Blind Nonparametric Determined and Underdetermined Signal Extraction Algorithm for Dependent Source Mixtures

Blind extraction or separation statistically independent source signals from linear mixtures have been well studied in the last two decades by searching for local extrema of certain objective functions, such as nonGaussianity (NG) measure. Blind source extraction (BSE) algorithm from underdetermined linear mixtures of the statistically dependent source signals is derived using nonparametric NG measure in this paper. After showing that maximization of the NG measure can also separate or extract the statistically weak dependent source signals, the nonparametric NG measure is defined by statistical distances between different source signals distributions based on the cumulative density function (CDF) instead of traditional probability density function (PDF), which can be estimated by the quantiles and order statistics using the \( L^{2} \) norm efficiently. The nonparametric NG measure can be optimized by a deflation procedure to extract or separate the dependent source signals. Simulation results for synthesis and real world data show that the proposed nonparametric extraction algorithm can extract the dependent signals and yield ideal performance.