Separation of instantaneous mixtures of a particular set of dependent sources using classical ICA methods
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RESEARCH
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Separation of instantaneous mixtures of a particular set of dependent sources using classical ICA methods Marc Castella1* , Selwa Rafi1 , Pierre Comon2 and Wojciech Pieczynski1
Abstract This article deals with the problem of blind source separation in the case of a linear and instantaneous mixture. We first investigate the behavior of known independent component analysis (ICA) methods in the case where the independence assumption is violated: specific dependent sources are introduced and it is shown that, depending on the source vector, the separation may be successful or not. For sources which are a probability mixture of the previous dependent ones and of independent sources, we introduce an extended ICA model. More generally, depending on the value of a hidden latent process at the same time, the unknown components of the linear mixture are assumed either mutually independent or dependent. We propose for this model a separation method which combines: (i) a classical ICA separation performed using the set of samples whose components are conditionally independent, and (ii) a method for estimation of the latent process. The latter task is performed by iterative conditional estimation (ICE). It is an estimation technique in the case of incomplete data, which is particularly appealing because it requires only weak conditions. Keywords: Blind source separation, Dependent sources, Independent Component Analysis (ICA), Higher order statistics, Iterative Conditional Estimation (ICE)
1 Introduction For the last decades, blind source separation (BSS) has been an active research problem: this popularity comes from the wide panel of potential applications such as audio processing, telecommunications, biology, etc. In the case of a linear multi-input/multi-output (MIMO) instantaneous system, BSS corresponds to independent component analysis (ICA), which is now a well recognized concept [1]. Contrary to other frameworks where techniques take advantage of a strong information on the diversity, for instance through the knowledge of the array manifold in antenna array processing, the core assumption in ICA is much milder and reduces to the statistical mutual independence between the inputs. However, the latter assumption is not mandatory in BSS. For instance, in the case of static mixtures, sources can be separated *Correspondence: [email protected] 1 Institut Mines-T´el´ecom/T´el´ecom Sudparis, CNRS UMR 5157 SAMOVAR, 9 rue ´ Cedex, France Charles Fourier, 91011 Evry Full list of author information is available at the end of the article
if they are only decorrelated, provided that their nonstationarity or their color can be exploited. Other properties such as the fact that sources belong to a finite alphabet can alternatively be utilized [2,3] and do not require statistical independence. We consider in this article the case of dependent sources without assuming nonstationarity nor color. To the best of authors’ knowledge, only few references have tackled the issue of dependent source separation [4
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