Study On Mixing Matrix Estimation Of Underdetermined Blind Source Separation

Blind source separation(BSS) theory has become one of the r esearch highlights in signal processing field. Study on blind source separation is of importance to theory and practice. The separation modal is more realistic when the number of observed signals is less than that of source signals, i.e. underdeter mined blind source separation. At present, the dominant method to solve the BSS is sparse component analysis(SCA) which is on the basis of sparse characteristic of source signals. The procedures of SCA are composed of two steps: first is the estimation of mixing matrix and second is the recovery and reconstruction of source signals. After an intensive research on the BSS status, this paper focus on the estimation algorithm of mixing matrix of underdetermined blind source separation(UBSS) in the condition of weak sparsity of source signals.Firstly, it presents the conception of sparsity degree and the common sparse transformation methods based on the relevant knowledge of UBSS. Furthermore, it introduces the performance criteria for evaluating the estimation error of mixing matrix and the recovery performance of source signals on the basis of traditional methods of mixing matrix estimation.Secondly, it proposed a phase angle processing method-based single source time-frequency points to enhance signals sparsity under the weak sparsity. There are some restrictions in conventional clustering algorithms, such as knowing the amount of source signals. To solve this problem, it puts forward an automatic classification method according to density-based spatial clustering of application with noise(DBSCAN) to pre-estimate the number of source signals. This method combined with Hough transform to modify the clustering center and improve the estimation accuracy. In this paper, it analyzed the peak clustering cause of Hough transform in details and proposed the algorithm combined DBSCAN and HT can overcome the peak clustering which is inherent problem of Hough transform. Aiming at the signals with weak sparsity, this paper proposed a local directional density detection method to discriminate and remove the outlier time-frequency points and achieve the linear clustering enhancement of mixed signals. Then the estimation of mixing matrix is realized by discrimination of local maximum points and determination of source signals number.Finally, simulation experiments are applied to verify these proposed methods and the estimated results are compared with other traditional methods. The last part depicted the recovery and reconstruction of source signals on the basis of estimated mixing matrix. It gave the reconstructed result comparisons between the one using compression perception and the one with sparse component analysis of K-means singular value decomposition. The experiment results showed this research results can achieve source signals reconstruction with less error.