Local mean decomposition for source separation in underdetermined mixing model

Most of the existing underdetermined blind source separation (BSS) approaches assume that the source signals are strictly or partially sparse. This paper, however, presents a BSS method in underdetermined mixing situation for non-sparse signals based on the local mean decomposition (LMD) algorithm. The BSS method firstly introduces LMD into the BSS problem to rebuild a few extra mixing signals. Such signals are then combined with the initial mixtures such that the underdetermined BSS problem is transformed into a determined one and the difficulty of the deficiency of the mixtures is overcome. For the rebuilt mixtures and the newly formed determined BSS problem, two BSS algorithms are proposed to recover the sources. One algorithm uses singular value decomposition on the second-order statistics matrix of the new mixtures to realize the separation, and the other employs an independent component analysis (ICA) type BSS algorithm with stable Frobenius norm constraint on the separating matrix. The simulation results have demonstrated that the proposed underdetermined BSS algorithms can process non-sparse signals, and can acquire a nearly 3dB lower mean square error than the previous non-sparse BSS algorithm.