Under-determined source separation via mixed-norm regularized minimization

We consider the problem of extracting the source signals from an under-determined convolutive mixture assuming that the mixing filters are known. We wish to exploit the sparsity and approximate disjointness of the time-frequency representations of the sources. However, classical time-frequency masking techniques cannot be directly applied due to the convolutive nature of the mixture. To address this problem, we first formulate it as the minimization of a functional combining a classical ℓ₂ discrepancy term between the observed mixture and the mixture reconstructed from the estimated sources and a sparse regularization term defined in terms of mixed ℓ₂/ℓ₁ norms of source coefficients in a time-frequency domain. The minimum of the functional is then obtained by a thresholded Landweber iteration algorithm. Preliminary results are discussed for two synthetic audio mixtures.