Regularized State Observers for Source Activity Estimation

  • Andrés Felipe Soler
  • Pablo Andrés Muñoz-GutiérrezEmail author
  • Eduardo Giraldo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11309)


The brain is a complex system and the activity inside can describe non-linear behaviors where the signals of the EEG which are taken from the scalp represent the mixture of the activity in each distributed source inside the brain. This activity can be represented by non-linear models and the inverse problem for source activity estimation can consider these models in the solutions. This paper presents the design of linear and nonlinear regularized observers for neural activity estimation, where the solutions involve a discrete physiologically-based non-linear model as spatio-temporal constraints. Furthermore, this document presents the estimation of the regularization hyper-parameters based on the application of a genetic algorithm over the Generalized Cross Validation cost function, which reduced the computational load. The aforementioned methods are compared with Multiple Sparse Priors (MSP) method of the state-of-the-art by using a simulated and real EEG signals.


EEG inverse problem Neuroimaging Regularization parameters Dynamic regularization 



This work was carried out under the funding of the Departamento Administrativo Nacional de Ciencia, Tecnología e Innovación (Colciencias). Research project: 111077757982 “Sistema de identificación de fuentes epileptogénicas basado en medidas de conectividad funcional usando registros electroencefalográficos e imágenes de resonancia magnética en pacientes con epilepsia refractaria: apoyo a la cirugía resectiva”.

This work is also part of the research project “Solución del problema inverso dinámico considerando restricciones espacio-temporales no homogéneas aplicado a la reconstrucción de la actividad cerebral” funded by the Universidad Tecnológica de Pereira under the code E6-17-2.

Author Contributions

AFS and PAM conceived, designed and performed the experiments. EG analyzed the data. All the authors wrote and refined the article.


  1. 1.
    Friston, K., et al.: Multiple sparse priors for the M/EEG inverse problem. NeuroImage 39(3), 1104–1120 (2008)CrossRefGoogle Scholar
  2. 2.
    Giraldo-Suarez, E., Martinez-Vargas, J.D., Castellanos-Dominguez, G.: Reconstruction of neural activity from EEG data using dynamic spatiotemporal constraints. Int. J. Neural Syst. 26(07), 1650026 (2016)CrossRefGoogle Scholar
  3. 3.
    Grech, R., et al.: Review on solving the inverse problem in EEG source analysis. J. NeuroEng. Rehabil. 5, 25 (2008)CrossRefGoogle Scholar
  4. 4.
    Hauk, O.: Keep it simple: a case for using classical minimum norm estimation in the analysis of EEG and MEG data. NeuroImage 21(4), 1612–1621 (2004)CrossRefGoogle Scholar
  5. 5.
    Henson, R.N., Wakeman, D.G., Litvak, V., Friston, K.J.: A parametric empirical bayesian framework for the EEG/MEG inverse problem: generative models for multi-subject and multi-modal integration. Front. Hum. Neurosci. 5, 1–16 (2011)CrossRefGoogle Scholar
  6. 6.
    Hyder, R., Kamel, N., Tang, T.B., Bornot, J.: Brain source localization techniques: evaluation study using simulated EEG data. In: 2014 IEEE Conference on Biomedical Engineering and Sciences (IECBES), December, pp. 942–947 (2014)Google Scholar
  7. 7.
    Kim, J.W., Robinson, P.A.: Compact dynamical model of brain activity. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 75(3), 1–10 (2007)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kim, J.W., Shin, H.-B., Robinson, P.A.: Compact continuum brain model for human electroencephalogram. In: Proceedings of SPIE 6802, 68020T–68020T-8 (2007)Google Scholar
  9. 9.
    López, J.D., Barnes, G.R.: Single: MEG/EEG source reconstruction with multiple sparse priors and variable patches. Dyna 79(174), 136–144 (2012)Google Scholar
  10. 10.
    Pascual-Marqui, R.D., Michel, C.M., Lehmann, D.: Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. Int. J. Psychophysiol. 18(1), 49–65 (1994)CrossRefGoogle Scholar
  11. 11.
    Soler, A.F.: Design of regularized state observer for estimation in large scale systems: source activity reconstruction from EEG signals. Master’s thesis, Universidad Tecnológica de Pereira, Colombia (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Andrés Felipe Soler
    • 1
  • Pablo Andrés Muñoz-Gutiérrez
    • 2
    Email author
  • Eduardo Giraldo
    • 1
  1. 1.Universidad Tecnológica de PereiraPereiraColombia
  2. 2.Universidad del QuindíoArmeniaColombia

Personalised recommendations