Mixing matrix estimation based on single-source point identification and improved clustering method

Mixing matrix is the key issue in the under-determined blind source separation with sparse representation. The performance of traditional clustering method degrades when the sources do not satisfy W-disjoint orthogonal condition. This paper puts forward an effective method, which sets less condition on the sparseness of the sources, to improve the estimation of the mixing matrix. Firstly, we detect the points in the time-frequency domain of the observations that only single source contributes. Samples at these points are more reliable for the mixing matrix estimation. Secondly, the number of sources, which often needs to be known a priori, is estimated through the characteristics of the observed signals. Finally, an improved initial cluster center selection method is presented for the defects of the traditional K-means cluster algorithm. The numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones, especially in the cases where the number of sources is unknown and the sources are relatively less sparse.