Research On Mixing Matrix Estimation Method For Underdetermined Blind Source Separation

Blind Source Separation(BSS)aims to restore the source signal only by using the observed signal in the absence of source signal information and information mixing mode information.With its strong technical advantages,it is widely used in biomedical signal processing,image processing,It has been widely used in mobile communication and other fields.In underdetermined blind source separation,the number of observed signals is less than the number of source signals,so it is more suitable for real-world scenarios than positive/overdetermined cases.When solving the underdetermined blind source separation problem,the mixing matrix is generally estimated first,and then the source signal is recovered using the estimated mixing matrix.Since the source signal recovery algorithm is relatively mature,this thesis will focus on the estimation of the mixing matrix.The mainstream idea of mixing matrix estimation includes: first,use the second-order statistics of the observed signal to construct a tensor and estimate the mixing matrix through tensor decomposition;second,use the sparsity of the source signal to select a single signal source point in the source signal And use the clustering algorithm to estimate the mixing matrix.In this paper,the work is carried out from the statistical characteristics of the observed signal and the sparsity of the source signal,and the specific work includes:In real life,observation signals are often disturbed by noise,and traditional underdetermined blind source separation results based on second-order statistics and signal sparsity are more sensitive to noise.In view of the advantages of third-order statistics in dealing with symmetrically distributed noise,this thesis utilizes the thirdorder statistics of observed signals to estimate the mixing matrix.Considering the autocorrelation of the source signal,a series of third-order statistical information of the observed signal under multiple time delays is calculated and stacked into a fourth-order tensor,and then the mixing matrix estimation problem is transformed into a canonical bimodal decomposition problem of the fourth-order tensor.This thesis further utilizes the generalized Gaussian model and the expectation-maximization algorithm to realize the source signal recovery.1000 Monte Carlo experiments show that the algorithm can effectively suppress the influence of noise.For the 3×4 mixture model,when the signalto-noise ratio is 15 d B,the average estimation error of the mixture matrix reaches –20.35 d B,and the average absolute correlation coefficient between the recovered source signal and the real source signal reaches 0.84,which is consistent with the present Compared with other methods,the best separation results were obtained.The traditional underdetermined blind source separation algorithm based on signal sparsity realizes the estimation of the mixing matrix by detecting a single signal source point in the signal,which has strong constraints on the sparsity of the signal.However,the sparsity of some signals is insufficient,and the algorithm using a single signal source point cannot achieve accurate estimation of the mixing matrix.In view of this,this thesis proposes an underdetermined blind source separation mixing matrix estimation method based on dual signal sources.After transforming the signal in the time-frequency domain,use the PSO algorithm to calculate the orthogonal complement space of the real part vector,imaginary part vector and auxiliary vector of the signal in the time-frequency domain;then use the DBSCAN algorithm to select dual signal source points,and finally use These dual signal source points result in a mixing matrix.In order to verify the performance of the algorithm,this thesis conducts 1000 Monte Carlo experiments on simulated EEG signals.Under the condition that the proportion of single signal source points remains unchanged and the proportion of double signal source points increases,based on the single signal source point The performance of the algorithm basically does not change,while the performance of the algorithm based on dual signal sources continues to improve.Among them,when the proportion of dualsignal source points in the source signal reaches 18%,the NMSE of the algorithm based on dual-signal source points is-42.64 d B.This thesis has 27 figures,8 tables and 83 references.