Independent component analysis of complex-valued functional magnetic resonance imaging data by complex nonlinearities

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. Functional magnetic resonance imaging (fMRI) is a technique that produces complex-valued data; however the vast majority of fMRI analyses utilize only magnitude images due in large part to the difficulty of developing a temporal phase model. We have successfully applied ICA to complex fMRI data but there is a need to further optimize the complex ICA. We recently proposed a number of complex nonlinear functions for ICA of complex valued data. We apply two of these functions to fMRI data and examine the properties of these nonlinearities and their efficiency in generating the higher order statistics needed for ICA. We show that the complex infomax using these efficient nonlinearities demonstrates superior performance compared to analysis of the magnitude data with either ICA or linear regression. Complex ICA thus provides a potentially powerful method for the analysis of fMRI data.