An Improved Underdetermined Blind Source Separation Method for Insufficiently Sparse Sources

Recovering M sources from N mixtures in underdetermined cases, i.e., M > N, is a great challenge, especially for insufficiently sparse sources in noisy cases. To solve this problem, an improved underdetermined blind source separation (UBSS) method is proposed based on single source points (SSPs) identification and l(0)-norm. Firstly, we present a mixing matrix estimation method based on SSPs that is identified by directly searching the identical normalized time-frequency (TF) vectors of mixed signals. This method considers the linear representation relations among these TF vectors and therefore could achieve more accurate SSPs identification even in noisy cases. Then, we prove that a non-SSP will be misjudged as SSP with probability zero under some assumptions, which guarantees the stability and effectiveness of the proposed method. Secondly, SSPs are only searched in some optimal frequency bins so that all SSPs in these frequency bins can be identified at one time. Then, the mixing matrix is estimated using hierarchical clustering technique. Thirdly, to recover source signals with real number of active sources, a l(0)-norm-based source recovery method is proposed which would be transformed to find the submatrix with the least column of the mixing matrix that can linearly represent TF vectors of mixed signals. Therefore, source signals can be recovered with the real number of active sources, which improves the estimation accuracy of source signals. Some experiments are carried out to show the effectiveness of the proposed method. The present research could improve the estimation accuracy of sources for insufficiently sparse sources with noise in underdetermined cases.