Complex ICA for FMRI analysis: Performance of several approaches

Independent component analysis (ICA) for separating complex-valued sources is needed for convolutive source-separation in the frequency domain, or for performing source separation on complex-valued data, such as functional magnetic resonance imaging data. Functional magnetic resonance imaging (fMRI) is a technique that produces complex-valued data; however the vast majority of fMRI analyses utilize only magnitude images. We compare the performance of the complex infomax algorithm that uses an analytic (and hence unbounded) nonlinearity with the traditional complex infomax approaches that employ bounded (and hence non-analytic) nonlinearities as well as with a cumulant-based approach. We compare the performances of these algorithms for processing both simulated and real fMRI data and show that the complex infomax using analytic nonlinearity has the ability to separate both sub- and super-Gaussian sources with a hyperbolic tangent nonlinearity. The complex infomax algorithm that uses analytic nonlinearity thus provides a potentially powerful method for exploratory analysis of fMRI data.