Fast NMF Blind Source Separation Algorithm

By using non-negative matrix factorization with rank one into blind source separation, the objective function of the blind source separation based on the Euclidean distance is transformed into the form of a quadratic function. The constraints of sparisity and orthogonality are imposed on the blind source separation algorithm to guarantee its separability. The mixing matrix and source signals iterative formulas are derived by utilizing the property of the quadratic function, and then a fast NMF blind source separation algorithm based on rank one (NMF-R1) is obtained. The number of multiplications required for each update of NMF-R1 blind source separation algorithm is less about 30% than that of NMF-BM, besides NMF-R1 doesn't need computation of matrix inversion, but NMF-BM needs computation of two matrix inversion. The simulation results of blind source separation for image signals’ overdetermined and underdetermined mixing show that all of source signals can be separated by NMF-R1 algorithm, but only overdetermined mixed signals can be separated by NMF-BM algorithm, and NMF-R1 algorithm has the better separated performance and the faster convergence rate compared with NMF-BM algorithm.