Learning the Proximity Operator in Unfolded ADMM for Phase Retrieval - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles IEEE Signal Processing Letters Year : 2022

Learning the Proximity Operator in Unfolded ADMM for Phase Retrieval


This paper considers the phase retrieval (PR) problem, which aims to reconstruct a signal from phaseless measurements such as magnitude or power spectrograms. PR is generally handled as a minimization problem involving a quadratic loss. Recent works have considered alternative discrepancy measures, such as the Bregman divergences, but it is still challenging to tailor the optimal loss for a given setting. In this paper we propose a novel strategy to automatically learn the optimal metric for PR. We unfold a recently introduced ADMM algorithm into a neural network, and we emphasize that the information about the loss used to formulate the PR problem is conveyed by the proximity operator involved in the ADMM updates. Therefore, we replace this proximity operator with trainable activation functions: learning these in a supervised setting is then equivalent to learning an optimal metric for PR. Experiments conducted with speech signals show that our approach outperforms the baseline ADMM, using a light and interpretable neural architecture.


Sound [cs.SD]
Fichier principal
Vignette du fichier
main.pdf (533.04 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03790178 , version 1 (28-09-2022)



Pierre-Hugo Vial, Paul Magron, Thomas Oberlin, Cedric Fevotte. Learning the Proximity Operator in Unfolded ADMM for Phase Retrieval. IEEE Signal Processing Letters, 2022, 29, pp.1619-1623. ⟨10.1109/LSP.2022.3189275⟩. ⟨hal-03790178⟩
30 View
33 Download



Gmail Facebook Twitter LinkedIn More