Blind extraction of sparse components based on ℓ0-norm minimization

We investigate the application of cost functions based on the ℓ₀-norm to the problem of blind source extraction (BSE). We show that if the sources have different levels of sparsity, then the minimization of the ℓ₀-norm leads to the extraction of the sparsest component even when the sources are statistically dependent. We also study the conditions guaranteeing BSE when an approximation of the ℓ₀-norm is considered. Finally, we provide a numerical example to illustrate the applicability of our proposal.