Localization of Brain Signals by Signal Subspace Matching

We present a novel approach for solving the inverse problem in electroencephalography (EEG) using the signal subspace matching (SSM) criterion. The proposed approach is based on an intuitively pleasing metric, aimed at matching the error-contaminated model-based signal subspace to its noisy sample-data counterpart. SSM is formulated using an iterative scheme inspired by the alternating projection (AP) solution to the deterministic maximum likelihood, which involves only 1-dimensional optimization. We compare the SSM algorithm to RAP-MUSIC and AP and show its advantages in various realistic settings. We find that SSM performs particularly well when (1) neural sources are highly correlated; and (2) noise at different channels is correlated. These scenarios are commonly encountered with real EEG recordings, therefore the SSM algorithm provides a significant improvement over other similar algorithms such as RAP-MUSIC and AP.