### Abstract

We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an ∈ > 0 such that, conditioned on a folklore conjecture in number theory, this matrix satisfies the restricted isometry property with sparsity parameter K = Ω(M1/2+∈), where M is the number of rows.

Original language | English (US) |
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Pages (from-to) | 372-381 |

Number of pages | 10 |

Journal | International Mathematics Research Notices |

Volume | 2017 |

Issue number | 2 |

DOIs | |

State | Published - 2017 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*International Mathematics Research Notices*,

*2017*(2), 372-381. DOI: 10.1093/imrn/rnv385

**A conditional construction of restricted isometries.** / Bandeira, Afonso S.; Mixon, Dustin G.; Moreira, Joel.

Research output: Contribution to journal › Article

*International Mathematics Research Notices*, vol 2017, no. 2, pp. 372-381. DOI: 10.1093/imrn/rnv385

}

TY - JOUR

T1 - A conditional construction of restricted isometries

AU - Bandeira,Afonso S.

AU - Mixon,Dustin G.

AU - Moreira,Joel

PY - 2017

Y1 - 2017

N2 - We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an ∈ > 0 such that, conditioned on a folklore conjecture in number theory, this matrix satisfies the restricted isometry property with sparsity parameter K = Ω(M1/2+∈), where M is the number of rows.

AB - We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an ∈ > 0 such that, conditioned on a folklore conjecture in number theory, this matrix satisfies the restricted isometry property with sparsity parameter K = Ω(M1/2+∈), where M is the number of rows.

UR - http://www.scopus.com/inward/record.url?scp=85014552285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014552285&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnv385

DO - 10.1093/imrn/rnv385

M3 - Article

VL - 2017

SP - 372

EP - 381

JO - International Mathematics Research Notices

T2 - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 2

ER -