A sparsity-relaxed algorithm for the under-determined convolutive blind source separation

Convolutive blind source separation (CBSS) is a kind of signal processing method by separating multiple sources from a convolutive mixing model. The concept of CBSS is to recover the latent sources in a reverberant environment. Usually, a two-stage scheme including the mixing matrix estimation and the source recovery are proposed to fulfill this target. In this paper, we mainly discuss the source recovery problem based on the knowledge of estimated mixing matrix. Specifically, this problem can be categorized as a sparse source construction optimization model, especially for the under-determined case where the number of sources is greater than the number of microphones. Inspirited by the fact that only few source components are active at each time-frequency slot, a new augmented Lagrange method is proposed to find the optimal sparse solution of sources with the ℓp norm (0<p<1) based measurement function. The proposed method relaxes the strict sparse assumption on sources, hence improve the source separation performance. The experiment results demonstrate that the proposed algorithm is superior than the state-of-the-art methods.