  Nonnegative Matrix Factorization (NMF) is a powerful tool for decomposing
mixtures of audio signals in the Time-Frequency (TF) domain. In the source
separation framework, the phase recovery for each extracted component is
necessary for synthesizing time-domain signals. The Complex NMF (CNMF) model
aims to jointly estimate the spectrogram and the phase of the sources, but
requires to constrain the phase in order to produce satisfactory sounding
results. We propose to incorporate phase constraints based on signal models
within the CNMF framework: a \textit{phase unwrapping} constraint that enforces
a form of temporal coherence, and a constraint based on the \textit{repetition}
of audio events, which models the phases of the sources within onset frames. We
also provide an algorithm for estimating the model parameters. The experimental
results highlight the interest of including such constraints in the CNMF
framework for separating overlapping components in complex audio mixtures.

Sound