AbstractIn biomedical engineering, dipole source localization is commonly used to identify brain activities from scalp recorded potentials, which is known as inverse problem of electroencephalography (EEG) source localization. However, this problem is fundamental in biomedical engineering, medicine and neuroscience. The EEG inverse problem is non-linear, in addition, it is ill-posed and the solver can be unstable, i.e. the solution is non-unique and it is highly sensitive to small changes of the measured signal (noise). For solving the EEG inverse problem iterative methods, like Levenberg-Marquardt algorithm, are usually considered. However, these techniques require good initial values and many electrodes N, since a large redundancy supports the finding of the right solution. Therefore, in this paper, a hybrid method of linear and non-linear modelling and least squares approach are proposed to overcome of these problems: the solutions calculated by means of a linear approximation of EEG inverse problems serve as initial values for solving the original non-linear model. In addition, independent component analysis (ICA) is combined with the proposed hybrid least squares method to separate different dipole sources from multiple EEG signals. The performance of the hybrid least squares method with and without ICA is measured in term of root mean square error. The simulation results show that the proposed method can estimate the location of dipole source with acceptable accuracy under high noise condition and small N comparing with linear least squares method considering larger N. Finally, it should be mentioned that the proposed method promises advantages in finding solutions of the EEG inverse problem effectively.
Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods
