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 $k = \Omega( n^{1/2+\varepsilon/4} )$.
翻译:我们利用最近在添加剂组合法方面的进展,展示了满足限制的测量属性的清晰矩阵,其参数较好。也就是说,对于 $\ varepsilon=3.26\cdot 10 ⁇ 7}美元、大 $2\\varepsilon}\le N\le k ⁇ 2 ⁇ varepsilon},我们用 $k =\ omega (n ⁇ 1/2 ⁇ varepsilon/4} 建造了 $n\ times N$ RIP 的订单矩阵,以 $k =\ omega (n ⁇ 1/2 ⁇ varepsilon/4} ) 。