Model-based phase recovery of spectrograms via optimization on riemannian manifolds

In acoustical signal processing, the importance of modifying the phase spectrogram has been shown. Recently, model-based phase recovery which is based on the sinusoidal model has been studied. Although their effectiveness has been proven, some of them deal with the phase in inflexible forms owing to the wrapping effect of phase. In addition, they need much pre-processing, including the estimation of the instantaneous frequency, which is not easy tasks. In order to overcome these issues, we propose a novel model-based phase recovery method which is formulated as an optimization over complex-valued phases. In the proposed method, the instantaneous frequency is not handled fixedly, which avoids the prior estimation of the instantaneous frequency. The technique of optimization on Riemannian manifolds is adopted for efficient computation. The proposed method is validated by noise reduction of audio signals.