Research On Mixing Matrix Estimation Method For Underdetermined Blind Source Separation

Blind Source Separation(BSS)refers to recovering source signals from the observed signals and a small amount of prior knowledge of the source signals with the source signals and transmit channel unknown.As its powerful information processing capabilities,blind source separation is widely used in biomedical systems,speech signal processing,image processing and other fields.The Undetermined Blind Source Separation(UBSS)model,which number of observed signals is less than the number of source signals,is more general and has research significance.At present,the dominant method to solve the UBSS is sparse component analysis(SCA)utilizing the sparse nature of the source signal.The procedures of SCA are composed of two steps: first is the estimation of mixing matrix by clustering method and second is the recovery and reconstruction of source signals.Based on the in-depth analysis of the BSS status at home and abroad,this paper foucs on the estimation algorithm of mixing matrix of UBSS model with instantaneous linear mixing.The main work and innovation of this paper are as follows:Firstly,a mixing matrix estimation method based on improved artificial bee colony optimization is proposed.In order to balance the population diversity and convergence speed of ABC algorithm,we present a modified method for solution update of the employed bees in this paper.The modified method combines both the deterministic and random search strategies which bases on the linear clustering characteristics of observation signals.The exploration ability of ABC algorithm is better than that of exploitation ability.This paper introduces a local search strategy based on Levy flight,and further searches for the neighborhood of the current optimal solution,thereby improving the local development capability of ABC algorithm.Experimental simulation and analysis show that the mixing matrix estimation method based on improved ABC obviously improves the precision of the mixed matrix estimation.At the same time,the algorithm still has better estimation performance when the number of source signals is significantly more than the number of sensors,and is insensitive to the initial value.Secondly,a mixing matrix estimation method based on DBSCAN and search density peak is proposed.For traditional clustering methods,the disadvantages of the number of clusters need to be set in advance.In this paper,the DBSCAN method is used to achieve the automatic classification obtaining the number of source signals and a preliminary estimate of the mixing matrix.However,the clustering center is the average of each category set,so it can be corrected by the density peak clustering method.Meanwhile,the DBSCAN algorithm can also overcome the lack of human intervention needed for the density peak clustering method.Experimental simulation and analysis show tha the algorithm can accurately estimate the mixing matrix when the number of source signals is unknown,and the estimation accuracy is higher than K-means algorithm,hierarchical clustering algorithm and DBSCAN algorithm.