Annals of Applied Statistics

Dynamic filtering of static dipoles in magnetoencephalography

Alberto Sorrentino, Adam M. Johansen, John A. D. Aston, Thomas E. Nichols, and Wilfrid S. Kendall

Full-text: Open access


We consider the problem of estimating neural activity from measurements of the magnetic fields recorded by magnetoencephalography. We exploit the temporal structure of the problem and model the neural current as a collection of evolving current dipoles, which appear and disappear, but whose locations are constant throughout their lifetime. This fully reflects the physiological interpretation of the model.

In order to conduct inference under this proposed model, it was necessary to develop an algorithm based around state-of-the-art sequential Monte Carlo methods employing carefully designed importance distributions. Previous work employed a bootstrap filter and an artificial dynamic structure where dipoles performed a random walk in space, yielding nonphysical artefacts in the reconstructions; such artefacts are not observed when using the proposed model. The algorithm is validated with simulated data, in which it provided an average localisation error which is approximately half that of the bootstrap filter. An application to complex real data derived from a somatosensory experiment is presented. Assessment of model fit via marginal likelihood showed a clear preference for the proposed model and the associated reconstructions show better localisation.

Article information

Ann. Appl. Stat., Volume 7, Number 2 (2013), 955-988.

First available in Project Euclid: 27 June 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Magnetoencephalography multi-object tracking particle filtering Resample-Move


Sorrentino, Alberto; Johansen, Adam M.; Aston, John A. D.; Nichols, Thomas E.; Kendall, Wilfrid S. Dynamic filtering of static dipoles in magnetoencephalography. Ann. Appl. Stat. 7 (2013), no. 2, 955--988. doi:10.1214/12-AOAS611.

