Blind extraction of sparse sources

In this paper we propose a new algorithm for solving the blind source extraction (BSE) problem when the desired source signals are sparse. Previous approaches for solving this problem are based on the independent component analysis (ICA ) technique, that extracts a source signal by finding a separating vector that maximizes the non-Gaussianity of the extracted source signal. These algorithms are general purpose algorithms and are not designed specifically for extracting sparse signals. In this paper we propose a new algorithm for extracting sparse source signals. The proposed algorithm is based on finding a separating vector that maximizes the sparsity of the extracted source signal. In the proposed algorithm, a nonconvex objective function that measures the sparsity of the separated signal is locally replaced by a quadratic convex function. This results in an iterative algorithm in which a new estimate of the separating vector is obtained by solving an eigenvalue decomposition problem. A numerical example is presented to investigate the superiority of the proposed algorithm in comparison with one of the well known ICA algorithm for extracting sparse sources.