Separation of rotating and stationary sound sources based on robust principal component analysis

Traditional beamforming techniques may not accurately locate sources in scenarios with both stationary and rotating sound sources. The existence of rotating sound sources can cause blurring in the stationary beamforming map. Current algorithms for separating different moving sound sources have limited effectiveness, leading to significant residual noise, especially when the rotating source is strong enough to mask stationary sources completely. To overcome these challenges, a novel solution utilizing a virtual rotating array in the modal domain combined with robust principal component analysis is proposed to separate sound sources with different rotational speeds. This approach, named Robust Principal Component Analysis in the Modal domain (RPCA-M), investigates the performance of convex nuclear norm and non-convex Schatten-p norm to distinguish stationary and rotating sources. By comparing the errors in Cross-Spectral Matrix (CSM) recovery and acoustic imaging across different algorithms, the effectiveness of RPCA-M in separating stationary and moving sound sources is demonstrated. Importantly, this method effectively separates sound sources, even when there are significant variations in their amplitudes at different rotation speeds.