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Unformatted text preview: 248 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 21, NO. 2, FEBRUARY 2010 Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size Vicente Zarzoso , Member, IEEE , and Pierre Comon , Fellow, IEEE Abstract Independent component analysis (ICA) aims at decomposing an observed random vector into statistically inde- pendent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referred to as RobustICA, is put forward in this paper. This simple technique consists of performing exact line search optimization of the kurtosis contrast function. The step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth-degree polynomial. This polynomial rooting can be performed algebraically, and thus at low cost, at each iteration. Among other practical benefits, RobustICA can avoid prewhitening and deals with real- and complex-valued mixtures of possibly noncircular sources alike. The absence of prewhitening improves asymptotic performance. The algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality, particularly for short data records. These features are demonstrated by a comparative numerical analysis on synthetic data. RobustICAs capabilities in processing real-world data involving noncircular complex strongly super-Gaussian sources are illustrated by the biomedical problem of atrial activity (AA) extraction in atrial fibrillation (AF) electrocardiograms (ECGs), where it outperforms an alternative ICA-based technique. Index Terms Atrial fibrillation (AF), blind source separation (BSS), independent component analysis (ICA), iterative optimiza- tion, kurtosis, optimal step size, performance analysis. I. INTRODUCTION A. Blind Source Separation and Independent Component Analysis I NTRODUCED over two decades ago , the problem of blind source separation (BSS) consists of recovering a set of unobservable source signals from observed mixtures of the sources. Independent component analysis (ICA) aims at decom- posing an observed random vector into statistically indepen- dent variables . Among its numerous applications, ICA is the most natural tool for BSS in instantaneous linear mixtures when the source signals are assumed to be independent. As Manuscript received March 11, 2009; revised October 13, 2009; accepted October 24, 2009. First published December 18, 2009; current version published February 05, 2010....
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This note was uploaded on 12/29/2011 for the course ECE 594C taught by Professor Madhow during the Fall '10 term at UCSB.
- Fall '10