Underdetermined blind source separation based on subspace representation
SangGyun Kim, Chang D. Yoo
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 be 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.
There is demo below which separate the four sources with the three mixtures.
1. Sanggyun Kim and Chang D. Yoo, "Underdetermined blind source separation based on subspace representation," IEEE Transactions on Signal Processing, vol. 57, no. 7, pp.2604-2614, July 2009.(Impact factor:2.335)
2. SangGyun Kim and Chang D. Yoo, "Underdetermined Blind Source Separation Based on Generalized Gaussian Distribution," In Proceedings of IEEE International Workshop on Machine Learning for Signal Processing, Maynooth, Ireland, pp. 103-108, September 2006.
3. SangGyun Kim and Chang D. Yoo, "Blind Separation of Speech and Sub-Gaussian Signals in Underdetermined Case," In Proceedings of International Conference on Spoken Language Processing, Jeju, Korea, pp. 2861-2864, October 2004.
4. SangGyun Kim and Chang D. Yoo, "Underdetermined Independent Component Analysis by Data Generation," In Proceedings of Independent Component Analysis and Blind Signal Separation, Granada, Spain, pp. 445-452, September 2004.
Underdetermined Convolutive BSS based on a Novel Mixing Matrix Estimation and MMSE based Source Estimation
Janghoon Cho, Jinho Choi, and Chang D. Yoo
This paper considers underdetermined blind source separation of super-Gaussian signals that are convolutively mixed. The separation is performed in three stages. In the first stage, the mixing matrix in each frequency bin is estimated by the proposed single source detection and clustering (SSDC) algorithm. In the second stage, by assuming complex-valued super-Gaussian distribution, the sources are estimated by minimizing a mean-square-error (MSE) criterion. Special consideration is given to reduce computational load without compromising accuracy. In the last stage, the estimated sources in each frequency bin are aligned for recovery. In our simulations, the proposed algorithm outperformed conventional algorithm in terms of the mixing-error-ratio and the signal-to-distortion ratio.
There is demo below which separate the three sources with the two mixtures those are convolutively mixed.
1.Janghoon Cho, Jinho Choi and Chang D. Yoo, "Underdetermined Convolutive BSS based on a Novel Mixing Matrix Estimation and MMSE based Source Estimation," in Proceedings of IEEE International Workshop on Machine Learning for Signal Processing, Beijing, China, September 2011.