Research Of Blind Source Separation Algorithm Based On NMF

Blind source separation is the method of separating the source signals from the observed mixture signals when the source signals and the transmission channel parameters are unknown. In real life, blind source separation is widely used in many fields,such as wireless communications, image processing, speech recognition and medicine signal processing,etc. So blind source separation technology has been paid extensive attention by scholars and researched. And it is a hot topic in the field of signal processing.There are blind source separation algorithm based on independent component analysis, blind source separation algorithm based on sparse component analysis and the blind source separation algorithm based on non-negative matrix factorization to solve the problem of blind source separation. Source signals with independence between each ather are needed by ICA algorithm and the signals with sparsity are needed by SCA algorithm, NMF algorithm achieve blind source separation mainly using the non-negative of signals, the independence and sparse of signals are not restricted. So the algorithm has attracted wide attention recently. In this paper, blind source separation algorithms based on NMF are studied.Firstly, blind source separation algorithm based on Euclidean distance NMF is researched and proposed under the orthogonal constraints or the correlation constraint. The simulation results show that the separation performance of the Euclidean distance NMF blind source separation algorithm with orthogonal constraints is almost equal to that with correlation constraint, but the former's computational complexity is lower.Secondly, the NMF blind source separation algorithms based on KL divergence are studied. Orthogonal constraint is used in the NMF blind source separation algorithm based on KL divergence, so the NMF blind source separation algorithms based on KL divergence are obtained. The experiments show that the algorithm is valid to underdetermined blind source separation of one-dimensional signal. At the same time, the KL divergence and feedback mechanisms are introduced to blind source separation, so the KL divergence NMF blind source separation algorithms based on feedback are obtained. The simulation results show that the separation performance of the algorithm is a little better than the Euclidean distance NMF blind source separation algorithm based on feedback. Incremental non-negative matrix factorization is used in blind source separation, incremental NMF blind source separation algorithms based on KL divergence are proposed, which improve the usability of blind source separation algorithms.Finally, the NMF blind source separation algorithms based on rank one is researched. The existing algorithms based on NMF use multiplicative update rules and part of the gradient information is lost, so the separation performance of these algorithms is not ideal. Rank one decomposition is introduced to blind source separation, and the NMF blind source separation algorithm based on rank one fast decomposition is proposed. The optimal solution is obtained by using the properties of a quadratic function. Not only is the separation performance improved greatly, but also the computational complexity is reduced greatly. The NMF algorithm based on least squares converges very fast, but the performance of the algorithm is unstable, therefore the algorithm based on rank one decomposition and the NMF algorithm based on least squares are combined, and mixed NMF blind source separation algorithm is obtained. Simulation results show that the computational complexity is reduced greatly and separation performance is improved further.