An Improved L1-Norm Algorithm for Underdetermined Blind Source Separation Using Sparse Representation

An algorithm is presented for underdetermined blind source separation, i.e., the number of observed signals is less than that of original sources. Traditional solutions based on minimizing the L
¹
-norm have some disadvantages in searching the optimal sub-matrix for separation. In the proposed algorithm, first we use a potential function to estimate the mixing matrix by clustering method. Then we present an improved L
¹
-norm algorithm by weighting the observed signals vectors at the different source clustering directions. This method makes good use of the super-Gaussian property of sources and overcomes the disadvantages of L
¹
-norm-based solutions. Furthermore, the case of an arbitrary mixing matrix is discussed in this paper. Simulation results have shown that the proposed approach can give better separation results than traditional methods in terms of signal-to-noise ratio.