Abstract
A matrix A ∈ Cq×N satisfies the restricted isometry property of order k with constant ∈ if it preserves the l2 norm of all k-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 N) rows from an N × N Fourier matrix satisfies the restricted isometry property of order k with a fixed ∈ 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) |
|---|---|
| Title of host publication | Lecture Notes in Mathematics |
| Publisher | Springer Verlag |
| Pages | 163-179 |
| Number of pages | 17 |
| DOIs | |
| State | Published - 2017 |
Publication series
| Name | Lecture Notes in Mathematics |
|---|---|
| Volume | 2169 |
| ISSN (Print) | 0075-8434 |
ASJC Scopus subject areas
- Algebra and Number Theory
Fingerprint Dive into the research topics of 'The restricted isometry property of subsampled fourier matrices'. Together they form a unique fingerprint.
Cite this
Haviv, I., & Regev, O. (2017). The restricted isometry property of subsampled fourier matrices. In Lecture Notes in Mathematics (pp. 163-179). (Lecture Notes in Mathematics; Vol. 2169). Springer Verlag. https://doi.org/10.1007/978-3-319-45282-1_11