Sparse And Redundant Representations

Author : Carlos G. Puntonet
Publisher : Springer
ISBN 13 : 3540301100
Total Pages : 1270 pages
Book Rating : 4.5/5 (43 download)

DOWNLOAD NOW!

Download or read book Independent Component Analysis and Blind Signal Separation written by Carlos G. Puntonet and published by Springer. This book was released on 2004-10-27 with total page 1270 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many situations found both in Nature and in human-built systems, a set of mixed signals is observed (frequently also with noise), and it is of great scientific and technological relevance to be able to isolate or separate them so that the information in each of the signals can be utilized. Blind source separation (BSS) research is one of the more interesting emerging fields now a days in the field of signal processing. It deals with the algorithms that allow the recovery of the original sources from a set of mixtures only. The adjective "blind" is applied because the purpose is to estimate the original sources without any a priori knowledge about either the sources or the mixing system. Most of the models employed in BSS assume the hypothesis about the independence of the original sources. Under this hypothesis, a BSS problem can be considered as a particular case of independent component analysis(ICA), a linear transformation technique that, starting from a multivariate representation of the data, minimizes the statistical dependence between the components of the representation. It can be claimed that most of the advances in ICA have been motivated by the search for solutions to the BSS problem and, the other way around, advances in ICA have been immediately applied to BSS. ICA and BSS algorithms start from a mixture model, whose parameters are estimated from the observed mixtures. Separation is achieved by applying the inverse mixture model to the observed signals(separating or unmixing model). Mixturem- els usually fall into three broad categories: instantaneous linear models, convolutive models and nonlinear models, the?rstone being the simplest but, in general, not near realistic applications. The development and test of the algorithms can be accomplished through synthetic data or with real-world data. Obviously, the most important aim(and most difficult) is the separation of real-world mixtures. BSS and ICA have strong relations also, apart from signal processing, with other fields such as statistics and artificial neural networks. As long as we can find a system that emits signals propagated through a mean, andthosesignalsarereceivedbyasetofsensorsandthereisaninterestinrecovering the original sources, we have a potential field of application for BSS and ICA. Inside that wide range of applications we can find, for instance: noise reduction applications, biomedical applications, audio systems, telecommunications, and many others. This volume comes out just 20 years after the first contributions in ICA and BSS 1 appeared . Therein after, the number of research groups working in ICA and BSS has been constantly growing, so that nowadays we can estimate that far more than 100 groups are researching in these fields. As proof of the recognition among the scientific community of ICA and BSS developments there have been numerous special sessions and special issues in several well- 1 J. Herault, B. Ans, "Circuits neuronaux à synapses modi?ables: décodage de messages composites para apprentissage non supervise", C.R. de l'Académie des Sciences, vol. 299, no. III-13,pp.525-528,1984