Optimal Pairwise Fourth-Order Independent Component Analysis

Blind source separation (BSS) aims at the reconstruction of unknown mutually independent signals, so-called sources, from their mixtures observed at the output of a sensor array. The BSS of instantaneous linear mixtures, which finds application in numerous fields, can be solved through the statistic...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2006-08, Vol.54 (8), p.3049-3063
Main Authors: Zarzoso, V., Murillo-Fuentes, J.J., Rafael Boloix-Tortosa, Nandi, A.K.
Format: Article
Language:English
Subjects:
Adaptive algorithm
Algorithms
Applied sciences
Array signal processing
Asymptotic properties
Blind source separation
Computer Science
Detection, estimation, filtering, equalization, prediction
Engineering Sciences
Estimators
Exact sciences and technology
Exact solutions
higher order statistics
Independent component analysis
Information, signal and communications theory
Jacobian matrices
Machine Learning
Mean square error methods
Mean square errors
Miscellaneous
Optimization
Optimization techniques
Performance analysis
Scattering parameters
Sensor arrays
Signal and communications theory
Signal and Image processing
Signal processing
Signal representation. Spectral analysis
Signal, noise
Source separation
Statistical methods
Statistics
Studies
Telecommunications and information theory
unsupervised learning
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Summary:Blind source separation (BSS) aims at the reconstruction of unknown mutually independent signals, so-called sources, from their mixtures observed at the output of a sensor array. The BSS of instantaneous linear mixtures, which finds application in numerous fields, can be solved through the statistical tool of independent component analysis (ICA). This paper concentrates on the analytic solutions for the fundamental two-signal ICA scenario. A novel estimation class, so-called general weighted fourth-order estimator (GWFOE), is put forward, which is based on the fourth-order statistics of the whitened sensor output. By means of a weight parameter, the GWFOE is able to unify a variety of apparently disparate estimation expressions previously scattered throughout the literature, including the well-known JADE method in the two-signal case. A theoretical asymptotic performance analysis is carried out, resulting in the GWFOE large-sample mean square error and the source-dependent weight value of the most efficient estimator in the class. To extend the pairwise estimators to the general scenario of more than two sources, an improved Jacobi-like optimization technique is proposed. The approach consists of calculating the necessary sensor-output fourth-order statistics at the initialization stage of the algorithm, which can lead to significant computational savings when large sample blocks are processed. Based on this idea, adaptive algorithms are also devised, showing very satisfactory convergence characteristics. Experiments illustrate the good performance of these optimal pairwise ICA strategies, in both off- and on-line processing modes
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2006.875391