Skip to main content
SpringerLink
Log in

Sparse Component Analysis Based on Hierarchical Hough Transform

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

Sparse component analysis (SCA) has been extensively studied to solve undetermined blind source separation problem in various fields over the last decades. This paper proposes a SCA algorithm based on hierarchical Hough transform. The hyperplanes clustering within the mixture space are revealed as local maxima in the parameter space after Hough transform is performed. Then, the local maxima are picked up, and the mixing matrix is calculated. The grid resolution in which the parameter space is divided plays an important role on the estimation error and the computational load. Therefore, the parameter space is divided into hypercubes recursively from low to high resolution, and Hough transform is performed only on the hypercubes with votes exceeding a selected threshold. The grid resolution selection problem is solved, and the computational load is reduced a lot in the meantime. After the mixing matrix is obtained, the sources are recovered with \(\ell _1\)-norm optimization. Numerical simulation and a speech separation application illustrate the superior performance of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. S. Barbarossa, Analysis of multicomponent lfm signals by a combined Wigner–Hough transform. IEEE Trans. Signal Process. 43(6), 1511–1515 (1995)

    Article  Google Scholar 

  2. A. Belouchrani, K. AbedMeraim, J.F. Cardoso, E. Moulines, A blind source separation technique using second-order statistics. IEEE Trans. Signal Process. 45(2), 434–444 (1997)

    Article  Google Scholar 

  3. P. Bofill, M. Zibulevsky, Underdetermined blind source separation using sparse representations. Signal Process. 81(11), 2353–2362 (2001)

    Article  MATH  Google Scholar 

  4. P.S. Bradley, O.L. Mangasarian, k-plane clustering. J. Glob. Optim. 16(1), 23–32 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. X.R. Cao, R.W. Liu, General approach to blind source separation. IEEE Trans. Signal Process. 44(3), 562–571 (1996)

    Article  Google Scholar 

  6. S.S.B. Chen, D.L. Donoho, M.A. Saunders, Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20(1), 33–61 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. S.S.B. Chen, D.L. Donoho, M.A. Saunders, Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. S.J. Choi, A. Cichocki, A. Belouchrani, Second order nonstationary source separation. J. Vlsi Signal Process. Syst. Signal Image Video Technol. 32(1–2), 93–104 (2002)

    Article  MATH  Google Scholar 

  9. A. Cichocki, S. Amari, Adaptive Blind Signal and Image Processing (Wiley, Chichester, 2002)

    Book  Google Scholar 

  10. L.A. Cirillo, A.M. Zoubir, M.G. Amin, Direction finding of nonstationary signals using a time-frequency Hough transform, in 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 1–5 (2005), pp. 501–504

  11. P. Comon, Independent component analysis, a new concept. Signal Process. 36(3), 287–314 (1994)

    Article  MATH  Google Scholar 

  12. D.L. Donoho, Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. P. Georgiev, F. Theis, A. Cichocki, Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Trans. Neural Netw. 16(4), 992–996 (2005)

    Article  Google Scholar 

  14. P.G. Georgiev, F. Theis, A. Cichocki, Optimization algorithms for sparse representations and applications. Multisc. Optim. Methods Appl. 82, 85–99 (2006)

    MathSciNet  MATH  Google Scholar 

  15. I.F. Gorodnitsky, B.D. Rao, Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm. IEEE Trans. Signal Process. 45(3), 600–616 (1997)

    Article  Google Scholar 

  16. Z.S. He, A. Cichocki, Y.Q. Li, S.L. Me, S. Sanei, K-hyperline clustering learning for sparse component analysis. Signal Process. 89(6), 1011–1022 (2009)

    Article  MATH  Google Scholar 

  17. P.V.C. Hough, Method and means for recognizing complex patterns: U.S. Patent 3,069,654[P]. 1962-12-18

  18. H.W. Li, M.A. Lavin, R.J. Lemaster, Fast Hough transform—a hierarchical approach. Comput. Vis. Graph. Image Process. 36(2–3), 139–161 (1986)

    Article  Google Scholar 

  19. J. Lin, D. Grier, J. Cowan, Feature extraction approach to blind source separation, in Proceedings of the 1997 IEEE Workshop (1997), pp. 398–405

  20. B.A. Olshausen, D.J. Field, Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381(6583), 607–609 (1996)

    Article  Google Scholar 

  21. J. Princen, J. Illingworth, J. Kittler, A hierarchical approach to line extraction based on the Hough transform. Comput. Vis. Graph. Image Process. 52(1), 57–77 (1990)

    Article  Google Scholar 

  22. V.G. Reju, S.N. Koh, I.Y. Soon, An algorithm for mixing matrix estimation in instantaneous blind source separation. Signal Process. 89(9), 1762–1773 (2009)

    Article  MATH  Google Scholar 

  23. I. Takigawa, M. Kudo, J. Toyama, Performance analysis of minimum l(1)-norm solutions for underdetermined source separation. IEEE Trans. Signal Process. 52(3), 582–591 (2004)

    Article  MathSciNet  Google Scholar 

  24. F.J. Theis, P. Georgiev, A. Cichocki, Robust sparse component analysis based on a generalized Hough transform. EURASIP J. Adv. Signal Process. 2007(1), 86–86 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Y. Tsaig, D.L. Donoho, Extensions of compressed sensing. Signal Process. 86(3), 549–571 (2006)

    Article  MATH  Google Scholar 

  26. E. van den Berg, M.P. Friedlander, SPGL1: a solver for large-scale sparse reconstruction (2007)

  27. E. van den Berg, M.P. Friedlander, Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31(2), 890–912 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  28. Y.C. Yang, S. Nagarajaiah, Output-only modal identification with limited sensors using sparse component analysis. J. Sound Vib. 332(19), 4741–4765 (2013)

    Article  Google Scholar 

  29. M. Zibulevsky, B.A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary. Neural Comput. 13(4), 863–882 (2001)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Key Basic Research Program of China (973 Program) under Grant No. 2014CB049500 and the Key Science and Technologies Program of Anhui Province under Grant No. 1301021005.

Author information

Authors and Affiliations

  1. Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China (USTC), Hefei, 230027, AnHui, People’s Republic of China

    Yi Jin, Shaoqian Qin & Changan Zhu

Authors
  1. Yi Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shaoqian Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Changan Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yi Jin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jin, Y., Qin, S. & Zhu, C. Sparse Component Analysis Based on Hierarchical Hough Transform. Circuits Syst Signal Process 36, 1569–1585 (2017). https://doi.org/10.1007/s00034-016-0374-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-016-0374-8

Keywords

Search

Navigation