A Unified Approach for Over and Under-Determined Blind Source Separation Based on Both Sparsity and Decorrelation

Over the last decades, independent component analysis (ICA) has been a major tool for blind source separation (BSS). Both theoretical and practical evaluations showed that the hypothesis of independence suits well for audio and musical signals. In the last few years, sparsity-based optimization has emerged as another efficient implement for BSS. This paper starts from introducing some new BSS methods that take advantage of both decorrelation, which is a direct consequence of independence , and sparsity using overcomplete Gabor representation. Theoretical proof and discussion supporting the convergence of the proposed algorithms are then presented. Numerical results are given illustrating the good performances of these approaches and their robustness to noise.