Super-Gaussian BSS Using Fast-ICA with Chebyshev–Pade Approximant

Abstract

Independent component analysis (ICA) is one of the most powerful techniques to solve the problem of blind source separation (BSS), and the well-known Fast-ICA is excellent for large-scale BSS. Fast-ICA tries to find the demixing matrix by optimizing the nonlinear objective (cost or contrast) functions. For Fast-ICA, there are three built-in contrast functions to separate non-Gaussian sources, and their derivatives are similar to nonlinearities used in neural networks. However, the contrast functions and their nonlinearities for separating super-Gaussian sources are not optimal owing to their high computational cost, which greatly affect the convergence rate of Fast-ICA. To address this issue, this paper proposes two rational nonlinearities to replace the built-in (original) nonlinearities. The rational nonlinearities are derived by the Chebyshev–Pade approximant from Chebyshev polynomials (series) of the original nonlinearities. To speed up the convergence of Fast-ICA, the degrees in both numerator and denominator of rational functions are designed to be relatively low, and thus the rational polynomials can be quickly evaluated. Simulation results of audio BSS show that the proposed rational nonlinearities can not only improve the convergence rate of Fast-ICA, but also improve the separation performance index; Experiment results of real electrocardiogram data also verify the validity of the proposed approach.