A Family of Reduced-Rank Neural Activity Indices for EEG/MEG Source Localization

  • Tomasz Piotrowski
  • David Gutiérrez
  • Isao Yamada
  • Jarosław Żygierewicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8609)


Localization of sources of brain electrical activity from electroencephalographic and magnetoencephalographic recordings is an ill-posed inverse problem. Therefore, the best one can hope for is to derive a source localization method which is guaranteed to find sources belonging to the set of possible solutions to this problem. Recently, a few methods with this property have been proposed as a non-trivial generalizations of the classical neural activity index based on the linearly constrained minimum-variance (LCMV) spatial filtering technique. In this paper we propose a family of reduced-rank activity indices achieving maximum value when evaluated at true source locations for uncorrelated dipole sources and any nonzero rank constraint. This fact shows in particular that this key property is not confined to a selected few activity indices. We present a series of numerical simulations evaluating localization performance of the proposed activity indices. We also give an overview of areas of future research which should be considered as an extension of the results of this paper. In particular, we discuss how new families of activity indices can be derived based on the proposed technique.


Electroencephalography magnetoencephalography beamforming reduced-rank signal processing dipole source localization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Van Veen, B.D., Van Drongelen, W., Yuchtman, M., Suzuki, A.: Localization of Brain Electrical Activity via Linearly Constrained Minimum Variance Spatial Filtering. IEEE Transactions on Biomedical Engineering 44(9), 867–880 (1997)CrossRefGoogle Scholar
  2. 2.
    Frost, O.T.: An Algorithm for Linearly Constrained Adaptive Array Processing. Proceedings of the IEEE 60(8), 926–935 (1972)CrossRefGoogle Scholar
  3. 3.
    Diwakar, M., Huang, M.-X., Srinivasan, R., Harrington, D.L., Robb, A., Angeles, A., Muzzatti, L., Pakdaman, R., Song, T., Theilmann, R.J., Lee, R.R.: Dual-Core Beamformer for Obtaining Highly Correlated Neuronal Networks in MEG. NeuroImage 54(1), 253–263 (2011)CrossRefGoogle Scholar
  4. 4.
    Moiseev, A., Gaspar, J.M., Schneider, J.A., Herdman, A.T.: Application of Multi-Source Minimum Variance Beamformers for Reconstruction of Correlated Neural Activity. NeuroImage 58(2), 481–496 (2011)CrossRefGoogle Scholar
  5. 5.
    Yamada, I., Elbadraoui, J.: Minimum-Variance Pseudo-Unbiased Low-Rank Estimator for Ill-Conditioned Inverse Problems. In: IEEE ICASSP 2006, pp. 325–328 (2006)Google Scholar
  6. 6.
    Piotrowski, T., Yamada, I.: MV-PURE Estimator: Minimum-Variance Pseudo-Unbiased Reduced-Rank Estimator for Linearly Constrained Ill-Conditioned Inverse Problems. IEEE Transactions on Signal Processing 56(8), 3408–3423 (2008)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Piotrowski, T., Cavalcante, R.L.G., Yamada, I.: Stochastic MV-PURE Estimator: Robust Reduced-Rank Estimator for Stochastic Linear Model. IEEE Transactions on Signal Processing 57(4), 1293–1303 (2009)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Piotrowski, T., Zaragoza-Martinez, C.C., Gutiérrez, D., Yamada, I.: MV-PURE Estimator of Dipole Source Signals in EEG. In: IEEE ICASSP 2013, pp. 968–972 (2013)Google Scholar
  9. 9.
    Piotrowski, T., Yamada, I.: Performance of the Stochastic MV-PURE Estimator in Highly Noisy Settings. Journal of the Franklin Institute (in press)Google Scholar
  10. 10.
    Piotrowski, T., Gutiérrez, D., Yamada, I., Żygierewicz, J.: Reduced-Rank Neural Activity Index for EEG/MEG Multi-Source Localization. In: IEEE ICASSP 2014 (in press, 2014)Google Scholar
  11. 11.
    Mosher, J.C., Leahy, R.M., Lewis, P.S.: EEG and MEG: Forward Solutions for Inverse Methods. IEEE Transactions on Biomedical Engineering 46(3), 245–259 (1999)CrossRefGoogle Scholar
  12. 12.
    Golub, G.H., Van Loan, C.F.: Matrix Computations. The Johns Hopkins University Press, Baltimore (1996)Google Scholar
  13. 13.
    Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, New York (1985)Google Scholar
  14. 14.
    Theobald, C.M.: An Inequality for the Trace of the Product of Two Symmetric Matrices. Math. Proc. Camb. Phil. Soc. 77, 265–267 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Stenroos, M., Mantynen, V., Nenonen, J.: A MATLAB Library for Solving Quasi-Static Volume Conduction Problems Using the Boundary Element Method. Computer Methods and Programs in Biomedicine 88(3), 256–263 (2007)CrossRefGoogle Scholar
  16. 16.
    Aine, C.J., Sanfratello, L., Ranken, D., Best, E., MacArthur, J.A., Wallace, T., Gilliam, K., Donahue, C.H., Montano, R., Bryant, J.E., Scott, A., Stephen, J.M.: MEG-SIM: A Web Portal for Testing MEG Analysis Methods Using Realistic Simulated and Empirical Data. Neuroinformatics 10(2), 141–158 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tomasz Piotrowski
    • 1
  • David Gutiérrez
    • 2
  • Isao Yamada
    • 3
  • Jarosław Żygierewicz
    • 4
  1. 1.Dept. of Informatics, Faculty of Physics, Astronomy and InformaticsNicolaus Copernicus UniversityToruńPoland
  2. 2.Center for Research and Advanced Studies, Monterrey’s UnitApodacaMéxico
  3. 3.Dept. of Communications and Computer EngineeringTokyo Institute of TechnologyTokyoJapan
  4. 4.Biomedical Physics Division, Institute of Experimental Physics, Faculty of PhysicsUniversity of WarsawWarsawPoland

Personalised recommendations