We present a nonlinear unmixing approach for extracting the ballistocardiogram from EEG recorded in an MR scanner during simultaneous acquisition of fMRI. First, an overcomplete basis is identified in the EEG based on a custom multi-path EEG electrode cap. Next, the overcomplete basis is used to infer non-Kirchhoffian latent variables which are not consistent with a conservative electric field. Neural activity is strictly Kirchhoffian while the BCG artifact is not, and the representation can hence be used to remove the artifacts from the data in a way that does not attenuate the neural signals needed for optimal single-trial classification performance. We compare our method to more standard methods for BCG removal, namely ICA and OBS, by looking at single-trial classification performance for an auditory oddball experiment. We show that our overcomplete representation method for removing BCG artifacts results in better single-trial classification performance compared to the conventional approaches, indicating that the derived neural activity in this representation retains the complex information in the trial-to-trial variability.
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