Title :
Sparsity and Morphological Diversity in Blind Source Separation
Author :
Bobin, Jérôme ; Starck, Jean-Luc ; Fadili, Jalal ; Moudden, Yassir
Author_Institution :
DAPNIA/SEDI-SAP, Gif sur Yvette
Abstract :
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.
Keywords :
blind source separation; signal representation; blind source separation; generalized morphological component analysis; morphological diversity; multivariate image processing; multivariate signal processing; signal representations; sparsity; Blind source separation; Convergence; Independent component analysis; Mutual information; Signal analysis; Signal processing algorithms; Signal representations; Size measurement; Source separation; Testing; Blind source separation (BSS); curvelets; morphological diversity; overcomplete representations; sparsity; wavelets; Algorithms; Image Enhancement; Image Interpretation, Computer-Assisted; Information Storage and Retrieval; Reproducibility of Results; Sensitivity and Specificity;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2007.906256