Mixing Matrix Recovery of Underdetermined Source Separation Based on Sparse Representation

This paper presents a new algorithm for recovering of the mixing matrix A of underdetermined source separation. Most of the existing algorithms for SCA assume that souce signals are strictly sparse, but the condition in this paper has been relaxed, i.e., there could be at most m-1 nonzero elements of the source signals in each time. Firstly, we can find that all m-1 linearly independent column vectors of observed signals X, which can span different hyperplanes, and then cluster the normal vectors of the hyperplanes in- stead of the hyperplanes themselves. Secondly, we deter- mine the hyperplanes by maximum analysis of the number of the observed signals, which are located the same hyper- plane. Finally, the mixing matrix is identified from the in- tersection lines of the hyperplanes. The simulation results have shown the effectiveness of the proposed algorithm.