Compressive Sensing of Multichannel EEG Signals Based on Graph Fourier Transform and Cosparsity

  • Xiuming Zou
  • Lei Feng
  • Huaijiang SunEmail author


Cosparsity as a useful prior has been extensively applied in accurate compressive sensing (CS) recovery of multichannel electroencephalogram (EEG) signals from only a few measurements. Latest studies proved that exploiting cosparsity and channel correlation in a unified framework can obtain accurate recovery results. However, all these methods ignore the adjacent relationship between the real physical electrodes and exploit the inaccurate channel correlation. Another problem is that most methods employ convex regularizations to exploit cosparsity and channel correlation, which cannot obtain competitive results. In this paper, a novel graph Fourier transform and nonconvex optimization (GFTN)-based method is proposed to enforce inherent correlation across different channels and cosparsity. Alternative direction method of multipliers is used to solve the resulting nonconvex optimization problem. Experiments show that GFTN can remarkably improve the performance of CS recovery for multichannel EEG signals.


Compressive sensing Multichannel EEG signals Cosparsity Graph Fourier transform Alternative direction method of multipliers 



The authors would like to express their gratitude to the anonymous referees as well as the Editor and Associate Editor for their valuable comments, which led to substantial improvements of the paper. This work was supported by the National Natural Science Foundation of China (Nos. 61772272 and 61801199), the Natural Science Fund Project of Colleges in Jiangsu Province (No. 18KJB520017) and the High-level Talent Scientific Research Foundation of Jinling Institute of Technology (No. jit-b-201801).


  1. 1.
    Abdulghani AM, Casson AJ, Rodriguez-Villegas E (2012) Compressive sensing scalp EEG signals: implementations and practical performance. Med Biol Eng Comput 50(11):1137–1145CrossRefGoogle Scholar
  2. 2.
    Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122CrossRefGoogle Scholar
  3. 3.
    Cand EJ, Wakin MB (2008) An introduction to compressive sampling. IEEE Signal Process Mag 25(2):21–30CrossRefGoogle Scholar
  4. 4.
    Casson AJ, Yates D, Smith S, Duncan JS, Rodriguez-Villegas E (2010) Wearable electroencephalography. IEEE Eng Med Biol Mag 29(3):44–56CrossRefGoogle Scholar
  5. 5.
    Chartrand R, Yin W (2008) Iteratively reweighted algorithms for compressive sensing. In: IEEE international conference on acoustics, speech & signal processing, pp 3869–3872Google Scholar
  6. 6.
    Dong W, Shi G, Li X, Ma Y, Huang F (2014) Compressive sensing via nonlocal low-rank regularization. IEEE Trans Image Process Publ IEEE Signal Process Soc 23(8):3618–3632MathSciNetCrossRefGoogle Scholar
  7. 7.
    Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306MathSciNetCrossRefGoogle Scholar
  8. 8.
    Feng L, Sun H, Sun Q, Xia G (2016) Image compressive sensing via truncated schatten-p norm regularization. Signal Process Image Commun 47:28–41CrossRefGoogle Scholar
  9. 9.
    Higashi H, Tanaka T, Tanaka Y (2015) Smoothing of spatial filter by graph Fourier transform for eeg signals. In: Asia-Pacific signal and information processing association, 2014 summit and conferenceGoogle Scholar
  10. 10.
    Hooda A, Sharma S (2013) Wireless body area network. In: Proceedings of international symposium on medical information & communication technology, vol 3, no 3, pp 203–210Google Scholar
  11. 11.
    Hosseini Kamal M, Shoaran M, Leblebici Y, Schmid A (2013) Compressive multichannel cortical signal recording. In: IEEE international conference on acoustics, speech & signal processing, pp 4305–4309Google Scholar
  12. 12.
    Liu Y, De VM, Van HS (2015) Compressed sensing of multichannel EEG signals: the simultaneous cosparsity and low-rank optimization. IEEE Trans Bio-med Eng 62(8):2055–2061CrossRefGoogle Scholar
  13. 13.
    Majumdar A, Ward RK (2015) Energy efficient EEG sensing and transmission for wireless body area networks: a blind compressed sensing approach. Biomed Signal Process Control 20:1–9CrossRefGoogle Scholar
  14. 14.
    Malmivuo J, Plonsey R (1995) Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. Part 1. Oxford University Press, New YorkCrossRefGoogle Scholar
  15. 15.
    Nam S, Davies ME, Elad M, Gribonval R (2011) The cosparse analysis model and algorithms. Appl Comput Harmon Anal 34(1):30–56MathSciNetCrossRefGoogle Scholar
  16. 16.
    Qi F, Li Y, Wu W (2017) RSTFC: a novel algorithm for spatio-temporal filtering and classification of single-trial EEG. IEEE Trans Neural Netw Learn Syst 26(12):3070–3082MathSciNetCrossRefGoogle Scholar
  17. 17.
    Rao BD, Kreutz-Delgado K (1999) An affine scaling methodology for best basis selection. IEEE Trans Signal Process 47(1):187–200MathSciNetCrossRefGoogle Scholar
  18. 18.
    Shu X, Yang J, Ahuja N (2014) Non-local compressive sampling recovery. In: International conference on computational photography, pp 1–8Google Scholar
  19. 19.
    Wang J, Wang M, Hu X, Yan S (2015) Visual data denoising with a unified schatten-p norm and q norm regularized principle component pursuit. Pattern Recognit 48(10):3135–3144CrossRefGoogle Scholar
  20. 20.
    Wormann J, Hawe S, Kleinsteuber M (2013) Analysis based blind compressive sensing. IEEE Signal Process Lett 20(5):491–494CrossRefGoogle Scholar
  21. 21.
    Wu W, Chen Z, Gao X, Li Y, Brown EN, Gao S (2015) Probabilistic common spatial patterns for multichannel EEG analysis. IEEE Trans Pattern Anal Mach Intell 37(3):639–653CrossRefGoogle Scholar
  22. 22.
    Wu W, Nagarajan S, Chen Z (2016) Bayesian machine learning: EEG/MEG signal processing measurements. IEEE Signal Process Mag 33(1):14–36CrossRefGoogle Scholar
  23. 23.
    Xie Y (2015) Weighted schatten $p$-norm minimization for image denoising with local and nonlocal regularization. Eprint ArxivGoogle Scholar
  24. 24.
    Zhang Z, Jung TP, Makeig S, Rao BD (2013) Compressed sensing of EEG for wireless telemonitoring with low energy consumption and inexpensive hardware. IEEE Trans Biomed Eng 60(1):221–4CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Computer Science and TechnologyHuaiyin Normal UniversityHuai’anChina
  2. 2.School of Computer Science and EngineeringNanjing University of Science and TechnologyNanjingChina
  3. 3.School of Computer EngineeringJinling Institute of TechnologyNanjingChina

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