Contributions to theory and algorithms of independent component analysis and signal separation
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Doctoral thesis (article-based)
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Date
2004-08-20
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Language
en
Pages
59
Series
Report / Helsinki University of Technology, Signal Processing Laboratory, 47
Abstract
This thesis addresses the problem of blind signal separation (BSS) using independent component analysis (ICA). In blind signal separation, signals from multiple sources arrive simultaneously at a sensor array, so that each sensor array output contains a mixture of source signals. Sets of sensor outputs are processed to recover the source signals or to identify the mixing system. The term blind refers to the fact that no explicit knowledge of source signals or mixing system is available. Independent component analysis approach uses statistical independence of the source signals to solve the blind signal separation problems. Application domains for the material presented in this thesis include communications, biomedical, audio, image, and sensor array signal processing. In this thesis reliable algorithms for ICA-based blind source separation are developed. In blind source separation problem the goal is to recover all original source signals using the observed mixtures only. The objective is to develop algorithms that are either adaptive to unknown source distributions or do not need to utilize the source distribution information at all. Two parametric methods that can adapt to a wide class of source distributions including skewed distributions are proposed. Another nonparametric technique with desirable large sample properties is also proposed. It is based on characteristic functions and thereby avoids the need to model the source distributions. Experimental results showing reliable performance are given on all of the presented methods. In this thesis theoretical conditions under which instantaneous ICA-based blind signal processing problems can be solved are established. These results extend the celebrated results by Comon of the traditional linear real-valued model. The results are further extended to complex-valued signals and to nonlinear mixing systems. Conditions for identification, uniqueness, and separation are established both for real and complex-valued linear models, and for a proposed class of non-linear mixing systems.Description
Keywords
independent component analysis, blind source separation, signal separation, multiple-input multiple-output models, identifiability, separation algorithms
Other note
Parts
- Eriksson J., Karvanen J. and Koivunen V., 2000. Source distribution adaptive maximum likelihood estimation of ICA model. In: Proceedings of the Second International Workshop on Independent Component Analysis and Blind Signal Separation (ICA 2000). Helsinki, Finland, 19-22 June 2000, pages 227-232. [article1.pdf] © 2000 by authors.
- Karvanen J., Eriksson J. and Koivunen V., 2000. Pearson system based method for blind separation. In: Proceedings of the Second International Workshop on Independent Component Analysis and Blind Signal Separation (ICA 2000). Helsinki, Finland, 19-22 June 2000, pages 585-590. [article2.pdf] © 2000 by authors.
- Karvanen J., Eriksson J. and Koivunen V., 2002. Adaptive score functions for maximum likelihood ICA. The Journal of VLSI Signal Processing – Systems for Signal, Image, and Video Technology 32, number 1, pages 83-92.
- Eriksson J. and Koivunen V., 2001. Blind separation using characteristic function based criterion. In: Proceedings of the 35th Conference on Information Sciences and Systems (CISS 2001). Baltimore, Maryland, USA, 21-23 March 2001, volume 2, pages 781-785. [article4.pdf] © 2001 by authors.
- Eriksson J., Kankainen A. and Koivunen V., 2001. Novel characteristic function based criteria for ICA. In: Proceedings of the Third International Conference on Independent Component Analysis and Blind Signal Separation (ICA 2001). San Diego, California, USA, 9-12 December 2001, pages 108-113. [article5.pdf] © 2001 by authors.
- Eriksson J. and Koivunen V., 2002. Blind identifiability of class of nonlinear instantaneous ICA models. In: Proceedings of the XI European Signal Processing Conference (EUSIPCO-2002). Toulouse, France, 3-6 September 2002, volume 2, pages 7-10. [article6.pdf] © 2002 by authors.
- Eriksson J. and Koivunen V., 2003. Characteristic-function-based independent component analysis. Signal Processing 83, number 10, pages 2195-2208.
- Eriksson J. and Koivunen V., 2004. Identifiability, separability, and uniqueness of linear ICA models. IEEE Signal Processing Letters 11, number 7, pages 601-604.
- Eriksson J. and Koivunen V., 2004. Complex random vectors and ICA models: identifiability, uniqueness and separability. IEEE Transactions on Information Theory, submitted for publication (March 2004). Material presented also in the technical report: Identifiability, separability, and uniqueness of complex ICA models. Helsinki University of Technology, Signal Processing Laboratory, Report 44 (2004).