Hybrid model and structured sparsity for under-determined convolutive audio source separation

We consider the problem of extracting the source signals from an under-determined convolutive mixture, assuming known filters. We start from its formulation as a minimization of a convex functional, combining a classical I₂ discrepancy term between the observed mixture and the one reconstructed from the estimated sources, and a sparse regularization term of source coefficients in a time-frequency domain. We then introduce a first kind of structure, using a hybrid model. Finally, we embed the previously introduced Windowed-Group-Lasso operator into the iterative thresholding/shrinkage algorithm, in order to take into account some structures inside each layers of time-frequency representations. Intensive numerical studies confirm the benefits of such an approach.