Underdetermined Blind Source Separation Based On Sparse Component Analysis

Blind source separation(BSS)is to process the received mixed signals to recover and reconstruct the source signals when the number of source signals and the conditions of signal transmission channel are unknown.In engineering practice,because the underdetermined blind source separation problem has more applicable scenarios and is more difficult to deal with,the research on underdetermined blind source separation problem has more important value.At present,the main method to solve the underdetermined blind source separation problem is based on the "two-step" framework of sparse component analysis theory,that is,firstly,the mixed matrix estimation of the signal is needed,and then the source signal is reconstructed by various signal reconstruction algorithms.Based on this theoretical framework,the mixed matrix estimation algorithm and signal reconstruction algorithm for underdetermined blind source separation are studied in this paper.Firstly,the model basis of underdetermined blind source separation(BSS)and the related theoretical knowledge to solve the underdetermined problem are sorted out.Several common source signal reconstruction algorithms are introduced under the framework of "two-step" basic model,and the estimation matrix and performance evaluation criteria of reconstructed signal are described.Then,the mixed matrix estimation algorithm is studied.An improved FCM clustering algorithm based on density structure analysis is proposed,which optimizes the traditional FCM algorithm from two dimensions of initial parameters and objective function.The improved algorithm is applied to the estimation of mixed matrix in underdetermined blind source separation(BSS).Finally,the improved algorithm is verified by simulation with speech signal as the experimental object.Finally,the signal reconstruction method of underdetermined blind source separation is studied.On the basis of compressed sensing theory,aiming at the problems of low reconstruction accuracy and large amount of computation in traditional K-SVD dictionary learning algorithm,this paper proposes an alm-brp dictionary learning algorithm from two stages of sparse coding and dictionary updating,and designs different signal reconstruction methods according to the presence or absence of training samples.Finally,on the basis of matrix estimation,the two signal reconstruction methods are further verified.