Algorithm for blind identification of underdetermined mixtures based on JADE and parallel factor decomposition

To solve the problem of the underdetermined blind source separation when the number of source signals unknown, this paper proposes a algorithm for blind identification of underdetermined mixtures based on joint approximate diagonalization of eigenmatrices (JADE) and parallel factor decomposition under the assumption of statistical independence between the source signals and at most one of the signals be Gaussian, do not need the sources are (quite) sparse. The novel blind identification algorithm stack the sampled quadric-covariance matrices in a third-order tensor firstly, and then parallel factor decomposition this tensor to estimate the number of the source signals and the mixing matrix. Because the parallel factor decomposition still satisfy unique identifiability in underdetermined situation, the proposed algorithm can solve the underdetermined blind source separation problem successfully. The simulation results illustrate that the performance of the algorithm is very better for determined and underdetermined mixed. The algorithm is relatively simple and effective, which can satisfy the demand of engineering application.