On compressed sensing matrices breaking the square-root bottleneck

Shohei Satake, Yujie Gu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publication2020 IEEE Information Theory Workshop, ITW 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728159621
DOIs
Publication statusPublished - Apr 11 2021
Event2020 IEEE Information Theory Workshop, ITW 2020 - Virtual, Riva del Garda, Italy
Duration: Apr 11 2021Apr 15 2021

Publication series

Name2020 IEEE Information Theory Workshop, ITW 2020

Conference

Conference2020 IEEE Information Theory Workshop, ITW 2020
Country/TerritoryItaly
CityVirtual, Riva del Garda
Period4/11/214/15/21

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Information Systems
  • Signal Processing
  • Software
  • Theoretical Computer Science

Fingerprint

Dive into the research topics of 'On compressed sensing matrices breaking the square-root bottleneck'. Together they form a unique fingerprint.

Cite this