Estimation of Auditory Event-Related Potentials using a Combination of Principal Component Analysis and Kalman Filtering

Abstract

This paper presents a method that aims to separate auditory event-related potentials (ERP) from noise. In practice, ERPs would be approximated by weighted sums of Principal Component (PCA) basis signals calculated from clean data. Projection of measured signals onto the PCA subspace greatly reduces noise. A second step uses Kalman filtering to optimally combine the PCA filtered signal with the ERP expected before measurement. Much of the power of the proposed algorithm comes from exploiting apriori cross-channel information in the form of a PCA weight covariance matrix. In this paper the performance of the method is quantified using synthetic multi-channel ERP signals to which known amounts of synthetic noise is added to all the channels. The use of synthetic data means and signal and noise are known and so signal-to-noise improvement can be determined. For a wide range of initial SNRs, PCA filtering increases SNR by 10 dB while Kalman filtering yields another 10 dB improvement.

Identification of Multi-Channel Simulated Auditory Event-Related Potentials using a Combination of Principal Component Analysis and Kalman Filtering

“…A method to produce synthetic, multichannel ERP signals has been presented in Paulson and Alfahad [11]. The multi-channel simulator assumes that all channels measure the same underlying brain process, but filtered by the bone and tissue between the activity and the electrode on the scalp.…”

“…For each trial, these parameters are determined from six independent samples from a Standard Normal distribution. Each trial is assumed to be independent [11].…”

“…Secondly, the PCA weights are refined using KF to find the optimal combination of measured and expected weights. In an earlier paper, [11], the authors present a similar method. That algorithm relied upon a PCA basis of signals for each channel of the EEG measurement.…”