We extended the classical Independent Component Analysis framework to allow for non-square mixing in the presence of Gaussian noise. By including a noise model, we are able to address a variety of important issues that exist in ICA applied to FMRI data. Most importantly, we address the issue of overfitting and can associate statistical significance to individual voxels within spatial maps that are modulated significantly by the associated time courses. Within the method, we take into account the very specific form of FMRI data: the general characteristics of autoregressive noise, possibly varying at different voxel locations, the necessity of voxel-wise variance normalisation and the fact that other image derived spatial information often is available and should be allowed to aid the estimation of signals of interest.
This model improves on the robustness and interpretability of IC maps as currently generated on FMRI data: experiments on artificial data suggest that the proposed methodology can accurately extract various sources of variability, not only from artificial noise that conforms to the model, but from artificial data generated from real FMRI noise.
The technique was illustrated on two examples of real FMRI data where the probabilistic independent component model is able to produce relevant patterns of activation that can neither be generated within the standard GLM nor standard ICA frameworks. We believe that PICA is a powerful technique complementary to existing methods that allows exploration of the complex structure of FMRI data in a statistically meaningful way.
The research described in this paper has been implemented as MELODIC (Multivariate Exploratory Linear Optimized Decomposition into Independent Components - a standalone C++ program). MELODIC is freely available as part of FSL (FMRIB's Software Library - www.fmrib.ox.ac.uk/fsl).