Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Underdetermined blind source separation based on sparse representation
IEEE Transactions on Signal Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Sparsity and Morphological Diversity in Blind Source Separation
IEEE Transactions on Image Processing
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This paper describes a new blind source separation method for instantaneous linear mixtures. This new method coined GMCA (Generalized Morphological Component Analysis) relies on morphological diversity. It provides new insights on the use of sparsity for blind source separation in a noisy environment. GMCA takes advantage of the sparse representation of structured data in large overcomplete signal dictionaries to separate sources based on their morphology. In this paper, we define morphological diversity and focus on its ability to be a helpful source of diversity between the signals we wish to separate. We introduce the blind GMCA algorithm and we show that it leads to good results in the overdetermined blind source separation problem from noisy mixtures. Both theoretical and algorithmic comparisons between morphological diversity and independence-based separation techniques are given. The effectiveness of the proposed scheme is confirmed in several numerical experiments.