Blind source separation with time series variational Bayes expectation maximization algorithm

Authors:
Shijun Sun;Chenglin Peng;Wensheng Hou;Jun Zheng;Yingtao Jiang;Xiaolin Zheng
Affiliations:
School of Physical Science and Technology, Zhanjiang Normal College, Zhanjiang Guangdong 524048, China;Bioengineering College, Chongqing University, Chongqing 400030, China;Bioengineering College, Chongqing University, Chongqing 400030, China;Department of Computer Science, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA;Department of Electrical and Computer Engineering, University of Nevada, Las Vegas, NV 89154, USA;Bioengineering College, Chongqing University, Chongqing 400030, China
Venue:
Digital Signal Processing
Year:
2012

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Abstract

This paper presents a variational Bayes expectation maximization algorithm for time series based on Attias@? variational Bayesian theory. The proposed algorithm is applied in the blind source separation (BSS) problem to estimate both the source signals and the mixing matrix for the optimal model structure. The distribution of the mixing matrix is assumed to be a matrix Gaussian distribution due to the correlation of its elements and the inverse covariance of the sensor noise is assumed to be Wishart distributed for the correlation between sensor noises. The mixture of Gaussian model is used to approximate the distribution of each independent source. The rules to update the posterior hyperparameters and the posterior of the model structure are obtained. The optimal model structure is selected as the one with largest posterior. The source signals and mixing matrix are estimated by applying LMS and MAP estimators to the posterior distributions of the hidden variables and the model parameters respectively for the optimal structure. The proposed algorithm is tested with synthetic data. The results show that: (1) the logarithm posterior of the model structure increases with the accuracy of the posterior mixing matrix; (2) the accuracies of the prior mixing matrix, the estimated mixing matrix, and the estimated source signals increase with the logarithm posterior of the model structure. This algorithm is applied to Magnetoencephalograph data to localize the source of the equivalent current dipoles.