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 $\epsilon =3.26\cdot 10^{-7}$, large $k$ and $k^{2-\epsilon }\le N\le k^{2+\epsilon }$, we construct $n\times N$ RIP matrices of order $k$ with $k=\Omega (n^{1/2+\epsilon /4})$.

Minor corrections