Phase recovery with Bregman divergences for audio source separation

TL;DR

This paper introduces a novel phase recovery method for audio source separation using Bregman divergences, which better align with perceptual audio properties and outperform traditional quadratic error minimization methods like MISI.

Contribution

It reformulates phase recovery as a Bregman divergence minimization problem and develops a projected gradient descent algorithm for optimization.

Findings

Bregman divergence-based phase recovery outperforms MISI in speech enhancement.

The proposed method better captures perceptual audio qualities.

Experiments demonstrate improved separation quality with alternative losses.

Abstract

Time-frequency audio source separation is usually achieved by estimating the short-time Fourier transform (STFT) magnitude of each source, and then applying a phase recovery algorithm to retrieve time-domain signals. In particular, the multiple input spectrogram inversion (MISI) algorithm has shown good performance in several recent works. This algorithm minimizes a quadratic reconstruction error between magnitude spectrograms. However, this loss does not properly account for some perceptual properties of audio, and alternative discrepancy measures such as beta-divergences have been preferred in many settings. In this paper, we propose to reformulate phase recovery in audio source separation as a minimization problem involving Bregman divergences. To optimize the resulting objective, we derive a projected gradient descent algorithm. Experiments conducted on a speech enhancement task show that this approach outperforms MISI for several alternative losses, which highlights their relevance for audio source separation applications.