Research On Blind Source Separation Algorithm Based On Second-order Statistics

Blind source separation can analyze high-order correlation and two-order correlation of observed data.Using joint diagonalization of multiple different time delay covariance matrices of pre-whitening data,and under conditions where the mixing channel is unknown,it can find hidden and independent information components,and complete the blind separation of independent source signals.Blind source separation has been widely applied in many fields,such as neural network,financial analysis and prediction,image enhancement and speech recognition.In this paper,we focus on the BSS problem with time structure,and propose a BSS algorithm with two positive definite matrices combined with joint diagonalization based on multi-delay statistics.The proposed BSS algorithm is successfully applied in image separation and speech separation,and the innovation of this work is as follows.(1)Aimed at the linear instantaneous mixed BSS model,some constraints about the mixing matrix and the source signals are given,and two inherent uncertainties in the BSS are discussed.Then the preprocessing of the BSS problem is introduced,including the centralization and pre-whitening of data.We briefly explain the reasons,advantages and disadvantages of data preprocessing.Also,we elaborate on several classic BSS algorithms: Informax algorithm,JADE algorithm,SOBI algorithm etc,and introduce several BSS performance evaluation indicators.(2)The classical JADE and SOBI algorithm is based on pre-whitening data,and the joint diagonalization of multiple different time delay statistics achieves the blind separation of signals.The BSS algorithm above can effectively realize the blind separation of signals,but the computational complexity is high and the pre-whitening process of data will increase the estimation error to a certain extent.In order to solve this problem,two positive definite matrices are constructed to extract the time structure of the observed data,based on the multiple different time delay statistics of observation data(or whitening data).The proposed algorithm is designed to accurately combine diagonalization the two positive definite matrices above to get the separation matrix,and then we estimate the source signal.Simulation results show that compared with other BSS algorithms,the proposed algorithm is not only simple and easy to understand,but also has good separation performance.(3)BSS algorithm can realize blind separation of all mixed signals.If we are only interested in a few of these signals,the BSS algorithm has shortcomings of large computation and redundant operation processes.To overcome these shortcomings,in this paper,we propose a generalized eigenvalue BSE algorithm based on the degree of variation of the time autocorrelation function,and successfully extend it to the noisy BSE problem.MATLAB experimental results show that compared with other algorithms,the proposed algorithm is not only simple in structure,small in computation,but also has good extraction performance.