Sparse component analysis and blind source separation of underdetermined mixtures

In this letter, we solve the problem of identifying matrices S ∈ R^n×N and A ∈ R^m×n knowing only their multiplication X = AS, under some conditions, expressed either in terms of A and sparsity of S (identifiability conditions), or in terms of X (sparse component analysis (SCA) conditions). We present algorithms for such identification and illustrate them by examples.