  For audio source separation applications, it is common to estimate the
magnitude of the short-time Fourier transform (STFT) of each source. In order
to further synthesizing time-domain signals, it is necessary to recover the
phase of the corresponding complex-valued STFT. Most authors in this field
choose a Wiener-like filtering approach which boils down to using the phase of
the original mixture. In this paper, a different standpoint is adopted. Many
music events are partially composed of slowly varying sinusoids and the STFT
phase increment over time of those frequency components takes a specific form.
This allows phase recovery by an unwrapping technique once a short-term
frequency estimate has been obtained. Herein, a novel iterative source
separation procedure is proposed which builds upon these results. It consists
in minimizing the mixing error by means of the auxiliary function method. This
procedure is initialized by exploiting the unwrapping technique in order to
generate estimates that benefit from a temporal continuity property.
Experiments conducted on realistic music pieces show that, given accurate
magnitude estimates, this procedure outperforms the state-of-the-art consistent
Wiener filter.
