Under-determined audio source separation using the convolutive narrowband approximation and flexible ℓ_p regularizer

Convolutive narrowband approximation (CNA) model is widely utilized in audio source separation, particularly in strongly reverberant scenarios. However, in under-determined audio source separation, the CNA model often faces a serious ill-conditioned inverse filtering problem due to its mixing matrices containing columns that approach zero. To mitigate this issue, a ℓ_p regularizer-based approach is proposed in this paper, assuming mixing filters of CNA model are known or pre-estimated. First, the STFT mixture components of all frames at each frequency bin are concatenated into a long vector, and the CNA system is accordingly expanded to a block-circulant structured linear mixing model. Next, a maximum likelihood estimation, constrained by the proposed mixing model, is introduced to exploit the sparsity of STFT source components with the ℓ_p regularizer, where these components are assumed to independently follow super-Gaussian distributions. Finally, an augmented Lagrange multiplier with efficient iterative strategy is developed to search for the suitable sparse solution. The proposed strategy with regularizer p can be flexibly selected in a range of (0,1] to achieve robustness and accuracy in performance. Experimental results in various under-determined cases demonstrate the superior performance of the proposed algorithm over state-of-the-art approaches.