Blind partial separation of underdetermined convolutive mixtures of complex sources based on differential normalized kurtosis

This paper concerns the blind separation of P complex convolutive mixtures of N statistically independent complex sources, with underdetermined or noisy mixtures i.e. P < N . Our approach exploits the assumed distinct statistical properties of the sources: P sources are non-stationary, while the others are stationary. Our method achieves the ”partial separation” of the P non-stationary sources. It uses a deflation procedure including extraction and coloration stages. The original criteria introduced in these stages use our differential source separation concept. They consist in optimizing the differential normalized kurtosis and differential power that we introduce. To optimize these criteria, we propose Netwon-like algorithms. Experimental results prove the efficiency of our method.