Event Related Potentials Mesurement: A Bayesian Approach to Perform Improved Averaging and Single-Trial Estimation

Several approaches, based on different assumptions and with various degree of theoretical sophistication and implementation complexity, have been developed for improving the measurement of event related potentials (ERP) performed by conventional averaging (CA). In many of these methods, one of the major challenges is the exploitation of a priori knowledge. In this paper, we present a new method where the 2nd order statistical information on the background EEG and on the unknown ERP, necessary for the optimal filtering of each sweep in a Bayesian estimation framework, is, respectively, estimated from pre-stimulus data and obtained through a multiple integration of a white noise process model. The latter model is flexible and simple enough to be easily identifiable from the post-stimulus data thanks to a smoothing criterion. The mean ERP is determined as the weighted average of the filtered sweeps, where each weight is inversely proportional to the expected value of the norm of the correspondent filter error, a quantity determinable thanks to the employment of the Bayesian approach. Then, single-sweep estimation is also dealt with within the same framework. The method is tested on both simulated and real data, with the aim of investigating the variability of the P300 component in subjects undertaken to a cognitive visual task.