Sparsity and Morphological Diversity in Blind Source Separation

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Authors: J. Bobin, J.-L. Starck, J. Fadili, Y. Moudden
Journal: IEEE
Year: 2007
Download: IEEE


Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-called blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. Here, we give some new and essential insights into the use of sparsity in source separation, and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper introduces a new BSS method coined generalized morphological component analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient BSS method. We present arguments and a discussion supporting the convergence of the GMCA algorithm. Numerical results in multivariate image and signal processing are given illustrating the good performance of GMCA and its robustness to noise.

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Author: Samuel Farrens

I have been a postdoctoral researcher at CEA Saclay since October 2015. I am currently working on the DEDALE project and the Euclid mission with Jean-Luc Starck.

My background is in optical detection of clusters of galaxies and photometric redshift estimation. I am now branching out into the field of PSF estimation using sparse signal processing techniques.

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