The Research On Undetermined Blind Source Separation Algorithm Based On On Sparse Properties

Blind source separation refers to the technique of recovering the source signal only through the mixed observation signal under the unknown source signal and the transmission channel.In recent years,blind source separation technology has been a hot research technology in the field of signal processing.Such as image processing,biological signal processing and voice signal processing are more commonly used in the field of application technology.As far as blind source separation is concerned,underdetermined blind source separationwith less number of sensors than the source number has gained more and more attention in the academic field because it is more practical.For underdetermined blind source separation,different methods are used depending on the sparseness of the source signal.We often use the “two steps” to solve this problem.Firstly,we estimate the mixing matrix and the source signals are recovered by using the estimated mixing matrix.According to the source signal of different sparsity of underdetermined blind source problem research,specifically including the following three areas:Firstly,when the source signal is sufficiently sparse,the observed signal will exhibit linear clustering.That is,at each observation moment,there is at most one source signal with a larger value.And then use this feature to estimate the mixing matrix.This paper introduces several common algorithms for estimating mixing matrix by using surface clustering characteristics without strict sparsity.K-Means algorithm,DBSCAN algorithm and potential function algorithm are introduced in this paper and propose an improved potential function algorithm to estimate the mixing matrix.The simulation results show that the improved algorithm improves the accuracy of the estimation to a certain extent and improves the anti-noise ability to a certain extent.Secondly,when the source signal is not sufficiently sparse,it will show the characteristics of surface clustering.That is,at the same time more than one source signal is working,it will show the characteristics of surface clustering instead of the characteristics of linear clustering.Scholars use this feature to estimate the mixing matrix.This paper presents three common algorithms for estimating the mixed matrix when they are not strictly sparse.Such as k-dimensional subspace algorithm and K-plane algorithm.In this paper,we use the improved K-plane algorithm to estimate the mixing matrix.The simulation experiments show that the improved algorithm proposed in this paper can improve the accuracy of the algorithm to a certain extent.Finally,after estimating the mixing matrix we can use this matrix to recover the source signal.Although the mixed matrix has been estimated,the source signal can not be recovered directly by using the inverse method because of the non-singularity of the mixed matrix.In this paper,several common source signal recovery methods are introduced,such as L1 norm,the shortest path algorithm based on angle and statistical sparse decomposition algorithm.In this paper the method of L1 norm is improved.It improves the defect of division.Simulation results show that this method can improve the accuracy of source signal recovery.