A Karhunen Loeve Transform Approach for Recovering Evoked Potentials from Electroencephalograph

A Karhunen Loeve Transform (KLT) approach for extracting evoked potentials (EPs) from the brain is proposed. The desired EP is heavily contaminated by colored electroencephalograph (EEG) noise which degrades the signal-to-noise ratio (SNR) to as low as -10 dB, making EP estimation highly challenging. The proposed time domain constrained KLT-based estimator explicitly applies pre-whitening on the noisy observation. The whitened data still enable the utilization of a symmetric basis matrix to be eigen-decomposed into its corresponding eigenvalue and eigenvector matrices. The diagonalization process actually decomposes the contaminated EP into decorrelated components; the components which are excessively dominated by EEG noise are discarded, and the ones which are less affected by the noise are preserved. Later, the preserved components are composed and correlated back to the original form to recover the desired EP. The performance of the filter in estimating the EP is then assessed using simulation and real patient data. The estimator produces reasonably low errors and high success rate in both experiments.