Covariance-domain Dictionary Learning for Overcomplete EEG Source Identification

TL;DR

This paper introduces Cov-DL, a novel covariance-domain dictionary learning algorithm for overcomplete EEG source identification, capable of recovering more sources than sensors without relying on source sparsity.

Contribution

The paper presents a new covariance-domain dictionary learning approach for overcomplete EEG source separation, overcoming limitations of sparsity-based methods.

Findings

Cov-DL outperforms existing overcomplete ICA algorithms in simulations.

The method successfully identifies more sources than sensors in real EEG data.

Cov-DL effectively handles non-sparse, overcomplete source scenarios.

Abstract

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.