Optimal sample complexity of subgradient descent for amplitude flow via non-Lipschitz matrix concentration

Hand, Paul; Leong, Oscar; Voroninski, Vladislav

doi:10.4310/cms.2021.v19.n7.a11

Cited by 2 publications

(2 citation statements)

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“…In contrast, for sparse priors, there is no known practical algorithm that achieves a recovery guarantee with a linear dependence on the sparsity s, even though doing so is known to be information-theoretically possible. See also [54] for simplified arguments in the case of phase retrieval without prior information (i.e., general signals in R n ).…”

Section: E Further Developmentsmentioning

confidence: 99%

Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Scarlett

Heckel

Rodrigues

et al. 2022

IEEE J. Sel. Areas Inf. Theory

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In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven by practical algorithms and experiments, it has also given rise to a variety of intriguing theoretical problems. In this paper, we survey some of the prominent theoretical developments in this line of works, focusing in particular on generative priors, untrained neural network priors, and unfolding algorithms. In addition to summarizing existing results in these topics, we highlight several ongoing challenges and open problems.

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Section: E Further Developmentsmentioning

confidence: 99%

Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Scarlett

Heckel

Rodrigues

et al. 2022

IEEE J. Sel. Areas Inf. Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…In contrast, for sparse priors, there is no known practical algorithm that achieves a recovery guarantee with a linear dependence on the sparsity s, even though doing so is known to be information-theoretically possible. See also [50] for simplified arguments in the case of phase retrieval without prior information (i.e., general signals in R n ).…”

Section: E Further Developmentsmentioning

confidence: 99%