Phase Recovery with Bregman Divergences for Audio Source Separation

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.

Online Spectrogram Inversion for Low-Latency Audio Source Separation

“…The updates for Y and Z have been derived previously (see Section II-B and II-C), thus we only need to obtain the update for S. To do so, we set the partial derivative of the objective function in (14) with respect to S j at 0 and solve, which yields:…”

“…Note that we recently investigated alternative magnitude discrepancy measures[14], but we focus on the Frobenius norm in this study.2 https://magronp.github.io/files/2023specinv sup.pdf…”