Blind separation of sparse sources in the presence of outliers


Authors: C.Chenot, J.Bobin
Journal: Signal Processing, Elsevier
Year: 2016
Download: Elsevier / Preprint





Blind Source Separation (BSS) plays a key role to analyze multichannel data since it aims at recovering unknown underlying elementary sources from observed linear mixtures in an unsupervised way. In a large number of applications, multichannel measurements contain corrupted entries, which are highly detrimental for most BSS techniques. In this article, we introduce a new {\it robust} BSS technique coined robust Adaptive Morphological Component Analysis (rAMCA). Based on sparse signal modeling, it makes profit of an alternate reweighting minimization technique that yields a robust estimation of the sources and the mixing matrix simultaneously with the removal of the spurious outliers. Numerical experiments are provided that illustrate the robustness of this new algorithm with respect to aberrant outliers on a wide range of blind separation instances. In contrast to current robust BSS methods, the rAMCA algorithm is shown to perform very well when the number of observations is close or equal to the number of sources.


Robust Sparse Blind Source Separation


Authors: C.Chenot, J.Bobin and J. Rapin
Journal: IEEE SPL 
Year: Nov. 2015
Download: IEEE Arxiv


Blind source separation is a widely used technique to analyze multichannel data. In many real-world applications, its results can be significantly hampered by the presence of unknown outliers. In this paper, a novel algorithm coined rGMCA (robust Generalized Morphological Component Analysis) is introduced to retrieve sparse sources in the presence of outliers. It explicitly estimates the sources, the mixing matrix, and the outliers. It also takes advantage of the estimation of the outliers to further implement a weighting scheme, which provides a highly robust separation procedure. Numerical experiments demonstrate the efficiency of rGMCA to estimate the mixing matrix in comparison with standard BSS techniques.