A novel underdetermined blind source separation method with noise and unknown source number

Abstract

Abstract It has been challenging to correctly separate sources from their mixtures with large noise and unknown source number in underdetermined cases. To address this problem, a novel underdetermined blind source separation (UBSS) method is proposed using synchrosqueezing transform (SST) and improved density peaks clustering (DPC). First, SST is employed to reassign time-frequency (TF) coefficients of short time Fourier transform (STFT) of mixed signals from their original position to the center of gravity along frequency direction, contributing to sparser TF representation than STFT. Second, a single source point (SSP) identification method is proposed by directly searching the identical normalized TF vectors, which considers linear representation relations among TF vectors and therefore can identify SSPs more accurately in noisy cases. Third, DPC is improved to automatically identify source number, with which the mixing matrix can be estimated. After that, sources are finally recovered using l1-norm decomposition method. The effectiveness of the proposed method is validated with some numerical studies and experimental studies. The results show that the proposed method can estimate source number correctly, and recover sources accurately even in noisy cases.