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EEG extended source imaging with structured sparsity and \(L_1\)-norm residual

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Abstract

It is a long-standing challenge to reconstruct the locations and extents of cortical neural activities from electroencephalogram (EEG) recordings, especially when the EEG signals contain strong background activities and outlier artifacts. In this work, we propose a robust source imaging method called \(L_1\)R-SSSI. To alleviate the effect of outliers in EEG, \(L_1\)R-SSSI employs the \(L_1\)-loss to model the residual error. To obtain locally smooth and globally sparse estimations, \(L_1\)R-SSSI adopts the structured sparsity constraint, which incorporates the \(L_1\)-norm regularization in both the variation and original source domain. The estimations of \(L_1\)R-SSSI are efficiently obtained using the alternating direction method of multipliers (ADMM) algorithm. Results of simulated and experimental data analysis demonstrate that \(L_1\)R-SSSI effectively suppresses the effect of the outlier artifacts in EEG. \(L_1\)R-SSSI outperforms the traditional \(L_2\)-norm-based methods (e.g., wMNE, LORETA), and SISSY, which employs \(L_2\)-norm loss and structured sparsity, indicated by the larger AUC (average AUC \(>0.80\)), smaller SD (average SD \(<50\) mm), DLE (average DLE \(<10\) mm) and RMSE (average RMSE \(<1.75\)) values under all the numerically simulated conditions. \(L_1\)R-SSSI also provides better estimations of extended sources than the method with \(L_1\)-loss and \(L_p\)-norm regularization term (e.g., LAPPS).

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Notes

  1. https://openneuro.org/datasets/ds000117.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61703065 and 61836003, Chongqing Research Program of Application Foundation and Advanced Technology under Grant cstc2018jcyjAX0151, the Science and Technology Research Program of Chongqing Municipal Education Commission under Grant KJQN201800612 and Chongqing Graduate Research and Innovation Project under Grant CYS20257.

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Authors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Furong Xu, Ke Liu, Xin Deng & Guoyin Wang

  2. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510641, China

    Zhuliang Yu

  3. Pazhou Lab, Guangzhou, 510335, China

    Zhuliang Yu

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  1. Furong Xu
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  2. Ke Liu
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  3. Zhuliang Yu
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  4. Xin Deng
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  5. Guoyin Wang
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Correspondence to Ke Liu or Guoyin Wang.

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Appendices

Appendix

The schema of \(L_1\)R-SSSI is summarized as follows.

figure a

Appendix

Figure 7 shows the performance metrics under different values of \(\lambda _1\) and \(\lambda _2\). Clearly, the selection of regularization parameters has a great impact on algorithm performance. According to Fig. 7, \(L_1R\)-SSSI achieves better performance for \(\lambda _1\in [1.6,2.1]\), \(\lambda _2\in [0.9,1.3]\), indicated by the relatively larger AUC, smaller SD, DLE, and RMSE values. For simplicity, we employed a fixed value \(\lambda _1=2.1\) and \(\lambda _2=1.0\) for the experimental simulations.

Fig. 7
figure 7

Performance metrics under different values \(\lambda _1\) and \(\lambda _2\)

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Xu, F., Liu, K., Yu, Z. et al. EEG extended source imaging with structured sparsity and \(L_1\)-norm residual. Neural Comput & Applic 33, 8513–8524 (2021). https://doi.org/10.1007/s00521-020-05603-1

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