Complex NMF under phase constraints based on signal modeling: application to audio source separation

TL;DR

This paper introduces phase constraints based on signal models into Complex NMF to improve audio source separation, emphasizing phase unwrapping and repetition modeling for better sound quality.

Contribution

It proposes novel phase constraints within CNMF, incorporating signal model-based phase unwrapping and repetition constraints for enhanced audio source separation.

Findings

Improved separation quality with phase constraints

Enhanced phase estimation accuracy

Better handling of overlapping audio components

Abstract

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.