Bayesian Inference for Brain Source Imaging with Joint Estimation of Structured Low-rank Noise

The inverse problem in brain source imaging is the reconstruction of brain activity from non-invasive recordings of electroencephalography (EEG) and magnetoencephalography (MEG). One key challenge is the efficient recovery of sparse brain activity when the data is corrupted by structured noise that is low-rank noise. This is often the case when there are a few active sources of environmental noise and the MEG/EEG sensor noise is highly correlated. In this paper, we propose a novel robust empirical Bayesian framework which provides us a tractable algorithm for jointly estimating a low-rank noise covariance and brain source activity. Specifically, we use a factor analysis model for the structured noise, and infer a sparse set of variance parameters for source activity, while performing Variational Bayesian inference for the noise. One key aspect of this algorithm is that it does not require any additional baseline measurements to estimate the noise covariance from the sensor data. We perform exhaustive experiments on both simulated and real datasets. Our algorithm achieves superior performance as compared to several existing benchmark algorithms.