Bayesian probabilistic approach by blind source separation for instantaneous mixtures

Abstract

In this work, the novel method of blind source separation using Bayesian Probabilistic approach is discussed for instantaneous mixtures. This work demonstrates the source separation problem which is well suited for the Bayesian approach. This work also provides a natural and logically consistent method in which prior knowledge can be incorporated to estimate the most probable solution. The distri-butions of the coefficients of the sources in the basis are modeled by a generalized Gaussian distribution (GGD) which is dependent on the sparsity parameter q. This method also utilizes prior distribution of the appropriate sparsity parameter of sources present in the mixture. Once, the prior distribution for each parameter (like mixing matrix, source matrix, sparsity parameter and error or noise covariance matrix) are defined, the Bayesian a posterior probabilistic approach using Markov chain Monte Carlo (MCMC) method is exploited in estimation of a posterior distribution of mixing matrix, source matrix, sparsity parameter and covariance matrix of error. The blind source separation provides the results in the form of signal to distortion ratio (SDR), signal to artifacts ratio (SAR) and signal to interference ratio (SIR) at different SNR.