| This study introduces two novel beamforming algorithms, namely the Multiple Correlated Source Model and Region Constrained beamformers, designed to localize and to reconstruct highly correlated brain sources from noisy EEG data. We have also derived two vector beamforrners, the Vector Weight Normalized and Vector Standardized Minimum Variance beamformers, using a modified optimization problem statement. In addition, we have proposed efficient algorithms to compute the normalized output power and signal-to-noise ratio of the Scalar Minimum Variance beamformer, the output power of the Vector Weight Normalized Minimum Variance beamformer, and the output signal-to-noise ratio of the Vector Standardized Minimum Variance beamformer. Single and multiple correlated source simulations have been carried out to evaluate the performance of the proposed beamforming algorithms. These simulations have been performed using a realistic 176 x 240 x 256 finite difference head model. Our simulation results show that the new vector beamforming algorithms provide higher localization accuracy than the conventional vector beamformers including the Linearly Constrained Minimum Variance beamformer and Borgiotti-Kaplan beamformer. Most importantly, the Region Constrained-Multiple Correlated Source Model beamformer, obtained by combining the Region Constrained and Multiple Correlated Source Model beamformers, allows us to localize three perfectly correlated brain sources with very high localization accuracy. Finally, the eigenspace version of this beamformer can be used to reconstruct three correlated brain sources correctly from simulated noisy EEC data. |
