Advertisement

Signal, Image and Video Processing

, Volume 11, Issue 6, pp 993–1000 | Cite as

A hybrid evolutionary algorithm for multiobjective sparse reconstruction

  • Bai Yan
  • Qi Zhao
  • Zhihai WangEmail author
  • Xinyuan Zhao
Original Paper

Abstract

Sparse reconstruction (SR) algorithms are widely used in acquiring high-quality recovery results in compressed sensing. Existing algorithms solve SR problem by combining two contradictory objectives (measurement error and sparsity) using a regularizing coefficient. However, this coefficient is hard to determine and has a large impact on recovery quality. To address this concern, this paper converts the traditional SR problem to a multiobjective SR problem which tackles the two objectives simultaneously. A hybrid evolutionary paradigm is proposed, in which differential evolution is employed and adaptively configured for exploration and a local search operator is designed for exploitation. Another contribution is that the traditional linearized Bregman method is improved and used as the local search operator to increase the exploitation capability. Numerical simulations validate the effectiveness and competitiveness of the proposed hybrid evolutionary algorithm with LB-based local search in comparison with other algorithms.

Keywords

Multiobjective sparse reconstruction Compressed sensing Hybrid evolutionary algorithm Linearized Bregman 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

References

  1. 1.
    Wilf, P., Zhang, S., Chikkerur, S., Little, S.A., Wing, S.L., Serre, T.: Computer vision cracks the leaf code. Proc. Natl. Acad. Sci. U. S. A. 113(12), 3305–3310 (2016)CrossRefGoogle Scholar
  2. 2.
    Zhang, S., Yao, H., Sun, X., Xiusheng, L.: Sparse coding based visual tracking: review and experimental comparison. Pattern Recognit. 46(7), 1772–1788 (2013)CrossRefGoogle Scholar
  3. 3.
    Zhang S: A biologically inspired appearance model for robust visual tracking. IEEE Trans. Neural Netw. Learn. Syst. 1–14 (2016)Google Scholar
  4. 4.
    Zhang, S., Yao, H., Sun, X., Wang, K., Zhang, J., Xiusheng, L., Zhang, Y.: Action recognition based on overcomplete independent components analysis. Inf. Sci. 281, 635–647 (2014)CrossRefGoogle Scholar
  5. 5.
    Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Candès, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Yeganli, F., Nazzal, M., Unal, M., H, O.: Image super-resolution via sparse representation over multiple learned dictionaries based on edge sharpness. Signal Image Video Process. 10(3), 535–542 (2016)CrossRefGoogle Scholar
  8. 8.
    Vinay, K.G., Haque, S.M., Babu, R.V., Ramakrishnan, K.R.: Sparse representation-based human detection: a scale-embedded dictionary approach. Signal Image Video Process. 10(3), 585–592 (2016)CrossRefGoogle Scholar
  9. 9.
    Peng, J., Luo, T.: Sparse matrix transform-based linear discriminant analysis for hyperspectral image classification. Signal Image Video Process. 10(4), 761–768 (2016)CrossRefGoogle Scholar
  10. 10.
    Seo, J.-W., Kim, S.-D.: Dynamic background subtraction via sparse representation of dynamic textures in a low-dimensional subspace. Signal Image Video Process. 10(1), 29–36 (2016)CrossRefGoogle Scholar
  11. 11.
    Tropp, J., Gilbert, A.C., et al.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Cai, T.T., Wang, L.: Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Trans. Inf. Theory 57(7), 4680–4688 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Dai, W., Milenkovic, O.: Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans. Inf. Theory 55(5), 2230–2249 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Figueiredo, M.A.T., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007)CrossRefGoogle Scholar
  15. 15.
    Kim, S.J., Koh, K., Lustig, M., Boyd, S., Gorinevsky, D.: An interior-point method for large-scale \(\ell \)1-regularized least squares. IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007)Google Scholar
