On compressed sensing matrices breaking the square-root bottleneck

Shohei Satake; Yujie Gu

doi:10.1109/ITW46852.2021.9457623

On compressed sensing matrices breaking the square-root bottleneck

Shohei Satake, Yujie Gu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Compressed sensing is a celebrated framework in signal processing and has many practical applications. One of the challenging problems in compressed sensing is to construct deterministic matrices having the restricted isometry property (RIP). So far, there are only a few publications providing deterministic RIP matrices beating the square-root bottleneck on the sparsity level. In this paper, we investigate RIP of certain matrices defined by higher power residues modulo primes. Moreover, we prove that the widely-believed generalized Paley graph conjecture implies that these matrices have RIP breaking the square-root bottleneck. Also the compression ratio realized by these RIP matrices is significantly larger than 2.

Original language	English
Title of host publication	2020 IEEE Information Theory Workshop, ITW 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781728159621
DOIs	https://doi.org/10.1109/ITW46852.2021.9457623
State	Published - 11 Apr 2021
Externally published	Yes
Event	2020 IEEE Information Theory Workshop, ITW 2020 - Virtual, Riva del Garda, Italy Duration: 11 Apr 2021 → 15 Apr 2021

Publication series

Name	2020 IEEE Information Theory Workshop, ITW 2020

Conference

Conference	2020 IEEE Information Theory Workshop, ITW 2020
Country/Territory	Italy
City	Virtual, Riva del Garda
Period	11/04/21 → 15/04/21

Access to Document

10.1109/ITW46852.2021.9457623

Cite this

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title = "On compressed sensing matrices breaking the square-root bottleneck",

abstract = "Compressed sensing is a celebrated framework in signal processing and has many practical applications. One of the challenging problems in compressed sensing is to construct deterministic matrices having the restricted isometry property (RIP). So far, there are only a few publications providing deterministic RIP matrices beating the square-root bottleneck on the sparsity level. In this paper, we investigate RIP of certain matrices defined by higher power residues modulo primes. Moreover, we prove that the widely-believed generalized Paley graph conjecture implies that these matrices have RIP breaking the square-root bottleneck. Also the compression ratio realized by these RIP matrices is significantly larger than 2.",

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doi = "10.1109/ITW46852.2021.9457623",

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Satake, S & Gu, Y 2021, On compressed sensing matrices breaking the square-root bottleneck. in 2020 IEEE Information Theory Workshop, ITW 2020., 9457623, 2020 IEEE Information Theory Workshop, ITW 2020, Institute of Electrical and Electronics Engineers Inc., 2020 IEEE Information Theory Workshop, ITW 2020, Virtual, Riva del Garda, Italy, 11/04/21. https://doi.org/10.1109/ITW46852.2021.9457623

On compressed sensing matrices breaking the square-root bottleneck. / Satake, Shohei; Gu, Yujie.
2020 IEEE Information Theory Workshop, ITW 2020. Institute of Electrical and Electronics Engineers Inc., 2021. 9457623 (2020 IEEE Information Theory Workshop, ITW 2020).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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On compressed sensing matrices breaking the square-root bottleneck

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