Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Morphological diversity and sparsity in blind source separation
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
An overview of inverse problem regularization using sparsity
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Sparsity and morphological diversity for hyperspectral data analysis
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Combining local filtering and multiscale analysis for edge, ridge, and curvilinear objects detection
IEEE Transactions on Image Processing
Learning the Morphological Diversity
SIAM Journal on Imaging Sciences
Maximum contrast analysis for nonnegative blind source separation
Computers & Mathematics with Applications
Image decomposition via learning the morphological diversity
Pattern Recognition Letters
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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.