Low-rankness of Complex-valued Spectrogram and Its Application to Phase-aware Audio Processing
This addresses a fundamental problem in audio signal processing for researchers and practitioners by enabling phase-aware methods, though it appears incremental as it builds on existing low-rank techniques.
The authors tackled the limitation of amplitude-only spectrogram methods in audio processing by showing that a complex-valued spectrogram can be made approximately low-rank with phase modification, and they applied this with a convex prior to achieve audio denoising.
Low-rankness of amplitude spectrograms has been effectively utilized in audio signal processing methods including non-negative matrix factorization. However, such methods have a fundamental limitation owing to their amplitude-only treatment where the phase of the observed signal is utilized for resynthesizing the estimated signal. In order to address this limitation, we directly treat a complex-valued spectrogram and show a complex-valued spectrogram of a sum of sinusoids can be approximately low-rank by modifying its phase. For evaluating the applicability of the proposed low-rank representation, we further propose a convex prior emphasizing harmonic signals, and it is applied to audio denoising.