A fast algorithm for blind extraction of smooth complex sources with application in EEG conditioning

A fast complex-valued blind source extraction algorithm designed for the extraction of smooth sources, is introduced. This is achieved based on a smoothness constrained cost and by considering the augmented statistics of the latent source signals. The methodology, based on the CR calculus and complex FastICA framework, is shown to be capable of extraction of both complex circular and noncircular smooth sources for real-time brain computer interfacing. The performance of the algorithm is verified on benchmark signals, followed by a biomedical application in the extraction of artifacts from recorded EEG signals in the order of smoothness.

[1]  D. Mandic,et al.  Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models , 2009 .

[2]  W. Wirtinger.  Zur formalen Theorie der Funktionen von mehr komplexen Veränderlichen , 1927 .

[3]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[4]  A. Bos.  Complex gradient and Hessian , 1994 .

[5]  Wei Liu,et al.  Blind Second-Order Source Extraction of Instantaneous Noisy Mixtures , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[7]  Danilo P. Mandic,et al.  Complex Valued Nonlinear Adaptive Filters , 2009 .

[8]  Nikolaos Mitianoudis,et al.  Smooth Signal Extraction From Instantaneous Mixtures , 2007, IEEE Signal Processing Letters.

[9]  Renbiao Wu,et al.  A Novel Approach to Blind Source Extraction Based on Skewness , 2006, 2006 8th international Conference on Signal Processing.

[10]  Tülay Adali,et al.  On Extending the Complex FastICA Algorithm to Noncircular Sources , 2008, IEEE Transactions on Signal Processing.

[11]  Seungjin Choi,et al.  Independent Component Analysis , 2009, Handbook of Natural Computing.

[12]  James L. Massey,et al.  Proper complex random processes with applications to information theory , 1993, IEEE Trans. Inf. Theory.

[13]  Andrzej Cichocki,et al.  Complex Blind Source Extraction From Noisy Mixtures Using Second-Order Statistics , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Ken Kreutz-Delgado,et al.  The Complex Gradient Operator and the CR-Calculus ECE275A - Lecture Supplement - Fall 2005 , 2009, 0906.4835.

[15]  Christian Jutten,et al.  Blind Extraction of Smooth Signals Based on a Second-Order Frequency Identification Algorithm , 2010, IEEE Signal Processing Letters.

[16]  Pascal Bondon,et al.  Second-order statistics of complex signals , 1997, IEEE Trans. Signal Process..

[17]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals , 2000, Int. J. Neural Syst..

[18]  D.P. Mandic,et al.  Why a Complex Valued Solution for a Real Domain Problem , 2007, 2007 IEEE Workshop on Machine Learning for Signal Processing.

[19]  Esa Ollila,et al.  On the Circularity of a Complex Random Variable , 2008, IEEE Signal Processing Letters.