Phase-recovery algorithm for harmonic/percussive source separation based on observed phase information and analytic computation

Phase recovery is a methodology of estimating a phase spectrogram that is reasonable for a given amplitude spectrogram. For enhancing the signals obtained from the processed amplitude spectrograms, it has been applied to several audio applications such as harmonic/percussive source separation (HPSS). Because HPSS is often utilized as preprocessing of other processes, its phase recovery should be simple. Therefore, practically effective methods without requiring much computational cost, such as phase unwrapping (PU), have been considered in HPSS. However, PU often results in a phase that is completely different from the true phase because (1) it does not consider the observed phase and (2) estimation error is accumulated with time. To circumvent this problem, we propose a phase-recovery method for HPSS using the observed phase information. Instead of accumulating the phase as in PU, we formulate a local optimization model based on the observed phase so that the estimated phase remains similar to the observed phase. The analytic solution to the proposed optimization model is provided to keep the computational cost cheap. In addition, iterative refinement of phase in the existing methods is applied for further improving the result. From the experiments, it was confirmed that the proposed method outperformed PU.