ICAR: a tool for blind source separation using fourth-order statistics only

• Published in: IEEE transactions on signal processing Vol. 53; no. 10; pp. 3633 - 3643
• Main Authors: Albera, L., Ferreol, A., Chevalier, P., Comon, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic properties; Biosensors; Blind source separation; Blinds; Computer Science; Density; Detection, estimation, filtering, equalization, prediction; Electrocardiography; Engineering Sciences; Exact sciences and technology; fourth-order statistics; Gaussian; Independent component analysis; Information theory; Information, signal and communications theory; overdetermined mixtures; Redundancy; Sensor arrays; Sensor phenomena and characterization; Separation; Signal and communications theory; Signal and Image Processing; Signal, noise; Source separation; Spectra; Speech analysis; Statistical analysis; Statistics; Telecommunications and information theory; Performance evaluation; Signal mixing; Second order; Source separation; Computer simulation; Redundancy; Spatial correlation; Independent component analysis; Signal estimation; Order statistic; Data processing; Blind source separation; fourth-order statistics; Blind separation; overdetermined mixtures; Gaussian noise; First order; Signal processing; Spectral density; Signal to noise ratio; Blind Source Separation; Overdetermined Mixtures; Fourth Order Statistics; Independent Component Analysis
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2005.855089

The problem of blind separation of overdetermined mixtures of sources, that is, with fewer sources than (or as many sources as) sensors, is addressed in this paper. A new method, called Independent Component Analysis using Redundancies in the quadricovariance (ICAR), is proposed in order to process complex data. This method, without any whitening operation, only exploits some redundancies of a particular quadricovariance matrix of the data. Computer simulations demonstrate that ICAR offers in general good results and even outperforms classical methods in several situations: ICAR i) succeeds in separating sources with low signal-to-noise ratios, ii) does not require sources with different second-order or/and first-order spectral densities, iii) is asymptotically not affected by the presence of a Gaussian noise with unknown spatial correlation, iv) is not sensitive to an over estimation of the number of sources.