Sparse Blind Source Separation Based On FCRM

Blind Source Separation (BSS) is a new subject in signal processing domain, and it intents to transform a set of mixed random signals into source signals that are absolutely unknown. Researchers have devoted themselves to this area when many areas attached importance to the technique.In traditional BSS, its main algorithm is independent component analysis (ICA) whoes purpose is by using merely observed signal vector x(t), to estimate the latent source signal vector s(t), or a demixing matrix W, such that all the components of y(t)= Wx(t) are as mutually independent as possible. However, there are many Underdetermined BSS in practice and it is intractable, ICA algorithms only finish extracting few source signals even they not mixed sufficiently. At present, in order to restore all source signals in underdetermined blind separation, researchers make use of some characteristics of signals, for example, Sparse Component Analysis (SCA).Based on linear features of sparse signals, first of all, the paper introduced a fuzzy regression model (FCRM) and the clustering validity function, and on this basis, formed improved fuzzy regression model(Improved-FCRM) and clustering validity function that adapt to lines clustering in European space.Secondly, this paper one hand proposes a new two-step clustering algorithms for underdetermined sparse blind signal separation based on improved FCRM. The algorithms uses the improved FCRM to estimate the mixing matrix, then separates signals by calculating a small number of vectors'generalized inverse and a range of vector inner product. The proposed algorithm provides a new approach for mixing matrix estimation and source signals separation. On the other hand, based on the clustering validity function of improved FCRM, this paper gives a new way of source number estimation algorithm.The simulation confirmed the validity of the algorithm.