A new two-stage approach to underdetermined blind source separation using sparse representation

In this paper we focus on the two-stage underdetermined blind source separation (BSS), which consists of the mixing matrix estimation stage, the first stage, and the source estimation stage, the second stage. In the first stage, both the mixing matrix and the number of sources are estimated by a new potential-function-based clustering method using a new potential function constructed by Laplacian-like window function. In the second stage, in order to overcome the disadvantage of 1(1)-norm solution, a new sparse representation based on high-order statistics in transformed domain, which is called statistically sparse component analysis (SSCA), is proposed to recover the sources. Compared with the existing two-stage methods, the proposed approach can achieve higher reconstructed signal-to-noise ratios (SNRs).