Phase retrieval with Bregman divergences and application to audio signal recovery
| Autor: | Pierre-Hugo Vial, Cédric Févotte, Paul Magron, Thomas Oberlin |
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| Přispěvatelé: | Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Centre National de la Recherche Scientifique (CNRS), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), European Project: CoG-6681839,ERC FACTORY, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Sound (cs.SD) Computer science Audio restoration 02 engineering and technology computer.software_genre Computer Science - Sound Quadratic equation Autre 0202 electrical engineering electronic engineering information engineering Electrical and Electronic Engineering Audio signal processing Phase retrieval Accelerated gradient descent Audio signal 020206 networking & telecommunications Bregman divergences Time–frequency analysis Alternating direction method of multipliers Computer Science::Sound Signal Processing [INFO.INFO-SD]Computer Science [cs]/Sound [cs.SD] Spectrogram Gradient descent computer Algorithm |
| Zdroj: | IEEE Journal of Selected Topics in Signal Processing IEEE Journal of Selected Topics in Signal Processing, IEEE, 2021, 15 (1) IEEE Journal of Selected Topics in Signal Processing, 2021, 15 (1) |
| ISSN: | 1932-4553 |
| Popis: | 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. Comment: 23 pages, 3 figures, accepted for publication in the IEEE Journal of Selected Topics in Signal Processing |
| Databáze: | OpenAIRE |
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