Complex Independent Component Analysis Using Three Types of Diversity: Non-Gaussianity, Nonwhiteness, and Noncircularity

By assuming latent sources are statistically independent, independent component analysis (ICA) separates underlying sources from a given linear mixture. Since in many applications, latent sources are non-Gaussian, noncircular, and have sample dependence, it is desirable to exploit all these properties jointly. Mutual information rate, which leads to the minimization of entropy rate, provides a natural cost for the task. In this paper, we establish the theory for complex-valued ICA giving Cramér-Rao lower bound and identification conditions, and present a new algorithm that takes all these properties into account. We propose an effective estimator of entropy rate and a complex-valued entropy rate bound minimization algorithm based on it. We show that the new method exploits all these properties effectively by comparing the estimation performance with the Cramér-Rao lower bound and by a number of examples.