Sparse representation and blind source separation of ill-posed mixtures

Bofill et al. discussed blind source separation (BSS) of sparse signals in the case of two sensors. However, as Bofill et al. pointed out, this method has some limitation. The potential function they introduced is lack of theoretical basis. Also the method could not be extended to solve the problem in the case of more than three sensors. In this paper, instead of the potential function method, a K-PCA method (combining K-clustering with PCA) is proposed. The new method is easy to be used in the case of more than three sensors. It is easy to be implemented and can provide accurate estimation of mixing matrix. Some criterion is given to check the effect of the mixing matrix A. Some simulations illustrate the availability and accuracy of the method we proposed.