Explicit RIP matrices: an update

Abstract

Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better parameters. Namely, for $\varepsilon=3.26\cdot 10^{-7}$, large $k$ and $k^{2-\varepsilon} \le N\le k^{2+\varepsilon}$, we construct $n \times N$ RIP matrices of order $k$ with $k = \Omega( n^{1/2+\varepsilon/4} )$.