Novel Quadratic Gaussianity Measures and their Application in Blind Source Separation/Extraction

Various existing criteria to characterize the statistical independence are applied in blind source separation and independent component analysis. However, almost all of them are based on parametric models. The distribution model mismatch between the output PDF (Probability Density Functions) and the chosen underlying distribution model is a serious problem in blind signal processing. Non-parametric PDF estimates like the Parzen window applied to the popular Kullback-Leibler divergence produce computational difficulties. Hence we propose a new measure, the Quadratic Gaussianity Measure, which is associated with the Euclidean distance between the marginal probability density function and the Gaussian distribution. We show that it outperforms other Gaussianity measures in signal processing applications, such as standardized kurtosis tests because our novel Gaussianity measure is robust to changes in the distribution form.