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Blind Source Separation by Sparse Decomposition in a Signal Dictionary

Michael Zibulevsky, Barak A. Pearlmutter
2001 Neural Computation  
The blind source separation problem is to extract the underlying source signals from a set of linear mixtures, where the mixing matrix is unknown. This situation is common in acoustics, radio, medical signal and image processing, hyperspectral imaging, and other areas. We suggest a twostage separation process: a priori selection of a possibly overcomplete signal dictionary (for instance, a wavelet frame or a learned dictionary) in which the sources are assumed to be sparsely representable,
more » ... representable, followed by unmixing the sources by exploiting the their sparse representability. We consider the general case of more sources than mixtures, but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures. Experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques.
doi:10.1162/089976601300014385 pmid:11255573 fatcat:lzpp24t66vfatp2r4dumiyn6uy