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      Phase retrieval with Bregman divergences and application to audio signal recovery

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          Abstract

          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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          Author and article information

          Journal
          01 October 2020
          Article
          2010.00392
          bdff59d7-021b-411c-ba7e-50933a7f0e2a

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          23 pages, 4 figures, submitted to the IEEE Journal of Selected Topics in Signal Processing
          cs.SD

          Graphics & Multimedia design
          Graphics & Multimedia design

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