A Class of Frobenius Norm-Based Algorithms Using Penalty Term and Natural Gradient for Blind Signal Separation

We consider the blind signal separation (BSS) problem of instantaneous mixtures using penalty term and natural gradient. A class of Frobenius norm-based algorithms consisting of the offline/block processing (BP), online processing (OP) algorithms, and their normalized versions is proposed for separating nonstationary and nonwhite signals. The BP and OP algorithms, respectively, suitable for blind separation with offline and online data, are derived by using the nonstationarity and nonwhiteness of signals and the natural gradient method in conjunction with an appropriate penalty term. Associated with almost all algorithms employing a gradient method is a gradient noise problem. We thus develop, from BP and OP, their normalized versions in which the update of an unknown demixing matrix is based on the minimal disturbance principle. We show that the resulting updates are in the same direction as those of the original algorithms but with a scaling factor whose upper bound is unity. Algorithms using the nonstationarity and nonwhiteness properties have been proposed before but, due to the use of logarithms in their derivation, they are not capable of separating signals that are not persistently active and require regularization parameters to mitigate the problem. In this paper, the superior performance of the proposed algorithms to the previously proposed logarithm-based algorithms with and without regularization when separating nonpersistently active source signals is presented through some illustrative numerical experiments.