Estimation of coherence using the median is robust against EEG artefacts

Coherence is a mathematical measure of correlation in the frequency domain, commonly used to quantify the oscillatory synchrony of bio-signals such as the electroencephalogram (EEG). In biomedical applications, such as assessment of functional connectivity, reliable estimation of coherence is of paramount importance for studying the function of complex brain networks, as well as their disruption in neurological disorders. A major challenge for robust estimation of coherence measures is the presence of artefacts. Here, we propose an alternative method for finding coherence by estimating auto- and cross-spectral densities based on the median or trimmed-mean values across trials, rather than the mean. The variance of the average cortico-cortical coherence measures, i.e., the inter-individual variability, was taken as a measure of robustness and tested on resting-state recordings from 34 healthy individuals, both without screening, as well as after screening by a statistical thresholding artefact rejection. The variability of average coherence in individual channels and frequency bands decreased by using the median-based estimation of coherence. Averaged across all channels and frequency bands, the variability of coherence estimates based on median was significantly lower than mean-based estimates for both unscreened data (F = 9.28, p = 0.003, 1-β_0.05 = 0.98) and screened data (F = 6.58, p = 0.01, 1-β_0.05 = 0.91). Moreover, the variability for median-based estimates was almost identical for unscreened and screened data (F = 0.004, p = 0.95), suggesting that coherence based on median without artefact rejection might be sufficient for robust estimation of coherence.