Complex ICA Using Nonlinear Functions

We introduce a framework based on Wirtinger calculus for nonlinear complex-valued signal processing such that all computations can be directly carried out in the complex domain. The two main approaches for performing independent component analysis, maximum likelihood, and maximization of non-Gaussianity-which are intimately related to each other-are studied using this framework. The main update rules for the two approaches are derived, their properties and density matching strategies are discussed along with numerical examples to highlight their relationships.