Multi-Source Neural Activity Indices and Spatial Filters for EEG/MEG Inverse Problem: An Extension to MNE-Python

Accurate EEG/MEG source localization is essential for understanding brain function, yet remains challenging because the inverse problem is inherently ill-posed. In spatial filtering (beamforming) approaches, single-source LCMV spatial filters, though widely used, suffer from source cancellation when sources are correlated - a common experimental scenario. Multi-source frameworks, such as the multi-source minimum-variance pseudo-unbiased reduced-rank (MV-PURE) method, offer improved reconstruction and robust neural activity indices, yet their adoption has been limited by incomplete theory and lack of accessible implementations. In this paper, we present a rigorous derivation of multi-source neural activity indices and spatial filters, establishing a complete analytical framework with automated parameter selection. The resulting compact algebraic forms enable straightforward implementation. To facilitate adoption, we provide a full implementation extending MNE-Python, along with an accompanying tutorial, and demonstrate its utility on EEG experimental data, highlighting the practical advantages of multi-source spatial filtering for source localization and reconstruction.