  16. 16.
    Blumensath, T., Davies, M.E.: Iterative thresholding for sparse approximations. J. Fourier Anal. Appl. 14, 629–654 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Yin, W.: Analysis and generalizations of the linearized Bregman method[J]. Siam J. Imaging Sci. 3(4), 856–877 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Yang, A.Y., Zhou, Z., Balasubramanian, A.G., et al.: Fast \(l\)1-minimization algorithms for robust face recognition. Image Process. IEEE Trans. 22(8), 3234–3246 (2013)CrossRefGoogle Scholar
  19. 19.
    Needell, D., Tropp, J.A.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26, 310–321 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. Siam J. Imaging Sci. 2(1), 183–202 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Malioutov, D.M., Cetin, M., Willsky, A.S.: Homotopy continuation for sparse signal representation[C]. Proc. (ICASSP ’05). IEEE Int. Conf. Acoust. Speech Signal Process. 5, 733–736 (2005)Google Scholar
  22. 22.
    Hale, E.T., Yin, W., Zhang, Y.: A Fixed-Point Continuation Method for ’1-Regularized Minimization with Applications to Compressed Sensing. Caam Tr (2007)Google Scholar
  23. 23.
    Wright, S., Nowak, R., Figueiredo, M.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 2479–2493 (2009)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Li, L., Yao, X., Stolkin, R., et al.: An evolutionary multiobjective approach to sparse reconstruction. IEEE Trans. Evolut. Comput. 18(6), 827–845 (2014)CrossRefGoogle Scholar
  25. 25.
    Price, K.V.: Differential evolution versus the functions of the 2nd, ICEO[C]. IEEE Int. Conf. Evolut. Comput. IEEE, 153–157 (1997)Google Scholar
  26. 26.
    Mierswa, I., Wurst, M.: Information preserving multi-objective feature selection for unsupervised learning[C]. Conf. Genet. Evolut. Comput. ACM, 1545–1552 (2006)Google Scholar
  27. 27.
    Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evolut. Comput. 15(1), 4–31 (2011)CrossRefGoogle Scholar
  28. 28.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength pareto evolutionary algorithm (2001)Google Scholar
  29. 29.
    Dehnad, K.: Density estimation for statistics and data analysis. Technometrics 29(4), 296–297 (1986)Google Scholar
  30. 30.
    Deb, K., Thiele, L., Laumanns M, et al. Scalable multi-objective optimization test problems[C] Evolutionary Computation, 2002. CEC ’02. Proceedings of the 2002 Congress on. IEEE, (2002) :825–830Google Scholar
  31. 31.
    Deb, K., Pratap, A., Agarwal, S., et al.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evolut. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  32. 32.
    Branke, J., Deb, K., Dierolf, H., et al.: Finding knees in multi-objective optimization. Lect. Notes Comput. Sci. 3242, 722–731 (2004)CrossRefGoogle Scholar
  33. 33.
    Handl, J., Knowles, J.D.: Feature subset selection in unsupervised learning via multiobjective optimization. Int. J. Comput. Intell. Res. 2(3), 217–238 (2006)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Mukhopadhyay, A., Maulik, U., Bandyopadhyay, S., et al.: Survey of multiobjective evolutionary algorithms for data mining: part II. IEEE Trans. Evolut. Comput. 18(1), 20–35 (2014)CrossRefGoogle Scholar
  35. 35.
    Wright, S.J., Nowak, R.D., Figueiredo, M., et al.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 3373–3376 (2009)MathSciNetCrossRefGoogle Scholar
  36. 36.
  37. 37.

Copyright information

© Springer-Verlag London 2017

Authors and Affiliations

  1. 1.Institute of Laser EngineeringBeijing University of TechnologyBeijingChina
  2. 2.School of Economics and ManagementBeijing University of TechnologyBeijingChina
  3. 3.Key Laboratory of Optoelectronics Technology, Ministry of EducationBeijing University of TechnologyBeijingChina
  4. 4.Beijing Institute for Scientific and Engineering ComputingBeijing University of TechnologyBeijingChina

Personalised recommendations