Noise reduction in brain evoked potentials based on third-order correlations

We use third-order correlations (TOC) in developing a filtering technique for the recovery of brain evoked potentials (EPs). The main idea behind the presented technique is to pass the noisy signal through a finite impulse response filter whose impulse response is matched with the shape of the noise-free signal. It is shown that it is possible to estimate the filter impulse response on basis of a selected third-order correlation slice (TOCS) of the input noisy signal. This is justified by two facts. The first one is that the noise-free EPs can be modeled as a sum of damped sinusoidal signals and the selected TOCS preserve the signal structure. The second fact is that the TOCS is insensitive to both Gaussian noise and other symmetrically distributed non-Gaussian noise, (white or colored). Furthermore, the approach can be applied to either nonaveraged or averaged EP observation data. In the nonaveraged data case, the approach therefore preserves information about amplitude and latency changes. Both fixed and adaptive versions of the proposed filtering technique are described. Extensive simulation results are provided to show the validity and effectiveness of the proposed cumulant-based filtering technique in comparison with the conventional correlation-based counterpart.