A Comparative Study of the Regularization Parameter Estimation Methods for the EEG Inverse Problem

Discussion Committee: 
Dr. Adnan Salman/supervisor
Dr. Hazem Abu Sara/external examiner
Prof. Mohamad Al-Said/internal examiner
Dr. Adnan Salman/supervisor
Mohammed Jamil Aburidi
Investigation of the functional neuronal activity in the human brain depends on the localization of Electroencephalographic (EEG) signals to their cortex sources, which requires solving the source localization inverse problem. The problem is ill-conditioned and under-determinate, and so it is ill-posed. To find a treatment of the ill-posed nature of the problem, a regularization scheme must be applied. A crucial issue in the application of any regularization scheme, in any domain, is the optimal selection of the regularization parameter. The selected regularization parameter has to find an optimal tradeoff between the data fitting term and the amount of regularization. Several methods exist for finding an optimal estimate of the regularization parameter of the ill-posed problems in general. In this thesis, we investigated three popular methods and applied them to the source localization problem. These methods are: L-curve, Normalized Cumulative Periodogram (NCP), and the Generalized-Cross Validation (GCV). Then we compared the performance of these methods in terms of accuracy and reliability. We opted the WMNE algorithm to solve the EEG inverse problem with the application of different noise levels and different simulated source generators. The forward solution, which maps the current source generators inside the brain to scalp potential, was computed using an efficient accurate Finite Difference Method (FDM) forward solver. Our results indicate that NCP method gives the best estimation for the regularization parameter in general. However, for some levels of noise, GCV method has similar performance. In contrast, both NCP and GCV methods outperforms the L-curve method and resulted in a better average localization error. Moreover, we compared the performance of two inverse solver algorithms, eLORETA and sLORETA. Our results indicate that eLORETA outperform sLORETA in all localization error measures that we used, which includes, the center of gravity and the spatial spreading.
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