Export citation


  • Andrieu, C., Doucet, A. and Holenstein, R. (2010). Particle Markov chain Monte Carlo methods. J. R. Stat. Soc. Ser. B Stat. Methodol. 72 269–342.
  • Briers, M., Doucet, A. and Maskell, S. (2010). Smoothing algorithms for state-space models. Ann. Inst. Statist. Math. 62 61–89.
  • Campi, C., Pascarella, A., Sorrentino, A. and Piana, M. (2008). A Rao–Blackwellized particle filter for magnetoencephalography. Inverse Problems 24 025023, 15.
  • Campi, C., Pascarella, A., Sorrentino, A. and Piana, M. (2011). Highly automated dipole estimation (HADES). Comput. Intell. Neurosci. 2011 982185.
  • Carpenter, J., Clifford, P. and Fearnhead, P. (1999). An improved particle filter for non-linear problems. IEE Proceedings Radar, Sonar & Navigation 146 2–7.
  • Chopin, N. (2004). Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32 2385–2411.
  • Chopin, N., Jacob, P. and Papaspiliopoulos, O. (2011). $\mathrm{SMC}^{2}$: An efficient algorithm for sequential analysis of state-space models. Available at arXiv:1101.1528.
  • Cohen, D. and Cuffin, B. N. (1983). Demonstration of useful differences between magnetoencephalogram and electroencephalogram. Electroencephalogr. Clin. Neurophysiol. 56 38–51.
  • Dale, A. M., Fischl, B. and Sereno, M. I. (1999). Cortical surface-based analysis. I. Segmentation and surface reconstruction. Neuroimage 9 179–194.
  • Dale, A. M., Liu, A. K., Fischl, B. R., Buckner, R. L., Belliveau, J. W., Lewine, J. D. and Halgren, E. (2000). Dynamic statistical parametric mapping: Combining fMRI and MEG for high-resolution imaging of cortical activity. Neuron 26 55–67.
  • de Hoyos, A., Portillo, J., Portillo, I., Marin, P., Maestu, F., Poch-Broto, J., Ortiz, T. and Hernando, A. (2012). Comparison and improvements of LCMV and MUSIC source localization techniques for use in real clinical environments. Journal of Neuroscience Methods 205 312–323.
  • Del Moral, P. (2004). Feynman–Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Springer, New York.
  • Douc, R., Cappé, O. and Moulines, E. (2005). Comparison of resampling schemes for particle filters. In Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis I 64–69. IEEE, Zagreb, Croatia.
  • Doucet, A., Godsill, S. and Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statist. Comput. 10 197–208.
  • Doucet, A. and Johansen, A. M. (2011). A tutorial on particle filtering and smoothing: Fifteen years later. In The Oxford Handbook of Nonlinear Filtering 656–704. Oxford Univ. Press, Oxford.
  • Geweke, J. (1989). Bayesian inference in econometric models using Monte Carlo integration. Econometrica 57 1317–1339.
  • Gilks, W. R. and Berzuini, C. (2001). Following a moving target—Monte Carlo inference for dynamic Bayesian models. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 127–146.
  • Golub, G. H. and Van Loan, C. F. (1984). Matrix Computation. Johns Hopkins Univ. Press, Baltimore.
  • Gordon, N. J., Salmond, D. J. and Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian estimation. IEE Proceedings F Radar and Signal Processing 140 107–113.
  • Gramfort, A., Kowalski, M. and Hämäläinen, M. (2012). Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods. Physics in Medicine and Biology 7 1937–1961.
  • Hämäläinen, M. and Ilmoniemi, R. J. (1984). Interpreting measured magnetic fields of the brain: Estimates of current distributions. Technical report, Helsinki Univ. Technology.
  • Hämäläinen, M. and Ilmoniemi, R. J. (1994). Interpreting magnetic fields of the brain: Minimum norm estimates. Medical & Biological Engineering & Computing 32 35–42.
  • Hämäläinen, M., Hari, R., Knuutila, J. and Lounasmaa, O. V. (1993). Magnetoencephalography: Theory, instrumentation and applications to non-invasive studies of the working human brain. Rev. Modern Phys. 65 413–498.
  • Jun, S. C., George, J. S., Parè-Blagoev, J., Plis, S. M., Ranken, D. M., Schmidt, D. M. and Wood, C. C. (2005). Spatiotemporal Bayesian inference dipole analysis for MEG neuroimaging data. NeuroImage 28 84–98.
  • Kantas, N., Doucet, A., Singh, S. S. and Maciejowski, J. M. (2009). An overview of sequential Monte Carlo methods for parameter estimation in general state-space models. In 15th IFAC System Identification (SysId) Meeting Saint-Malo, France 774–785.
  • Kong, A., Liu, J. S. and Wong, W. H. (1994). Sequential imputations and Bayesian missing data problems. J. Amer. Statist. Assoc. 93 278–288.
  • Lee, A., Yau, C., Giles, M. B., Doucet, A. and Holmes, C. C. (2010). On the utility of graphics card to perform massively parallel simulation with advanced Monte Carlo methods. J. Comput. Graph. Statist. 19 769–789.
  • Lin, F. H., Witzel, T., Ahlfors, S. P., Stufflebeam, S. M., Belliveau, J. V. and Hamalainen, M. S. (2006). Assessing and improving the spatial accuracy in MEG source localization by depth-weighted minimum-norm estimates. NeuroImage 31 160–171.
  • Long, C. J., Purdon, P. L., Temeranca, S., Desai, N. U., Hämäläinen, M. and Brown, E. N. (2006). Large scale Kalman filtering solutions to the electrophysiological source localization problem—a MEG case study. In Proceedings of the 28th IEEE EMBS Annual International Conference 4532–4535. IEEE, New York.
  • Long, C. J., Purdon, P. L., Temereanca, S., Desai, N. U., Hämäläinen, M. S. and Brown, E. N. (2011). State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing. Ann. Appl. Stat. 5 1207–1228.
  • Mauguiere, F., Merlet, I., Forss, N., Vanni, S., Jousmaki, V., Adeleine, P. and Hari, R. (1997). Activation of a distributed somatosensory cortical network in the human brain. A dipole modelling study of magnetic fields evoked by median nerve stimulation. Part I: Location and activation timing of SEF sources. Electroencephalography and Clinical Neurophysiology 104 281–289.
  • Mosher, J. C. and Leahy, R. M. (1999). Source localization using recursively applied and projected (RAP) MUSIC. IEEE Trans. Signal Process. 47 332–340.
  • Mosher, J. C., Lewis, P. S. and Leahy, R. M. (1992). Multiple dipole modeling and localization from spatio-temporal MEG data. IEEE Trans. Biomed. Eng. 39 541–557.
  • Ou, W., Hämäläinen, M. S. andGolland, P. (2009). A distributed spatio-temporal EEG/MEG inverse solver. Neuroimage 44 932–946.
  • Pascarella, A., Sorrentino, A., Campi, C. and Piana, M. (2010). Particle filtering, beamforming and multiple signal classification for the analysis of magnetoencephalography time series: A comparison of algorithms. Inverse Probl. Imaging 4 169–190.
  • Sarvas, J. (1987). Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys. Med. Biol. 32 11–22.
  • Scherg, M. and Von Cramon, D. (1986). Evoked dipole source potentials of the human auditory cortex. Electroencephalogr. Clin. Neurophysiol. 65 344–360.
  • Schuhmacher, D., Vo, B.-T. and Vo, B.-N. (2008). A consistent metric for performance evaluation of multi-object filters. IEEE Trans. Signal Process. 56 3447–3457.
  • Somersalo, E., Voutilainen, A. and Kaipio, J. P. (2003). Non-stationary magnetoencephalography by Bayesian filtering of dipole models. Inverse Problems 19 1047–1063.
  • Sorrentino, A. (2010). Particle filters for magnetoencephalography. Arch. Comput. Methods Eng. 17 213–251.
  • Sorrentino, A., Parkkonen, L., Pascarella, A., Campi, C. and Piana, M. (2009). Dynamical MEG source modeling with multi-target Bayesian filtering. Hum. Brain Mapp. 30 1911–1921.
  • Taulu, S., Kajola, M. and Simola, J. (2004). Suppression of interference and artifacts by the signal space separation method. Brain Topogr. 16 269–275.
  • Tian, T. S. and Li, Z. (2011). A spatio-temporal solution for the EEG/MEG inverse problem using group penalization methods. Stat. Interface 4 521–533.
  • Tian, T. S., Huang, J. Z., Shen, H. and Li, Z. (2012). A two-way regularization method for MEG source reconstruction. Ann. Appl. Stat. 6 1021–1046.
  • Uutela, K., Hämäläinen, M. and Somersalo, E. (1999). Visualization of magnetoencephalographic data using minimum current estimates. Neuroimage 10 173–180.
  • Van Veen, B. D., van Drongelen, W., Yuchtman, M. and Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans. Biomed. Eng. 44 867–880.
  • Vo, B. N., Singh, S. and Doucet, A. (2005). Sequential Monte Carlo methods for multi-target filtering with random finite sets. IEEE Transactions on Aerospace and Electronic Systems 41 1224–1245.
  • Wu, S. C., Swindlehurst, A. L., Wang, P. T. and Nenadic, Z. (2012). Efficient dipole parameter estimation in EEG systems with near-ML performance. IEEE Trans. Biomed. Eng. 59 1339–1348.