Estimating the mixing matrix in Sparse Component Analysis (SCA) using EM algorithm and iterative Bayesian clustering

In this paper, we focus on the mixing matrix estimation which is the first step of Sparse Component Analysis. We propose a novel algorithm based on Expectation-Maximization (EM) algorithm in the case of two-sensor set up. Then, a novel iterative Bayesian clustering is applied to yield better results in estimating the mixing matrix. Also, we compute the Maximum Likelihood (ML) estimates of the elements of the second row of the mixing matrix based on each cluster. The simulations show that the proposed method has better accuracy and less failure than the EM-Laplacian Mixture Model (EM-LMM) method.

[1]  C. Jutten,et al.  Source Estimation in Noisy Sparse Component Analysis , 2007, 2007 15th International Conference on Digital Signal Processing.

[2]  Simon J. Godsill,et al.  A Bayesian Approach for Blind Separation of Sparse Sources , 2006, IEEE Transactions on Audio, Speech, and Language Processing.

[3]  C. Tomasi.  Estimating Gaussian Mixture Densities with EM – A Tutorial , 2004 .

[4]  Barak A. Pearlmutter,et al.  Soft-LOST: EM on a Mixture of Oriented Lines , 2004, ICA.

[5]  Daniel W. C. Ho,et al.  Underdetermined blind source separation based on sparse representation , 2006, IEEE Transactions on Signal Processing.

[6]  Christian Jutten,et al.  Estimating the mixing matrix in Sparse Component Analysis (SCA) based on partial k-dimensional subspace clustering , 2008, Neurocomputing.

[7]  Christian Jutten,et al.  Sparse ICA via cluster-wise PCA , 2006, Neurocomputing.

[8]  N. Mitianoudis,et al.  Simple mixture model for sparse overcomplete ICA , 2004 .

[9]  L. Vielva,et al.  UNDERDETERMINED BLIND SOURCE SEPARATION USING A PROBABILISTIC SOURCE SPARSITY MODEL , 2001 .

[10]  Nikolaos Mitianoudis,et al.  Overcomplete source separation using Laplacian mixture models , 2005, IEEE Signal Processing Letters.

[11]  Barak A. Pearlmutter,et al.  Blind Source Separation by Sparse Decomposition in a Signal Dictionary , 2001, Neural Computation.

[12]  Fabian J. Theis,et al.  Sparse component analysis and blind source separation of underdetermined mixtures , 2005, IEEE Transactions on Neural Networks.

[13]  Rémi Gribonval,et al.  A survey of Sparse Component Analysis for blind source separation: principles, perspectives, and new challenges , 2006, ESANN.