Enhanced Localization and Orientation Estimations in Focal EEG Source Imaging Using SVD-Based Coordinate Transform

Accurate localization and orientation estimation of neural sources are crucial in electroencephalography (EEG) source imaging, particularly for focal brain activities. This study introduces an enhanced method that integrates a Singular Value Decomposition (SVD)-based coordinate transform to improve the performance of Hierarchical Adaptive L1-Regression (HAL1R). By applying the SVD transform to the lead field matrix columns corresponding to individual source locations, we derive physiologically meaningful orientation bases that align with the brain's structural and functional properties. Enforcing sparsity into these bases mitigates orientation biases inherent in standard L1-norm algorithms applied in traditional Cartesian systems. Numerical simulations and somatosensory evoked potential (SEP) data validate the proposed approach, demonstrating improved localization stability and orientation accuracy compared to conventional methods, such as Adaptive Group LASSO, Unit Noise Gain (UNG) Beamformer, and Dipole Scanning (DS). The SVD-based HAL1R framework establishes a robust and generalizable methodology for EEG source imaging, enhancing its accuracy and utility in clinical and research settings, including pre-surgical planning and non-invasive cortical mapping.