Complex Random Vectors and ICA Models: Identifiability, Uniqueness and Separability

Details Complex Random Vectors and ICA Models: Identifiability, Uniqueness and Separability Complex Random Vectors and ICA Models: Identifiability, Uniqueness and Separability

2005-12-15

arxiv.org/abs/cs/0512063v1

Information Theory, IEEE Transactions on , vol.52, no.3pp. 1017- 1029, March 2006

Computer Science

Information Theory

To appear in IEEE TR-IT March 2006

Scientific paper

10.1109/TIT.2005.864440

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.

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