### Abstract

A matrix A ∈ C^{q×N} satisfies the restricted isometry property of order k with constant e if it preserves the l_{2} norm of all κ-sparse vectors up to a factor of 1 ± ϵ. We prove that a matrix A obtained by randomly sampling q = O(k· log^{2} k · log TV) rows from an N × N Fourier matrix satisfies the restricted isometry property of order k with a fixed e with high probability. This improves on Rudelson and Vershynin (Comm. Pure Appl. Math., 2008), its subsequent improvements, and Bourgain (GAFA Seminar Notes, 2014).

Original language | English (US) |
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Title of host publication | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 |

Publisher | Association for Computing Machinery |

Pages | 288-297 |

Number of pages | 10 |

Volume | 1 |

ISBN (Print) | 9781510819672 |

State | Published - 2016 |

Event | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States Duration: Jan 10 2016 → Jan 12 2016 |

### Other

Other | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 |
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Country | United States |

City | Arlington |

Period | 1/10/16 → 1/12/16 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016*(Vol. 1, pp. 288-297). Association for Computing Machinery.

**The restricted isometry property of subsampled Fourier matrices.** / Haviv, Ishay; Regev, Oded.

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

*27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016.*vol. 1, Association for Computing Machinery, pp. 288-297, 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, Arlington, United States, 1/10/16.

}

TY - GEN

T1 - The restricted isometry property of subsampled Fourier matrices

AU - Haviv, Ishay

AU - Regev, Oded

PY - 2016

Y1 - 2016

N2 - A matrix A ∈ Cq×N satisfies the restricted isometry property of order k with constant e if it preserves the l2 norm of all κ-sparse vectors up to a factor of 1 ± ϵ. We prove that a matrix A obtained by randomly sampling q = O(k· log2 k · log TV) rows from an N × N Fourier matrix satisfies the restricted isometry property of order k with a fixed e with high probability. This improves on Rudelson and Vershynin (Comm. Pure Appl. Math., 2008), its subsequent improvements, and Bourgain (GAFA Seminar Notes, 2014).

AB - A matrix A ∈ Cq×N satisfies the restricted isometry property of order k with constant e if it preserves the l2 norm of all κ-sparse vectors up to a factor of 1 ± ϵ. We prove that a matrix A obtained by randomly sampling q = O(k· log2 k · log TV) rows from an N × N Fourier matrix satisfies the restricted isometry property of order k with a fixed e with high probability. This improves on Rudelson and Vershynin (Comm. Pure Appl. Math., 2008), its subsequent improvements, and Bourgain (GAFA Seminar Notes, 2014).

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M3 - Conference contribution

AN - SCOPUS:84962826200

SN - 9781510819672

VL - 1

SP - 288

EP - 297

BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

PB - Association for Computing Machinery

ER -