Brain Activity Estimation using EEG-only Recordings Calibrated with joint EEG-fMRI Recordings using Compressive Sensing

Electroencephalogram (EEG) is a noninvasive, low-cost brain recording tool with high temporal but poor spatial resolution. In contrast, functional magnetic resonance imaging (fMRI) is a rather expensive brain recording tool with high spatial and poor temporal resolution. In this study, we aim at recovering the brain activity (source localization and activity-intensity) with high spatial resolution using only EEG recordings. Each EEG electrode records a linear combination of the activities of various parts of the brain. As a result, a multi-electrode EEG recording represents the brain activities via a linear mixing matrix. Due to distance attenuation, this matrix is almost sparse. Using simultaneous recordings of fMRI and EEG, we estimate the mixing matrix (calibration). Since Blood Oxygen Level Dependent (BOLD) signal of fMRI is a measure of energy used by active brain region, it has a quadratic relation with the electric potential waveform emitted from each fMRI volume pixel (voxel). Assuming uncorrelated time series from different regions, we reformulate the (underdetermined) forward problem as a linear problem and solve it using the Orthogonal Matching Pursuit (OMP) method. Besides the mixing matrix, the brain activities are often sparse spatially. Thus, we employ the estimated mixing matrix to extract the activity intensity of various brain regions from EEG recordings using iterative shrinkage thresholding algorithm (ISTA). We verify the proposed method on synthetic data. In particular, we divide the gray matter of the brain into 300 regions and assume a 30%-sparse measurement matrix, as well as 5% of regions to be active simultaneously. Simulations results show 88% accuracy in localizing the sources and and 66% accuracy in activity intensity estimation.