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Evaluation of K-SVD Embedded with Modified \(\ell _{1}\)-Norm Sparse Representation Algorithm

  • Meixi Wang
  • Jingjing Liu
  • Shiwei Ma
  • Wanquan Liu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 762)

Abstract

The K-SVD algorithm aims to find an adaptive dictionary for a set of signals by using the sparse representation optimization and constrained singular value decomposition. In this paper, firstly, the original K-SVD algorithm, as well as some sparse representation algorithms including \(\ell _{0}\)-norm OMP and \(\ell _{1}\)-norm Lasso were reviewed. Secondly, the revised Lasso algorithm was embedded into the K-SVD process and a new different K-SVD algorithms with \(\ell _{1}\)-norm Lasso embedded in (RL-K-SVD algrithm) was established. Finally, extensive experiments had been completed on necessary parameters determination, further on the performance compare of recovery error and recognition for the original K-SVD and RL-K-SVD algorithms. The results indicate that within a certain scope of parameter settings, the RL-K-SVD algorithm performs better on image recognition than K-SVD; the time cost for training sample number is lower for RL-K-SVD in case that the sample number is increased to a certain extend.

Keywords

K-SVD algorithm Sparse representation Dictionary Pursuit methods 

Notes

Acknowledgments

This work was supported by the National Science Foundation of China (Nos. 61171145, 61671285).

References

  1. 1.
    Mairal, J., Sapiro, G., Elad, M.: Learning multiscale sparse representations for image and video restoration. Multiscale Model. Simul. 7(1), 214–241 (2008)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Davis, G., Mallat, S., Avellaneda, M.: Adaptive greedy approximations. Constr. Approx. 13(1), 57–98 (1997)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Meinshausen, N., Yu, B.: Lasso-type recovery of sparse representations for high-dimensional data. Ann. Stat. 37, 246–270 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Aharon, M., Elad, M., Bruckstein, A.: \( rm k \)-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Sig. Process. 54(11), 4311–4322 (2006)CrossRefGoogle Scholar
  5. 5.
    Jiang, Z., Lin, Z., Davis, L.S.: Learning a discriminative dictionary for sparse coding via label consistent K-SVD. In: 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1697–1704. IEEE (2011)Google Scholar
  6. 6.
    Zhang, H., Yang, J., Zhang, Y., et al.: Close the loop: joint blind image restoration and recognition with sparse representation prior. In: 2011 IEEE International Conference on Computer Vision (ICCV), pp. 770–777. IEEE (2011)Google Scholar
  7. 7.
    Xie, S., Rahardja, S.: An alternating direction method for frame-based image deblurring with balanced regularization. In: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1061–1064. IEEE (2012)Google Scholar
  8. 8.
    Studer, C., Baraniuk, R.G.: Dictionary learning from sparsely corrupted or compressed signals. In: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3341–3344. IEEE (2012)Google Scholar
  9. 9.
    Wright, J., Yang, A.Y., Ganesh, A., et al.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 210–227 (2009)CrossRefGoogle Scholar
  10. 10.
    Zhang, Q., Li, B.: Discriminative K-SVD for dictionary learning in face recognition. In: 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2691–2698. IEEE (2010)Google Scholar
  11. 11.
    Mallat, S.G., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Sig. Process. 41(12), 3397–3415 (1993)CrossRefMATHGoogle Scholar
  12. 12.
    Needell, D., Tropp, J.A.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Gorodnitsky, I.F., Rao, B.D.: Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Trans. Sig. Process. 45(3), 600–616 (1997)CrossRefGoogle Scholar
  15. 15.
    Rao, B.D., Kreutz-Delgado, K.: An affine scaling methodology for best basis selection. IEEE Trans. Sig. Process. 47(1), 187–200 (1999)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Rao, B.D., Engan, K., Cotter, S.F., et al.: Subset selection in noise based on diversity measure minimization. IEEE Trans. Sig. Process. 51(3), 760–770 (2003)CrossRefGoogle Scholar
  17. 17.
    Jung, H., Park, J., Yoo, J., et al.: Radial k-t FOCUSS for high resolution cardiac cine MRI. Magn. Reson. Med. 63(1), 68–78 (2010)Google Scholar
  18. 18.
    Aad, G., Abat, E., Abbott, B., et al.: Charged-particle multiplicities in pp interactions at measured with the ATLAS detector at the LHC. Phys. Lett. B 688(1), 21–42 (2010)CrossRefGoogle Scholar
  19. 19.
    He, Z., Xie, S., Zhang, L., et al.: A note on Lewicki-Sejnowski gradient for learning overcomplete representations. Neural Comput. 20(3), 636–643 (2008)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Blumensath, T., Davies, M.E.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265–274 (2009)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Blumensath, T., Davies, M.E.: Iterative thresholding for sparse approximations. J. Fourier Anal. Appl. 14(5–6), 629–654 (2008)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Blumensath, T., Davies, M.E.: Normalized iterative hard thresholding: guaranteed stability and performance. IEEE J. Sel. Top. Sig. Process. 4(2), 298–309 (2010)CrossRefGoogle Scholar
  23. 23.
    Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B (Methodol.) 58, 267–288 (1996)MathSciNetMATHGoogle Scholar
  24. 24.
    Jiang, Z., Lin, Z., Davis, L.S.: Label consistent K-SVD: learning a discriminative dictionary for recognition. IEEE Trans. Pattern Anal. Mach. Intell. 35(11), 2651–2664 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Meixi Wang
    • 1
  • Jingjing Liu
    • 1
  • Shiwei Ma
    • 1
  • Wanquan Liu
    • 2
  1. 1.School of Mechatronic Engineering and AutomationShanghai UniversityShanghaiChina
  2. 2.Department of Computer ScienceCurtin UniversityPerthAustralia

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