Accelerated gradient with optimal step size for second-order blind signal separation

This paper proposes an algorithm for the second-order blind signal separation problem with convolutive mixtures. An iterative first order gradient method based on the accelerated gradient is developed for solving the optimization problem. For each search direction, the question becomes how to effectively calculate the optimal step size in each iteration. Here, we propose an efficient algorithm for obtaining the step size by first reformulating the objective function as a fourth order polynomial in terms of the step size, where the polynomial coefficients are required to be calculated only once per iteration. An optimal step size search procedure using the Newton’s method is developed with the step size is efficiently obtained for each iteration. Simulation results in a simulated room environment and a real environment show that the proposed algorithm converges faster than the existing methods with a lower number of iterations and a lower computational complexity. In addition, the proposed algorithm can separate the speech signals and reduce the background noise simultaneously.