An improved BLUES with adaptive threshold of condition number for separating underdetermined speech mixtures

Speech separation has been studied for decades, to which one challenge is the underdetermined problem, where there are more sources than microphones. To solve this problem, Pedersen et al. proposed recently an effective algorithm called BLUES (BLind Underdetermined Extraction of Sources) by combining ICA and time-frequency masking, and it works well on instantaneous/convolutive mixtures of both speech and music. One key ingredient to BLUES is the stopping criterion of the separation process, where the condition number of the outputs is compared with a fixed threshold in the original version. However, as audio recordings are always varying in speech sources and their number, using a fixed threshold would not fit in with these changes, and then deteriorate the overall performance. As such, we propose a threshold update strategy to improve BLUES by adapting the threshold with an increasing rate to find the most suitable condition number. A new criterion based on detection of the number of the sources is then presented to stop the algorithm. The experiments are carried out by using the synthetic and real recorded underdetermined mixtures. The results show that our approach obtains improved performance compared to the original BLUES when the number of the speeches included in the underdetermined mixtures is increased.