Non-stationary sources separation based on maximum likelihood criterion using source temporal-spatial model

Abstract In this paper, we propose a new non-stationary sources separation algorithm, which is referred to as autoregressive hidden Markov Gaussian process (AR-HMGP), in which the sources are non-stationary and temporally correlated. For the proposed algorithm, a generative model is employed to track the non-stationarity of the source where the temporal dependencies of sources are represented by autoregressive model (AR) and the distribution of the associated innovation process is described using non-stationary Gaussian process with hidden Markov model (HMM). We further explore the maximum likelihood (ML) method to estimate the parameters of the source model by using the expectation maximum (EM) algorithm. Our important findings reveal that (a) AR-HMGP algorithm outperforms the other three BSS algorithms for non-stationary sources separation, the instantaneous mixture system is also well corroborated with the effectiveness of our algorithm; (b) both independent and dependent non-stationary sources have been successfully separated; (c) the proposed algorithm is robust with respect to noise, while the other three algorithms are not.

[1]  Liangmo Mei,et al.  An MA model based blind source separation algorithm , 1999, Proceedings of IEEE. IEEE Region 10 Conference. TENCON 99. 'Multimedia Technology for Asia-Pacific Information Infrastructure' (Cat. No.99CH37030).

[2]  Aapo Hyvärinen,et al.  Fast and robust fixed-point algorithms for independent component analysis , 1999, IEEE Trans. Neural Networks.

[3]  Reinhold Häb-Umbach,et al.  Blind speech separation exploiting temporal and spectral correlations using 2D-HMMs , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[4]  Hang Zhang,et al.  Noisy Blind Signal-jamming Separation Algorithm Based on VBICA , 2014, Wirel. Pers. Commun..

[5]  V. G. Reju,et al.  A GMM Post-Filter for Residual Crosstalk Suppression in Blind Source Separation , 2014, IEEE Signal Processing Letters.

[6]  Alper T. Erdogan,et al.  Convolutive Bounded Component Analysis Algorithms for Independent and Dependent Source Separation , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Hugo Van hamme,et al.  Under-determined reverberant audio source separation using Bayesian Non-negative Matrix Factorization , 2016, Speech Commun..

[8]  J. Cardoso.  Infomax and maximum likelihood for blind source separation , 1997, IEEE Signal Processing Letters.

[9]  Jeff A. Bilmes,et al.  A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models , 1998 .

[10]  Sergio Cruces,et al.  On a new blind signal extraction algorithm: different criteria and stability analysis , 2002, IEEE Signal Processing Letters.

[11]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[12]  Dirk Van Compernolle,et al.  Signal separation by symmetric adaptive decorrelation: stability, convergence, and uniqueness , 1995, IEEE Trans. Signal Process..

[13]  Sepideh Hajipour Sardouie,et al.  Denoising of interictal EEG signals using ICA and Time Varying AR modeling , 2014, 2014 21th Iranian Conference on Biomedical Engineering (ICBME).

[14]  Hang Zhang,et al.  Blind separation of non-stationary sources using continuous density hidden Markov models , 2013, Digit. Signal Process..

[15]  Hichem Snoussi,et al.  Bayesian blind separation of generalized hyperbolic processes in noisy and underdeterminate mixtures , 2006, IEEE Transactions on Signal Processing.

[16]  Amrit Mukherjee,et al.  Spectrum Sensing for Cognitive Radio Using Blind Source Separation and Hidden Markov Model , 2014, 2014 Fourth International Conference on Advanced Computing & Communication Technologies.

[17]  Adel Belouchrani,et al.  Separation of Dependent Autoregressive Sources Using Joint Matrix Diagonalization , 2015, IEEE Signal Processing Letters.

[18]  Saeid Sanei,et al.  Constrained Blind Source Extraction of Readiness Potentials From EEG , 2013, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[19]  Hiroshi Sawada,et al.  A Multichannel MMSE-Based Framework for Speech Source Separation and Noise Reduction , 2013, IEEE Transactions on Audio, Speech, and Language Processing.

[20]  Tobias Rydén,et al.  EM versus Markov chain Monte Carlo for estimation of hidden Markov models: a computational perspective , 2008 .

[21]  H. Abdi,et al.  Principal component analysis , 2010 .

[22]  Nicholas G. Polson,et al.  MCMC maximum likelihood for latent state models , 2007 .

[23]  Arie Yeredor,et al.  Cramér–Rao-Induced Bound for Blind Separation of Stationary Parametric Gaussian Sources , 2007, IEEE Signal Processing Letters.

[24]  Jose C. Principe,et al.  A unifying criterion for blind source separation and decorrelation: simultaneous diagonalization of correlation matrices , 1997, Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop.

[25]  Hiroshi Saruwatari,et al.  Multichannel blind source separation based on non-negative tensor factorization in wavenumber domain , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[26]  Tülay Adali,et al.  Noncircular Complex ICA by Generalized Householder Reflections , 2013, IEEE Transactions on Signal Processing.

[27]  Wei Zhao,et al.  A fast algorithm for the separation of dependent sources based on bounded component analysis , 2016, 2016 IEEE/CIC International Conference on Communications in China (ICCC).

[28]  Zhongfu Ye,et al.  A Compressed Sensing Approach to Blind Separation of Speech Mixture Based on a Two-Layer Sparsity Model , 2013, IEEE Transactions on Audio, Speech, and Language Processing.

[29]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[30]  Xiaofei Wang,et al.  Dynamic group sparsity for non-negative matrix factorization with application to unsupervised source separation , 2016, 2016 IEEE International Workshop on Acoustic Signal Enhancement (IWAENC).

[31]  Hirokazu Kameoka,et al.  Statistical Model of Speech Signals Based on Composite Autoregressive System with Application to Blind Source Separation , 2010, LVA/ICA.

[32]  W Chan,et al.  Maximum Likelihood Estimation in Generalized Linear Mixed Models Using Monte Carlo Methods: Application to Small-Area Estimation of Breast Cancer Mortality , 2006 .

[33]  Joseph Tabrikian,et al.  MIMO-AR System Identification and Blind Source Separation for GMM-Distributed Sources , 2009, IEEE Transactions on Signal Processing.

[34]  S. Cruces.  Bounded Component Analysis of Noisy Underdetermined and Overdetermined Mixtures , 2015, IEEE Transactions on Signal Processing.

[35]  Mohamed Sahmoudi,et al.  Blind source separation of noisy mixtures using a semi-parametric approach with application to heavy-tailed signals , 2005, 2005 13th European Signal Processing Conference.