Complex NMF under phase constraints based on signal modeling: application to audio source separation
This work addresses the challenge of producing high-quality audio signals in source separation, but it is incremental as it builds on existing CNMF methods with specific constraints.
The authors tackled the problem of phase recovery in audio source separation by incorporating phase constraints into Complex NMF, resulting in improved separation of overlapping components in complex audio mixtures.
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.