Normalized Cumulative Periodogram Method For Tuning A Regularization Parameter of The EEG Inverse Problem

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 paper, authors investigate the normalized cumulative periodogram (NCP) and apply it to the source localization problem. Furthermore, authors compare its performance with other two parameter choice methods which are L-curve and Generalized-Cross Validation (GCV) in terms of accuracy and reliability. Authors opted the WMNE algorithm to solve the EEG inverse problem with the application of different noise levels and different simulated source generators. 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 outperform the L-curve method and resulted in a better average localization error.