Complex infomax: Convergence and approximation of infomax with 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, such as functional magnetic resonance imaging or radar data. Previous complex Infomax approaches that use nonlinear functions in the updates have proposed using bounded (and hence non-analytic) nonlinearities. In this paper, we propose using an analytic (and hence unbounded) complex nonlinearity for Infomax for processing complex-valued sources. We show by simulation examples that using an analytic nonlinearity for processing complex data has a number of advantages. First, when compared to split-complex approaches (i.e., approaches that split the real and imaginary data into separate channels), the shape of the performance surface is improved resulting in better convergence characteristics. We also show that using an analytic complex-valued function for the nonlinearity is more effective in generating the higher order statistics required to establish independence when compared to complex nonlinear functions, i.e., functions that are ℂ → ℂ.