In this paper we propose a new algorithm for solving the blind source separation (BSS) problem when the source signals are known to be sparse, or can be sparsely represented in some dictionary.

The algorithm capitalizes on a previous result that shows certain classes of nonconvex functions perform better than the convex l1-norm in measuring sparsity of a signal.

In this paper we propose a majorization–minimization (MM) method for minimizing such a nonconvex objective function. The MM technique is based on locally replacing the original nonconvex function by a smooth convex function that can be efficiently minimized.

We proof that the global minimum of the suggested surrogate function is guaranteed to reduce the value of the original nonconvex function.

Following the proposed technique, the sparse BSS problem is reduced to an iterative computation of the minor eigenvectors of particular covariance matrices. These features permit a computationally efficient implementation.

The proposed algorithm enjoys several advantages such as robustness to noise and the ability to estimate the number of source signals.

Numerical results show that the proposed algorithm outperforms other well-known algorithms that solve the same problem.