Schrödinger filtering: a precise EEG despiking technique for EEG-fMRI gradient artifact.

In EEG data acquired in the presence of fMRI, gradient-related spike artifacts contaminate the signal following the common preprocessing step of average artifact subtraction. Spike artifacts compromise EEG data quality since they overlap with the EEG signal in frequency, thereby confounding frequency-based inferences on activity. As well, spike artifacts can inflate or deflate correlations among time series, thereby confounding inferences on functional connectivity. We present Schrödinger filtering, which uses the Schrödinger equation to decompose the spike-containing input. The basis functions of the decomposition are localized and pulse-shaped, and selectively capture the various input peaks, with the spike components clustered at the beginning of the spectrum. Schrödinger filtering automatically subtracts the spike components from the data. On real and simulated data, we show that Schrödinger filtering (1) simultaneously accomplishes high spike removal and high signal preservation without affecting evoked activity, and (2) reduces spurious pairwise correlations in spontaneous activity. In these regards, Schrödinger filtering was significantly better than three other despiking techniques: median filtering, amplitude thresholding, and wavelet denoising. These results encourage the use of Schrödinger filtering in future EEG-fMRI pipelines, as well as in other spike-related applications (e.g., fMRI motion artifact removal or action potential extraction).