Proximity Operators of Discrete Information Divergences

Gheche, Mireille El; Chierchia, Giovanni; Pesquet, Jean-Christophe

doi:10.1109/tit.2017.2782789

Cited by 13 publications

(8 citation statements)

References 85 publications

(123 reference statements)

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“…A closed-form expression of the proximal operator can be obtained for some of the usual Bregman divergences, such as the quadratic distance and the KL right and left divergences [81], [82]. These are summarized in Table III.…”

Section: B Proximal Operator Of Usual Bregman Divergencesmentioning

confidence: 99%

See 1 more Smart Citation

Phase Retrieval With Bregman Divergences and Application to Audio Signal Recovery

Vial

Magron

Oberlin

et al. 2021

IEEE J. Sel. Top. Signal Process.

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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.

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Section: B Proximal Operator Of Usual Bregman Divergencesmentioning

confidence: 99%

“…Since we only use ADMM algorithms with d = 1 in our experiments, we focus hereafter on this setting. By using again (60), we compute the gradient of the loss in (82) and set it at 0:…”

Section: Appendix D Algorithms Derivations For Real-valued Signalsmentioning

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.

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show abstract

Section: C2 Proximal Operator Of Usual Bregman Divergencesmentioning

confidence: 99%

Phase retrieval with Bregman divergences and application to audio signal recovery

Vial,

Magron,

Oberlin

et al. 2020

Preprint

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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.

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“…The smoothing constant ≥ 0 allows to avoid singularities around z i = 0 and is common practice, see, e.g., [7]. Several algorithms have been proposed in the literature for tackling problem (1) [4,7,8,9]. In this paper, we propose a variable elimination technique called safe screening that can accelerate most of the existing solvers.…”

Section: Introductionmentioning

confidence: 99%

Safe Screening for Sparse Regression with the Kullback-Leibler Divergence

Dantas

Soubies

Févotte

2021

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

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Safe screening rules are powerful tools to accelerate iterative solvers in sparse regression problems. They allow early identification of inactive coordinates (i.e., those not belonging to the support of the solution) which can thus be screened out in the course of iterations. In this paper, we extend the GAP Safe screening rule to the 1 -regularized Kullback-Leibler divergence which does not fulfil the regularity assumptions made in previous works. The proposed approach is experimentally validated on synthetic and real count data sets.

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Proximity Operators of Discrete Information Divergences

Cited by 13 publications

References 85 publications

Phase Retrieval With Bregman Divergences and Application to Audio Signal Recovery

Phase Retrieval With Bregman Divergences and Application to Audio Signal Recovery

Phase retrieval with Bregman divergences and application to audio signal recovery

Safe Screening for Sparse Regression with the Kullback-Leibler Divergence

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