Advertisement

Signal, Image and Video Processing

, Volume 13, Issue 3, pp 499–506 | Cite as

Sparse time–frequency distributions based on the \(\ell _1\)-norm minimization with the fast intersection of confidence intervals rule

  • Ivan Volaric
  • Victor SucicEmail author
Original Paper
  • 80 Downloads

Abstract

Methods based on the sparsity constraint have been recently introduced to the time–frequency (TF) signal processing, achieving artifact suppression by exploiting the fact that most real-life signals are sparse in the TF domain. In this paper, we propose a sparse reconstruction algorithm based on the two-step iterative shrinkage/thresholding (TwIST) algorithm. In the proposed TwIST algorithm modification, the soft-thresholding value is adaptively determined by the fast intersection of the confidence intervals (FICI) rule in each iteration of the reconstruction algorithm. The FICI rule is used to determine the TF region with the lowest mean value, and the soft-thresholding value is set to the largest sample value inside the region. The performance of the proposed algorithm has been compared to the performance of the state-of-the-art reconstruction algorithms in terms of their execution time and concentration of the resulting TF distribution.

Keywords

Sparse time–frequency distributions Ambiguity function Compressive sensing Fast intersection of confidence intervals (FICI) rule 

References

  1. 1.
    Candès, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Barkan, O., Weill, J., Averbuch, A., Dekel, S.: Adaptive compressed tomography sensing. In: 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2195–2202 (2013)Google Scholar
  4. 4.
    Gramfort, A., Strohmeier, D., Haueisen, J., Hmlinen, M., Kowalski, M.: Time–frequency mixed-norm estimates: sparse M/EEG imaging with non-stationary source activations. NeuroImage 70, 410–422 (2013)CrossRefGoogle Scholar
  5. 5.
    Bioucas-Dias, J.M., Figueiredo, M.A.: A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans. Image Process. 16(12), 2992–3004 (2007)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Romberg, J.: Imaging via compressive sampling [introduction to compressive sampling and recovery via convex programming]. IEEE Signal Process. Mag. 25(2), 14–20 (2008)CrossRefGoogle Scholar
  7. 7.
    Afonso, M., Bioucas-Dias, J., Figueiredo, M.: Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Process. 19(9), 2345–2356 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    El Mouatasim, A., Wakrim, M.: Control subgradient algorithm for image \(\ell _1\) regularization. Signal Image Video Process. 9(1), 275–283 (2015)CrossRefGoogle Scholar
  9. 9.
    Lan, X., Ma, A.J., Yuen, P.C.: Multi-cue visual tracking using robust feature-level fusion based on joint sparse representation. In: 2014 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1194–1201 (2014)Google Scholar
  10. 10.
    Lan, X., Ma, A.J., Yuen, P.C., Chellappa, R.: Joint sparse representation and robust feature-level fusion for multi-cue visual tracking. IEEE Trans. Image Process. 24(12), 5826–5841 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lan, X., Zhang, S., Yuen, P.C., Chellappa, R.: Learning common and feature-specific patterns: a novel multiple-sparse-representation-based tracker. IEEE Trans. Image Process. 27(4), 2022–2037 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Gholami, A.: Sparse time–frequency decomposition and some applications. IEEE Trans. Geosci. Remote Sens. 51(6), 3598–3604 (2013)CrossRefGoogle Scholar
  13. 13.
    Flandrin, P., Borgnat, P.: Time–frequency energy distributions meet compressed sensing. IEEE Trans. Signal Process. 58(6), 2974–2982 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Stankovic, L., Orovic, I., Stankovic, S., Amin, M.: Compressive sensing based separation of nonstationary and stationary signals overlapping in time–frequency. IEEE Trans. Signal Process. 61(18), 4562–4572 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Stankovic, L., Stankovic, S., Orovic, I., Amin, M.G.: Robust time–frequency analysis based on the L-estimation and compressive sensing. IEEE Signal Process. Lett. 20(5), 499–502 (2013)CrossRefzbMATHGoogle Scholar
  16. 16.
    Orović, I., Stanković, S., Thayaparan, T.: Time–frequency-based instantaneous frequency estimation of sparse signals from incomplete set of samples. IET Signal Process. 8(3), 239–245 (2014)CrossRefGoogle Scholar
  17. 17.
    Volaric, I., Sucic, V., Car, Z.: A compressive sensing based method for cross-terms suppression in the time–frequency plane. In: 2015 IEEE 15th International Conference on Bioinformatics and Bioengineering (BIBE), pp. 1–4 (2015)Google Scholar
  18. 18.
    Volaric, I., Sucic, V.: On the noise impact in the l1 based reconstruction of the sparse time–frequency distributions. In: 2016 International Conference on Broadband Communications for Next Generation Networks and Multimedia Applications (CoBCom), pp. 1–6 (2016)Google Scholar
  19. 19.
    Volaric, I., Sucic, V., Stankovic, S.: A data driven compressive sensing approach for time–frequency signal enhancement. Signal Process. 141, 229–239 (2017)CrossRefGoogle Scholar
  20. 20.
    Boashash, B.: Time–Frequency Signal Analysis and Processing: A Comprehensive Reference, 2nd edn. Elsevier, Amsterdam (2016)Google Scholar
  21. 21.
    Becker, S., Bobin, J., Candès, E.J.: NESTA: a fast and accurate first-order method for sparse recovery. SIAM J. Imaging Sci. 4(1), 1–39 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Yang, J., Zhang, Y.: Alternating direction algorithms for \(\ell _1\)-problems in compressive sensing. SIAM J. Sci. Comput. 33(1), 250–278 (2011)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Volaric, I., Lerga, J., Sucic, V.: A fast signal denoising algorithm based on the LPA–ICI method for real-time applications. Circuits Syst. Signal Process. 36(11), 4653–4669 (2017)CrossRefGoogle Scholar
  24. 24.
    Figueiredo, M.A., 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(4), 586–597 (2007)CrossRefGoogle Scholar
  25. 25.
    Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57, 1416–1457 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Wright, S.J., Nowak, R.D., Figueiredo, M.A.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 2479–2493 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    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
  28. 28.
    Needell, D., Tropp, J.: Cosamp: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Blumensath, T.: Accelerated iterative hard thresholding. Signal Process. 92(3), 752–756 (2012)CrossRefGoogle Scholar
  30. 30.
    Foucart, S.: Hard thresholding pursuit: an algorithm for compressive sensing. SIAM J. Numer. Anal. 49(6), 2543–2563 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Qiu, K., Dogandzic, A.: Sparse signal reconstruction via ECME hard thresholding. IEEE Trans. Signal Process. 60(9), 4551–4569 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Zhang, Z., Xu, Y., Yang, J., Li, X., Zhang, D.: A survey of sparse representation: algorithms and applications. IEEE Access 3, 490–530 (2015)CrossRefGoogle Scholar
  33. 33.
    Lerga, J., Vrankic, M., Sucic, V.: A signal denoising method based on the improved ICI rule. IEEE Signal Process. Lett. 15, 601–604 (2008)CrossRefzbMATHGoogle Scholar
  34. 34.
    Stankovic, L.: A measure of some time–frequency distributions concentration. Signal Process. 81(3), 621–631 (2001)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversity of RijekaRijekaCroatia

Personalised recommendations