Convolutive Blind Separation Of Non-stationary Sources In Tensor Framework

Blind Source Separation is a hot research issue topic in the last decades,which refers to the recovery of unknown statistically independent source signals and unknown mixed matrix by observing signals.It has been widely used in computer vision,speech signal processing,biomedical signal processing and other fields.Tensor diagonalization is a very important method in signal processing.Joint blind separation refers to the recovery of unified mixed matrix and different source signals from multiple data sets by means of inter-group correlation and intra-group independence between signals from multiple data sets.Tensor diagonalization is the method of converting a tensor into a diagonal tensor or approximate diagonal tensor by multiplying each dimension of a tensor by one or a series of matrices.This paper mainly adopts the method of tensor diagonalization,and focuses on the blind separation of convolutive non-stationary source signals.Considering the frequency domain algorithm of convolutive blind source separation usually convert convolutive mixed problem in time domain to instantaneous mixed problem at each frequency point with the method of short-time Fourier transform or wavelet transform method,etc,in order to make full use of the statistical properties of the data set signal.In this paper,the only scenario considered is the source of non-stationary signals with smooth mixed matrix,so the mixed signal in each frequency point can be regarded as a set of data for joint blind signal separation,and translate joint blind signal separation into a tensor diagonalization problem.The factor matrix of each dimension of tensors is non-unitary(non-orthogonal)matrix,so as to avoid the degradation of algorithm performance caused by the pre-whitening of the orthogonal(unitary)matrix.Therefore,this paper mainly makes the following work:(1)For the problem of joint blind separation algorithm based on second-order statistics,a Jacobi-like tensor diagonalization algorithm is proposed.The proposed method is inspired by the ideas of the Jacobi rotation framwork,a special matrix with only a pair of non-zero elements that are symmetric about the main diagonal,instead of Givens,is put forword to make continuous rotation to update each tensor factor matrix of different dimensions until convergence and to estimate the diagonal tensor and mixed matrix.The tensors are constructed by the correlation matrixes of the signals.In the simulation experiment,compared with other algorithms,this algorithm is found that this algorithm has better separation performance and has certain advantages in separation accuracy and permutation ambiguity.(2)For the problem of joint blind separation algorithm based on fourth-order statistics,a Jacobi-like tensor diagonalization algorithm is proposed.Tensors are constructed by the fourth order mutual accumulation quantity of signals,and the special parameter structure proposed above replays Givens matrix to do a Jacobi-like continuous rotation.The optimal solution of the parameters in the algorithm is calculated to estimate the diagonal tensors and the mixing matrix.The simulation results show that the algorithm has better separation accuracy and permutation ambiguity,the separation effect of sound signals is good.