1. Blind Source Separation in Nonlinear Mixtures: Separability and a Basic Algorithm
- Author
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Christian Jutten, Massoud Babaie-Zadeh, Bertrand Rivet, Bahram Ehsandoust, GIPSA - Vision and Brain Signal Processing (GIPSA-VIBS), Département Images et Signal (GIPSA-DIS), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Department of Electrical Engineering [Tehran] (EE department of SUT [Tehran]), Sharif University of Technology [Tehran] (SUT), and ERC CHESS Project - 2012-ERC-Adv-320684
- Subjects
Local linear ,Stochastic process ,Nonlinear Mixtures ,020206 networking & telecommunications ,02 engineering and technology ,Blind signal separation ,Independent component analysis ,Independent Component Analysis ,Nonlinear system ,Blind Source Separation ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,Signal Processing ,0202 electrical engineering, electronic engineering, information engineering ,Signal processing algorithms ,020201 artificial intelligence & image processing ,Nonlinear Regression ,Electrical and Electronic Engineering ,Algorithm ,Nonlinear regression ,Random variable ,Computer Science::Databases ,Mathematics - Abstract
International audience; In this paper, a novel approach for performing Blind Source Separation (BSS) in nonlinear mixtures is proposed, and their separability is studied. It is shown that this problem can be solved under a few assumptions, which are satisfied in most practical applications. The main idea can be considered as transforming a time-invariant nonlinear BSS problem to local linear ones varying along the time, using the derivatives of both sources and observations. Taking into account the proposed idea, numerous algorithms can be developed performing the separation. In this regard, an algorithm, supported by simulation results, is also proposed in this paper. It can be seen that the algorithm well separates the mixed sources, however, as the conventional linear BSS methods, the nonlinear BSS suffers from ambiguities, which are discussed in the paper.
- Published
- 2017