:349–396CrossRefMATHGoogle Scholar
  9. 9.
    Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Donoho DL, Huo XM (2001) Uncertainty principles and ideal atomic decomposition. IEEE Trans Inf Theory 47(7):2845–2862MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Donoho DL, Tsaig Y (2006) Extensions of compressed sensing [J]. Signal Process 86(3):533–548CrossRefMATHGoogle Scholar
  12. 12.
    Donoho DL, Tsaig Y (2008) Fast solution of l 1-norm minimization problems when the solution may be sparse. IEEE Trans Inf Theory 54(11):4789–812MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Signal Process 15(12):3736–3745MathSciNetGoogle Scholar
  14. 14.
    Liu W, Yu Z, Yang M, Lu L, Zou Y (2015) Joint kernel dictionary and classifier learning for sparse coding via locality preserving K-SVD, in: Proceedings of IEEE International Conference on Mutimedia and Expo (ICME), pp.1-6Google Scholar
  15. 15.
    Liu XM, Zhai DM, Zhao DB, Gao W (2013) Image super-resolution via hierarchical and collaborative sparse representation. In: Proceedings of the 2013 Data Compression Conference. Snowbird, USA: IEEE, 93–102Google Scholar
  16. 16.
    Mailhe B, Barchiesi D, Plumbley MD (2012) INK-SVD: learning incoherent dictionaries for sparse representation. In: Proceedings of the 2012 International Conference on Acoustics, Speech, and Signal Processing (ICASSP). Kyoto, Japan, USA: IEEE, 3573–3576Google Scholar
  17. 17.
    Protter M, Elad M (2009) Image sequence denoising via sparse and redundant representations. IEEE Trans Image Process 18(1):27–36MathSciNetCrossRefGoogle Scholar
  18. 18.
    Ravishankar S, Bresler Y (2011) MR image reconstruction from highly undersampled K-space data by dictionary learning. IEEE Trans Med Imaging 30(5):1028–1041CrossRefGoogle Scholar
  19. 19.
    ROWEISS (1998) EM algorithms for PCA and SPCA [C] // Proceedings of the 1997 Conference on Advances in Neural Information Processing System. Cambridge: Press, 626-632Google Scholar
  20. 20.
    Rubinstein R, Bruckstein A, Elad M (2010) Dictionaries for sparse representation modeling. Proc IEEE 98(6):1045–1057CrossRefGoogle Scholar
  21. 21.
    Rubinstein R, Zibulevsky M, Elad M (2010) Double sparsity: learning sparse dictionaries for sparse signal approximation. IEEE Trans Signal Process 58(3):1553–1564MathSciNetCrossRefGoogle Scholar
  22. 22.
    Zhang Q and Li B (2010) “Discriminative K-SVD for dictionary learning in face recognition,” in Proc. IEEE Conf. CVPR, pp. 2691–2698Google Scholar
  23. 23.
    Zhang L, Zhang L, Mou X, Zhang D (2012) FSIM: a feature SIMilarity index for image quality assessment. IEEE Trans Image Process 20(8):2378–2386MathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhang J, Zhao C, Zhao D et al (2014) Image compressive sensing recovery using adaptively learned sparsifying basis via l 0 minimization [J]. Signal Process 103(10):114–126CrossRefGoogle Scholar
  25. 25.
    Zheng H, Tao D (2015) Discriminative dictionary learning via fisher discrimination K-SVD algorithm. Neurocomputing 162:9–15CrossRefGoogle Scholar
  26. 26.
    Zhou FF and Li L (2015) A novel K-RBP dictionary learning algorithm for video image sparse representation, Journal of Computational Information Systems, vol. 11 (1), pp.1-11Google Scholar

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of ScienceNanjing University of Posts and TelecommunicationsNanjingChina
  2. 2.Center for Visual Cognitive Computation and Its ApplicationNanjing University of Posts and TelecommunicationsNanjingChina

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