Underdetermined Blind Source Separation Based on Subspace Representation

This paper considers the problem of blindly separating sub- and super-Gaussian sources from underdetermined mixtures. The underlying sources are assumed to be composed of two orthogonal components: one lying in the rowspace and the other in the nullspace of a mixing matrix. The mapping from the rowspace component to the mixtures by the mixing matrix is invertible using the pseudo-inverse of the mixing matrix. The mapping from the nullspace component to zero by the mixing matrix is noninvertible, and there are infinitely many solutions to the nullspace component. The latent nullspace component, which is of lower complexity than the underlying sources, is estimated based on a mean square error (MSE) criterion. This leads to a source estimator that is optimal in the MSE sense. In order to characterize and model sub- and super-Gaussian source distributions, the parametric generalized Gaussian distribution is used. The distribution parameters are estimated based on the expectation-maximization (EM) algorithm. When the mixing matrix is unavailable, it must he estimated, and a novel algorithm based on a single source detection algorithm, which detects time-frequency regions of single-source-occupancy, is proposed. In our simulations, the proposed algorithm, compared to other conventional algorithms, estimated the mixing matrix with higher accuracy and separated various sources with higher signal-to-interference ratio.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2009-07
Language
ENG
Keywords

OVERCOMPLETE REPRESENTATIONS; SPARSE REPRESENTATION; SIGNAL SEPARATION; EM ALGORITHM; MIXTURES; DECOMPOSITION

Citation

IEEE TRANSACTIONS ON SIGNAL PROCESSING, v.57, no.7, pp.2604 - 2614

ISSN
1053-587X
DOI
10.1109/TSP.2009.2017570
URI
http://hdl.handle.net/10203/100395
Appears in Collection
EE-Journal Papers(저널논문)
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