Underdetermined Blind Source Separation Based on Linear Membership Function

The blind source separation (BSS) using a two-stage sparse representation approach is discussed in this paper. The first challenging task of this approach is how to estimate the unknown mixing matrix precisely, to solve this problem, the algorithm based on linear membership function is proposed. And then, we proposed the optimization algorithm based on integral to get the max value of the function. Compared with the classical methods, this proposed method can estimate the unknown mixing matrix faster and more precisely. Meanwhile for the good locality of the function, the required key condition on sparsity of the sources can be considerably relaxed and the noise problem which the classical method can´t solve can be solved well using the method proposed. Another contribution described in this paper is the discussion of the impact of noise on the estimating the mixing matrix. Given the impact of noise, we set weights to put more emphasis on the more reliable data. Several experiments involving speech signals show the effectiveness and efficiency of this method.