On the performance of metahuristic algorithms in the solution of the EEG inverse problem

The problem of electroencephalographic (EEG) source localization involves an optimization problem that can be solved through global optimization methods. In this paper, we evaluate the performance in localizing EEG sources of simulated annealing (SA) and genetic algorithm (GA) as a function of the optimization's initialization parameters and the signal-to-noise ratio (SNR). We use the concentrated likelihood function (CLF) as objective function and the Cramér-Rao bound (CRB) as a reference on the performance. The CRB sets the lower limit on the variance of our estimated values. Then, through simulations on realistic EEG data we show that both SA and GA are highly sensitive to noise, but adjustments on their parameters for a fixed SNR value do not improve performance significantly. However SA is more sensitive to noise and its performance may be affected by correlated sources. Our results also confirm that in both algorithms the mean square error (MSE) in the location EEG sources is minimum.

[1]  Carlos H. Muravchik,et al.  Estimating brain conductivities and dipole source signals with EEG arrays , 2004, IEEE Transactions on Biomedical Engineering.

[2]  David J. Evans,et al.  Medical image reconstruction using a multi-objective genetic local search algorithm , 2000, Int. J. Comput. Math..

[3]  R. Leahy,et al.  EEG and MEG: forward solutions for inverse methods , 1999, IEEE Transactions on Biomedical Engineering.

[4]  Harry L. Van Trees,et al.  Detection, Estimation, and Modulation Theory, Part I , 1968 .

[5]  R. Salmelin,et al.  Global optimization in the localization of neuromagnetic sources , 1998, IEEE Transactions on Biomedical Engineering.

[6]  P. Stoica,et al.  On the concentrated stochastic likelihood function in array signal processing , 1995 .

[7]  Arye Nehorai,et al.  Array Response Kernels for EEG and MEG in Multilayer Ellipsoidal Geometry , 2008, IEEE Transactions on Biomedical Engineering.

[8]  D. Khosla,et al.  Spatio-temporal EEG source localization using simulated annealing , 1997, IEEE Transactions on Biomedical Engineering.

[9]  Aleksandar Dogandzic,et al.  Estimating evoked dipole responses in unknown spatially correlated noise with EEG/MEG arrays , 2000, IEEE Trans. Signal Process..

[10]  H. Shakouri G.,et al.  Investigation on the choice of the initial temperature in the Simulated Annealing: A mushy state SA for TSP , 2009, 2009 17th Mediterranean Conference on Control and Automation.

[11]  Colin R. Reeves,et al.  Genetic Algorithms: Principles and Perspectives: A Guide to Ga Theory , 2002 .

[12]  W. Drongelen,et al.  Localization of brain electrical activity via linearly constrained minimum variance spatial filtering , 1997, IEEE Transactions on Biomedical Engineering.

[13]  E. Michielssen,et al.  Multiple source localization using genetic algorithms , 1996, Journal of Neuroscience Methods.

[14]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[15]  Liming Zhang,et al.  Multiple Signal Classification Based on Genetic Algorithm for MEG Sources Localization , 2007, ISNN.

[16]  Michael N. Vrahatis,et al.  Tackling magnetoencephalography with particle swarm optimization , 2009, Int. J. Bio Inspired Comput..

[17]  Petre Stoica,et al.  MUSIC, maximum likelihood and Cramer-Rao bound , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[18]  I. Hidalgo,et al.  A Genetic Algorithm Approach for Localization of Deep Sources in MEG , 2005 .

[19]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[20]  André Neubauer,et al.  Adaptive Non-uniform Mutation for Genetic Algorithms , 1997, Fuzzy Days.