An Algorithm for Underdetermined Blind Source Separation Based on l1 norm

A new two-step algorithm for underdetermined source separation is proposed. Mixing matrix was estimated via clustering methods based on potential functions. Sources were estimated by means of a fast sparse reconstructed algorithm. Every solution to the system equation A（st)=x(t)was expressed as the sum of one of its special solution and a group of linear combination of the basic solution to the corresponding homogeneous linear equation。The number of independent variable needed for estimation was reduced from n to n m. Blind source separation of signals was done by means of sparse representation. The new algorithm is easily implemented and runs fast, which can well meet the requirements of the blind separation for speed. Simulation experiments show that the proposed algorithm has very good separation efficiency and precision.