Blind source separation of linear mixtures with singular matrices

Abstract

We consider the Blind Source Separation problem of linear mixtures with singular matrices and show that it can be solved if the sources are sufficiently sparse. More generally, we consider the problem of identifying the source matrix S if a linear mixture X = AS is known only, where A is an (m x n)-matrix, m=n and the rank of A is less than m. A sufficient condition for solving this problem is that the level of sparsity of S is bigger than m - rank(A) in sense that the number of zeros in each column of S is bigger than m-rank(A). We present algorithms for such identification and illustrate them by examples.