  This paper introduces a novel technique for reconstructing the phase of
modified spectrograms of audio signals. From the analysis of mixtures of
sinusoids we obtain relationships between phases of successive time frames in
the Time-Frequency (TF) domain. To obtain similar relationships over
frequencies, in particular within onset frames, we study an impulse model.
Instantaneous frequencies and attack times are estimated locally to encompass
the class of non-stationary signals such as vibratos. These techniques ensure
both the vertical coherence of partials (over frequencies) and the horizontal
coherence (over time). The method is tested on a variety of data and
demonstrates better performance than traditional consistency-based approaches.
We also introduce an audio restoration framework and observe that our technique
outperforms traditional methods.
