Research On Underdetermined Blind Source Separation

In this article, we analyze and summarize the previous work of blind source separation including classical algorithm and theoretical foundation. On the basis of the study, we make research on underdetermined case.In the first part, relevant theoretical knowledge and the analysis to some kinds of algorithms in a two-stage method of on underdetermined blind source separation will be given.In the second part, conditions that sources can be separated in underdetermined case are discussed. First, the feasibility of underdetermined blind source separation to sparse signals is shown by three theorems, and then gives the measure degrees of sparse signals based on generalized Gaussian function. The sparse degrees of signals in time-domain that can be separated under underdetermined case are given at the end of the second part.In the third part, a new Two-Stage Approach to underdetermined blind source separation using sparse representation is introduced. In the first stage, that is the matrix estimation stage, the approach of enhanced potential-based function is employed. By choosing different scale factors and change the weighted parameters, more accurate separation is achieved. First using small scale to estimate the maximum number of potential function and the region of peaks to determine the number of sources, and then in the neighborhood of every local peak, a large scale is used to estimate the mixing matrix accurately. Furthermore threshold is also set up to reduce computation and the influence of small values. In the second stage, that is the sources estimation stage, a new combination of the L1-norm solution and Bayesian estimation method is employed by analyzing the sparse of signals to estimate the signal sources. The sparse points of signals are estimated by Bayesian estimation and the remaining points are solved by L1-norm method. Compared to L1-norm method, the new method reduces the computational complexity and improves the signal consistency.Finally, the MATLAB simulations of the proposed enhanced algorithm using speech and flute signals are given. Simulations indicate that the new algorithm can access better accuracy and the separation of low computational complexity, and achieve better signal clarities.