High-Fidelity Imaging of the Brain’s Electrophysiological Activity Based on a Fast Direct Solver

Imaging of the electrophysiologic activity of the brain is important for diagnosing or treating several neurological diseases. Electroencephalography source imaging (ESI) is a modality that reconstructs the electrophysiologic activity from external potential measurement at the scalp. Despite being non-invasive and being capable of offering high temporal and spatial resolutions, its adoption is hampered by its complexity and high computational cost caused by its need to solve a complex forward problem from hundreds to thousands of times per subject. In this contribution, we tackle this issue by presenting a fast direct solver for ESI that yields a low-rank skeleton form of the inverse of the forward problem, allowing for a drastic reduction in the computational load of the imaging modality.