Complex random vectors and ICA models: Identifiability, uniqueness and separability
Jan Eriksson Member, Visa Koivunen, Senior Member · 2006
Abstract — In this paper the conditions for identifiability, separability and uniqueness of linear complex valued independent component analysis (ICA) models are established. These results extend the well-known conditions for solving real-valued ICA problems to complex-valued models. Relevant properties of complex random vectors are described in order to extend the Darmois-Skitovich theorem for complex-valued models. This theorem is used to construct a proof of a theorem for each of the above ICA model concepts. Both circular and noncircular complex random vectors are covered. Examples clarifying the above concepts are presented. Index Terms — Blind methods, circularity, complex linear models, complex Darmois-Skitovich theorem, differential entropy, independent component analysis (ICA), noncircular complex random vectors, properness. I.