Research On Blind Source Separation Algorithm Based On Nonnegative Matrix Factorization

In the field of signal processing, blind source separation is one of the hot issues of research, it not only has important theoretical research value, but also has been applied to various aspects of scientific research, and has a broad application prospect. Nonnegative matrix decomposition as a new effective method to solve the problem of blind source separation has caused the attention of the researchers. This article is based on the researches at home and abroad, and makes research on solving the problem of blind source separation using nonnegative matrix decomposition method.Firstly, the research status of blind source separation and nonnegative matrix factorization is analyzed, and introduces the nonnegative matrix factorization methods of dealing with the blind source separation which often used mathematical knowledge in detail. On this basis, and introduces the gradient descent method, the optimization problem with constraints and basic nonnegative matrix decomposition algorithm.Secondly, in view of the overdetermined blind source separation of mixed model, sparse constrained non-negative matrix factorization method is studied. This method increase sparse constraint by giving nonnegative matrix factorization algorithm based on objective function, to update the factor matrix iteration rules, it can realize the overdetermined blind source separation. Then, add feedback mechanism to nonnegative matrix factorization with constrained second-order optimization, this method effectively solves the positive definite blind source separation, and than nonnegative matrix factorization with constrained second-order optimization algorithm has better performance.Finally, this paper puts forward using joint nonnegative matrix factorization method to solve the underdetermined blind source separation problem. The first stage of this method with determinant and sparse constraint of nonnegative matrix factorization algorithm to deal with mixed signals, and choose the best signal separation effect, until the mixed signal matrix is not underdetermined matrix, it will be successfully converted the underdetermined mixing matrix to the positive definite mixing matrix. The second stage mixed signals are processed with constrained second-order optimization nonnegative matrix factorization. This method solves the blind source separation problem under the underdetermined mixed model.