Spectral Independent Component Analysis with Noise Modeling for M/EEG Source Separation

Background: Independent Component Analysis (ICA) is a widespread tool for exploration and denoising of electroencephalography (EEG) or magnetoencephalography (MEG) signals. In its most common formulation, ICA assumes that the signal matrix is a noiseless linear mixture of independent sources that are assumed non-Gaussian. A limitation is that it enforces to estimate as many sources as sensors or to rely on a detrimental PCA step.

Methods: We present the Spectral Matching ICA (SMICA) model. Signals are modelled as a linear mixing of independent sources corrupted by additive noise, where sources and the noise are stationary Gaussian time series. Thanks to the Gaussian assumption, the negative log-likelihood has a simple expression as a sum of 'divergences' between the empirical spectral covariance matrices of the signals and those predicted by the model. The model parameters can then be estimated by the expectation-maximization (EM) algorithm.

Results: On phantom MEG datasets with low amplitude dipole sources (20 nAm), SMICA makes a median dipole localization error of 1.5 mm while competing methods make an error ≥7 mm. Experiments on EEG datasets show that SMICA identifies a source subspace which contains sources that have less pairwise mutual information, and are better explained by the projection of a single dipole on the scalp. With 10 sources, the number of strongly dipolar sources (dipolarity >90%) is more than 80% for SMICA while competing methods do not exceed 65%.

Comparison With Existing Methods: With the noisy model of SMICA, the number of sources to be recovered is controlled by choosing the size of the mixing matrix to be fitted rather than by a preprocessing step of dimension reduction which is required in traditional noise-free ICA methods.

Conclusions: SMICA is a promising alternative to other noiseless ICA models based on non-Gaussian assumptions.