  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.
