Exact asymptotics for phase retrieval and compressed sensing with random generative priors - CEA - Commissariat à l’énergie atomique et aux énergies alternatives Access content directly
Journal Articles Proceedings of Machine Learning Research Year : 2020

Exact asymptotics for phase retrieval and compressed sensing with random generative priors

Antoine Baker
  • Function : Author
  • PersonId : 765939
  • IdRef : 15730406X
Florent Krzakala

Abstract

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm for an ensemble of generative priors consisting of fully connected deep neural networks with random weight matrices and arbitrary activations. We compare the performance to sparse separable priors and conclude that generative priors might be advantageous in terms of algorithmic performance. In particular, while sparsity does not allow to perform compressive phase retrieval efficiently close to its information-theoretic limit, it is found that under the random generative prior compressed phase retrieval becomes tractable.
Fichier principal
Vignette du fichier
AuLoBaKr20.pdf (520.72 Ko) Télécharger le fichier
Origin : Publication funded by an institution

Dates and versions

cea-02529402 , version 1 (02-04-2020)
cea-02529402 , version 2 (06-12-2022)

Identifiers

Cite

Benjamin Aubin, Bruno Loureiro, Antoine Baker, Florent Krzakala, Lenka Zdeborová. Exact asymptotics for phase retrieval and compressed sensing with random generative priors. Proceedings of Machine Learning Research, 2020, 107, pp.55-73. ⟨cea-02529402v2⟩
51 View
44 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More