Abstract
Cognitive functions are often studied using event-related potentials (ERPs) that are usually estimated by an averaging algorithm. Clearly, estimation of single-trial ERPs can provide researchers with many more details of cognitive activity than the averaging algorithm. A novel method to estimate single-trial ERPs is proposed in this paper. This method includes two key ideas. First, singular value decomposition was used to construct a matrix, which mapped single-trial electroencephalographic recordings (EEG) into a low-dimensional vector that contained little information from the spontaneous EEG. Second, we used the theory of compressed sensing to build a procedure to restore single-trial ERPs from this low-dimensional vector. ERPs are sparse or approximately sparse in the frequency domain. This fact allowed us to use the theory of compressed sensing. We verified this method in simulated and real data. Our method and dVCA (differentially variable component analysis), another method of single-trial ERPs estimation, were both used to estimate single-trial ERPs from the same simulated data. Results demonstrated that our method significantly outperforms dVCA under various conditions of signal-to-noise ratio. Moreover, the single-trial ERPs estimated from the real data by our method are statistically consistent with the theories of cognitive science.