Underdetermined Source Separation And Its Application To Speech Processing

Source separation and reconstruction is a hot research topic in the field of signal processing in recent years, and it has been widely applied to the speech and image signal processing, biomedical signal processing, radar, communications and many other fields. Under the condition of unknown mixing process and source signals, using a small amount of a priori information to recover the source signals is called blind source separation. Previous studies mostly assume that the number of observed signals more than or equal to the number of source signals, but in the practical applications, this condition can not be satisfied. So the research on underdetermined source separation with the number of source signals more than that of observed signals has more practical significance.This dissertation will study the problem of underdetermined source separation, including multi-channel underdetermined source separation, single channel source separation and their application to speech separation and speech enhancement. The main work is summarized as follows:1. In order to solve the problem of poor robustness of underdetermined blind source separation for weak sparse signals, a method is proposed based on single-source-points detection and artificial bee colony algorithm. Firstly, the deficiency of the existing methods for single-source-points detection is analyzed and the real and imaginary parts of the observed signals in adjacent frames is utilized to detect single-source-points. Then, a two-stage artificial bee colony algorithm with different search strategies and coding schemes is proposed to estimate the mixing matrix. In the global search phase, a global objective function suitable for line clustering is defined and the convergence rate of the algorithm is accelerated by fully utilizing clustering feature and changing the bees’searching behavior; In the local search phase, local objective function is defined and the estimation precision is enhanced by collaboration between the bee colonies.Finally.the source signals are recovered by linear programming technique. The simulation results show that the proposed method not only can perform very well even in the case of large-scale, weak sparse and low signal noise ratio, but also need not a large amount of calculation.2. The underdetermined blind source separation algorithm based on local mixture model and judgement of source signals’states is proposed in the case that the source signals overlap each other at time-frequency points. Under the condition that the number of dominant source signals does not exceed the number of observed signals and source signals have local stationarity, a local mixture model is obtained to describe the local distribution of the observed signals. The source signals’states are taken as latent variables, the variance and weighting factors are estimated by expectation-maximization method.The proposed method does not require that the dominant sources must be exactly the same at each time-frequency point.Experiment results show that this method has very fast convergence rate and better separation performance.3. In order to separate signals with different distribution types, a subspace method for underdetermined blind separation is proprosed based on generalized Gaussian distribution and Markov chain monte carlo. The generalized Gaussian distribution is used to model the source signals distribution and model parameters are taken as random variables.To solve the problem that high dimensional multiple integral of the joint posterior conditional probability density function of latent nullspace variables and parameters cannot be achieved, all full conditional probability density functions are derived according to subspace feature and the least mean square error estimation of source signals is obtained by hybrid of Gibbs and Metropolis-Hastings samplings,.The proposed method not only can separate super-Gaussian sources(i.e. sparse sources) and sub-Gaussian sources(i.e.non-sparse sources),but also can solve the problem that the model parameters estimation easily falls into a local extremum point and has poor robustness. This method is used to separate signals on non-sparse zones and a underdetermined blind separation method based on non-sparse judgment criterion is proposed to enhance speech separation accuracy.4. Underdetermined blind source separation of speech signals in reverberation environment is studied. In allusion to the solution of convolutive blind source separation in the frequency domain, a method for permutation alignment based on sub-frequency band and artificial bee colony algorithm is proposed, which can better solve the permutation ambiguity problem. In allusion to the pseudoanechoic solution, the local generalized Gaussian mixture model of observed signals is put forward, and the best local distribution of speech signal is discussed,and then this model is used to separate speech signals. This method can improve the separation effect, and need not to solve the problem of permutation ambiguities.5. Single channel source separation is applied to speech enhancement and a single channel speech enhancement algorithm based on non-negative matrix factorization is proposed. The speech enhancement method based on non-negative matrix factorization for non-stationary noise has better denoising ability. Through non-negative matrix factorization of noisy speech’s amplitude spectrum into the basis matrix and time-varying gain coefficients matrix, speech and noise are separated from each other by wiener filtering. Due to the fact that time-varying gain coefficients of noise in adjacent time frames has strong correlation, time-varying gain coefficients of noise can be smoothen by adding a constraint term of correlation in the objective function, by which the estimation precision of noise power spectral density is improved. For optimization of the objective function, an effective algorithm is proposed to better achieve the goal of speech enhancement.