Online Spectrogram Inversion for Low-Latency Audio Source Separation

Magron, Paul; Virtanen, Tuomas

doi:10.1109/lsp.2020.2970310

Cited by 14 publications

(7 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…FGLA was shown experimentally to reach lower local minima of the problem (1) with d = 1, yet without theoretical convergence guarantee. Other improvements of GLA include real-time purposed versions [50], [51] and its extension to multiple signals for source separation [52], [53].…”

Section: A Alternating Projectionsmentioning

confidence: 99%

Phase Retrieval With Bregman Divergences and Application to Audio Signal Recovery

Vial

Magron

Oberlin

et al. 2021

IEEE J. Sel. Top. Signal Process.

Self Cite

View full text Add to dashboard Cite

Phase retrieval (PR) aims to recover a signal from the magnitudes of a set of inner products. This problem arises in many audio signal processing applications which operate on a short-time Fourier transform magnitude or power spectrogram, and discard the phase information. Recovering the missing phase from the resulting modified spectrogram is indeed necessary in order to synthesize time-domain signals. PR is commonly addressed by considering a minimization problem involving a quadratic loss function. In this paper, we adopt a different standpoint. Indeed, the quadratic 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. Therefore, we formulate PR as a new minimization problem involving Bregman divergences. Since these divergences are not symmetric with respect to their two input arguments in general, they lead to two different formulations of the problem. To optimize the resulting objective, we derive two algorithms based on accelerated gradient descent and alternating direction method of multipliers. Experiments conducted on audio signal recovery from spectrograms that are either exact or estimated from noisy observations highlight the potential of our proposed methods for audio restoration. In particular, leveraging some of these Bregman divergences induce better performance than the quadratic loss when performing PR from spectrograms under very noisy conditions.

show abstract

Section: A Alternating Projectionsmentioning

confidence: 99%

Phase Retrieval With Bregman Divergences and Application to Audio Signal Recovery

Vial

Magron

Oberlin

et al. 2021

IEEE J. Sel. Top. Signal Process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The GL algorithm has been extended to handle multiple sources in a source separation framework [13]. Given an observed mixture x ∈ R L of C sources sc ∈ R L , whose target nonnegative TF measurements are rc, this problem can be formulated as [23]:…”

Section: Multiple Input Spectrogram Inversion (Misi)mentioning

confidence: 99%

“…The MISI algorithm has been introduced heuristically in [13]. In [23], it was derived using a majorizationminimization strategy, which proved its convergence.…”

Section: Multiple Input Spectrogram Inversion (Misi)mentioning

confidence: 99%

Phase Recovery with Bregman Divergences for Audio Source Separation

Magron

Vial

Oberlin

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…FGLA was shown experimentally to reach lower local minima of the problem (1) with d = 1, yet without theoretical convergence guarantee. Other improvements of GLA include real-time purposed versions [43,44] and its extension to multiple signals for source separation [45,46].…”

Section: Alternating Projectionsmentioning

confidence: 99%

Phase retrieval with Bregman divergences and application to audio signal recovery

Vial,

Magron,

Oberlin

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

Phase retrieval (PR) aims to recover a signal from the magnitudes of a set of inner products. This problem arises in many audio signal processing applications which operate on a short-time Fourier transform magnitude or power spectrogram, and discard the phase information. Recovering the missing phase from the resulting modified spectrogram is indeed necessary in order to synthesize time-domain signals. PR is commonly addressed by considering a minimization problem involving a quadratic loss function. In this paper, we adopt a different standpoint. Indeed, the quadratic 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. Therefore, we formulate PR as a new minimization problem involving Bregman divergences. We consider a general formulation that actually addresses two problems, since it accounts for the non-symmetry of these divergences in general. To optimize the resulting objective, we derive two algorithms based on accelerated gradient descent and alternating direction method of multiplier. Experiments conducted on audio signal recovery from either exact or modified spectrograms highlight the potential of our proposed methods for audio restoration. In particular, leveraging some of these Bregman divergences induce better performance than the quadratic loss when performing PR from highly degraded spectrograms.

show abstract

Online Spectrogram Inversion for Low-Latency Audio Source Separation

Cited by 14 publications

References 44 publications

Phase Retrieval With Bregman Divergences and Application to Audio Signal Recovery

Phase Retrieval With Bregman Divergences and Application to Audio Signal Recovery

Phase Recovery with Bregman Divergences for Audio Source Separation

Phase retrieval with Bregman divergences and application to audio signal recovery

Contact Info

Product

Resources

About