The Research On Mixing Matrix Estimation Algorithm Of Underdetermined Blind Separation

Blind source separation is a technology that restore the source signal only according to the observed signal while the details of source signal and transmission channel are unknown. Because of widely use in medical signal processing, speech signal separation and sensor network, blind source separation technology has been a popular research direction in the field of signal processing for many years. Underdetermined blind source separation technology refers to the situation that the number of source signal is greater than the number of observed signal. Because of the widely use in the practical application, underdetermined blind source separation has received extensive attention of the academia.For the underdetermined blind source separation, different methods should be adopted according to the sparsity of source signal. The two-step method is commonly used:(1) estimate the mixing matrix;(2) on the basis of the mixing matrix, restore the source signal. Mixing matrix estimation is very important in the blind source separation. The estimation accuracy affects the recovery of the source signal. Based on the sparse degree of the source signal, mixing matrix estimation is divided into different categories, sufficiently sparse mixing matrix estimation and not sufficiently sparse mixing matrix estimation.The first step in the two-step method, mixing matrix estimation,is mainly researched in this thesis.(1) When the source signal is sufficiently sparse, the line-clustering feature of the observed signal can be used to estimate the mixing matrix. Three classic mixing matrix estimation algorithms for the sufficiently sparse source signal are introduced in this thesis, the k-means algorithm, the Hough transform estimation algorithm and the refactoring observed signal estimation algorithm. The block segmentation mixing matrix estimation algorithm is proposed in this thesis for the sufficiently sparse source signal. Through the simulation with the other three estimation algorithms, the advantages of the block segmentation algorithm on time complexity and precision are proved for different SNR. In addition, the advantages of the block segmentation algorithm on estimation precision are also proved for different sparse degree.(2) When the source signal is not sufficiently sparse, the plane-clustering feature of the observed signal can be used to estimate the mixing matrix. Three classical mixing matrix estimation algorithms for not sufficiently sparse signal are introduced in this thesis, the k-plane algorithm, the potential function of clustering plane estimation algorithm and the k dim subspace algorithm. Based on the k-plane algorithm, the improved k-plane mixing matrix estimation algorithm is proposed for not sufficiently sparse signal. Through the simulation with the other three algorithms, the advantages of the improved k-plane algorithm on time complexity and precision are proved.