  We propose an algorithm targeting the identification of more sources than
channels for electroencephalography (EEG). Our overcomplete source
identification algorithm, Cov-DL, leverages dictionary learning methods applied
in the covariance-domain. Assuming that EEG sources are uncorrelated within
moving time-windows and the scalp mixing is linear, the forward problem can be
transferred to the covariance domain which has higher dimensionality than the
original EEG channel domain. This allows for learning the overcomplete mixing
matrix that generates the scalp EEG even when there may be more sources than
sensors active at any time segment, i.e. when there are non-sparse sources.
This is contrary to straight-forward dictionary learning methods that are based
on the assumption of sparsity, which is not a satisfied condition in the case
of low-density EEG systems. We present two different learning strategies for
Cov-DL, determined by the size of the target mixing matrix. We demonstrate that
Cov-DL outperforms existing overcomplete ICA algorithms under various scenarios
of EEG simulations and real EEG experiments.
