Complex random vectors and ICA models: identifiability, uniqueness, and separability

Author

Eriksson, Jan ; Koivunen, Visa

Author_Institution

Dept. of Electr. Eng., Helsinki Univ. of Technol.

Volume

52

Issue

3

fYear

2006

fDate

3/1/2006 12:00:00 AM

Firstpage

1017

Lastpage

1029

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

Keywords

blind source separation; entropy; independent component analysis; random processes; vectors; Darmois-Skitovich theorem; blind method; complex random vector; differential entropy; identifiability-separability-uniqueness; independent component analysis; linear complex valued ICA; Biomedical signal processing; Blind source separation; Data analysis; Entropy; Independent component analysis; Random variables; Signal analysis; Signal processing algorithms; Source separation; Vectors; Blind methods; circularity; complex Darmois–Skitovich theorem; complex linear models; differential entropy; independent component analysis (ICA); noncircular complex random vectors; properness;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2005.864440

Filename

1603769