On convolutive Blind Source Separation in a noisy context and a total variation regularization

We propose a new strategy for improving classical Blind Source Separation (BSS) methods. This strategy consists in denoising both the observed and the estimated source signals, and is based on the minimization of a regularized criterion which takes into account the Total Variation of the signal. We prove by the way that the method leads to a projection problem which is solved by means of projected gradient algorithm. The effectiveness and the robustness of the proposed separating process are shown on numerical examples.