Complex Random Vectors and ICA Models: Identifiability, Uniqueness and Separability
arXiv:cs/0512063 · doi:10.1109/TIT.2005.864440
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.
To appear in IEEE TR-IT March 2006